LMFDB - Embedded newform 624.2.q.h.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(289,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("624.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.q (of order $3$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	624.289
Dual form			624.2.q.h.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} -3.56155 q^{5} +(0.280776 - 0.486319i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} -3.56155 q^{5} +(0.280776 - 0.486319i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 3.57071i) q^{13} +(-1.78078 - 3.08440i) q^{15} +(0.780776 - 1.35234i) q^{17} +(3.56155 - 6.16879i) q^{19} +0.561553 q^{21} +(1.00000 + 1.73205i) q^{23} +7.68466 q^{25} -1.00000 q^{27} +(-3.34233 - 5.78908i) q^{29} -2.56155 q^{31} +(1.00000 - 1.73205i) q^{33} +(-1.00000 + 1.73205i) q^{35} +(-3.78078 - 6.54850i) q^{37} +(3.34233 - 1.35234i) q^{39} +(0.780776 + 1.35234i) q^{41} +(2.28078 - 3.95042i) q^{43} +(1.78078 - 3.08440i) q^{45} -8.24621 q^{47} +(3.34233 + 5.78908i) q^{49} +1.56155 q^{51} -0.684658 q^{53} +(3.56155 + 6.16879i) q^{55} +7.12311 q^{57} +(-1.43845 + 2.49146i) q^{59} +(-1.93845 + 3.35749i) q^{61} +(0.280776 + 0.486319i) q^{63} +(-1.78078 + 12.7173i) q^{65} +(2.28078 + 3.95042i) q^{67} +(-1.00000 + 1.73205i) q^{69} +(7.00000 - 12.1244i) q^{71} -10.1231 q^{73} +(3.84233 + 6.65511i) q^{75} -1.12311 q^{77} -5.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +0.876894 q^{83} +(-2.78078 + 4.81645i) q^{85} +(3.34233 - 5.78908i) q^{87} +(-2.43845 - 4.22351i) q^{89} +(-1.59612 - 1.24573i) q^{91} +(-1.28078 - 2.21837i) q^{93} +(-12.6847 + 21.9705i) q^{95} +(4.28078 - 7.41452i) q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 6 q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 6 * q^5 - 3 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} - 6 q^{5} - 3 q^{7} - 2 q^{9} - 4 q^{11} + 2 q^{13} - 3 q^{15} - q^{17} + 6 q^{19} - 6 q^{21} + 4 q^{23} + 6 q^{25} - 4 q^{27} - q^{29} - 2 q^{31} + 4 q^{33} - 4 q^{35} - 11 q^{37} + q^{39} - q^{41} + 5 q^{43} + 3 q^{45} + q^{49} - 2 q^{51} + 22 q^{53} + 6 q^{55} + 12 q^{57} - 14 q^{59} - 16 q^{61} - 3 q^{63} - 3 q^{65} + 5 q^{67} - 4 q^{69} + 28 q^{71} - 24 q^{73} + 3 q^{75} + 12 q^{77} - 30 q^{79} - 2 q^{81} + 20 q^{83} - 7 q^{85} + q^{87} - 18 q^{89} - 27 q^{91} - q^{93} - 26 q^{95} + 13 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^5 - 3 * q^7 - 2 * q^9 - 4 * q^11 + 2 * q^13 - 3 * q^15 - q^17 + 6 * q^19 - 6 * q^21 + 4 * q^23 + 6 * q^25 - 4 * q^27 - q^29 - 2 * q^31 + 4 * q^33 - 4 * q^35 - 11 * q^37 + q^39 - q^41 + 5 * q^43 + 3 * q^45 + q^49 - 2 * q^51 + 22 * q^53 + 6 * q^55 + 12 * q^57 - 14 * q^59 - 16 * q^61 - 3 * q^63 - 3 * q^65 + 5 * q^67 - 4 * q^69 + 28 * q^71 - 24 * q^73 + 3 * q^75 + 12 * q^77 - 30 * q^79 - 2 * q^81 + 20 * q^83 - 7 * q^85 + q^87 - 18 * q^89 - 27 * q^91 - q^93 - 26 * q^95 + 13 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−3.56155			−1.59277			−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−3.56155			−1.59277			−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	0.280776	−	0.486319i	0.106124	−	0.183811i	−0.808073	−	0.589082i	$-0.799489\pi$
$7$	0.280776	−	0.486319i	0.106124	−	0.183811i	0.914197	+	0.405271i	$0.132823\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	0.500000	−	3.57071i	0.138675	−	0.990338i
$13$	0.500000	−	3.57071i	0.138675	−	0.990338i
$14$		0			0
$15$	−1.78078	−	3.08440i	−0.459794	−	0.796387i
$16$		0			0
$17$	0.780776	−	1.35234i	0.189366	−	0.327992i	−0.755673	−	0.654949i	$-0.772690\pi$
$17$	0.780776	−	1.35234i	0.189366	−	0.327992i	0.945039	+	0.326957i	$0.106023\pi$
$18$		0			0
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	−0.0907512	−	0.995874i	$-0.528927\pi$
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	0.907827	−	0.419344i	$-0.137740\pi$
$20$		0			0
$21$	0.561553			0.122541
$22$		0			0
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$		0			0
$25$	7.68466			1.53693
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.34233	−	5.78908i	−0.620655	−	1.07501i	−0.989364	−	0.145461i	$-0.953533\pi$
$29$	−3.34233	−	5.78908i	−0.620655	−	1.07501i	0.368709	−	0.929545i	$-0.379800\pi$
$30$		0			0
$31$	−2.56155			−0.460068			−0.230034	−	0.973183i	$-0.573884\pi$
$31$	−2.56155			−0.460068			−0.230034	+	0.973183i	$0.573884\pi$
$32$		0			0
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$		0			0
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$		0			0
$37$	−3.78078	−	6.54850i	−0.621556	−	1.07657i	−0.989196	−	0.146598i	$-0.953168\pi$
$37$	−3.78078	−	6.54850i	−0.621556	−	1.07657i	0.367640	−	0.929968i	$-0.380166\pi$
$38$		0			0
$39$	3.34233	−	1.35234i	0.535201	−	0.216548i
$40$		0			0
$41$	0.780776	+	1.35234i	0.121937	+	0.211201i	0.920531	−	0.390669i	$-0.127756\pi$
$41$	0.780776	+	1.35234i	0.121937	+	0.211201i	−0.798595	+	0.601869i	$0.794423\pi$
$42$		0			0
$43$	2.28078	−	3.95042i	0.347815	−	0.602433i	−0.638046	−	0.769998i	$-0.720257\pi$
$43$	2.28078	−	3.95042i	0.347815	−	0.602433i	0.985861	+	0.167565i	$0.0535903\pi$
$44$		0			0
$45$	1.78078	−	3.08440i	0.265462	−	0.459794i
$46$		0			0
$47$	−8.24621			−1.20283			−0.601417	−	0.798935i	$-0.705397\pi$
$47$	−8.24621			−1.20283			−0.601417	+	0.798935i	$0.705397\pi$
$48$		0			0
$49$	3.34233	+	5.78908i	0.477476	+	0.827012i
$50$		0			0
$51$	1.56155			0.218661
$52$		0			0
$53$	−0.684658			−0.0940451			−0.0470225	−	0.998894i	$-0.514973\pi$
$53$	−0.684658			−0.0940451			−0.0470225	+	0.998894i	$0.514973\pi$
$54$		0			0
$55$	3.56155	+	6.16879i	0.480240	+	0.831800i
$56$		0			0
$57$	7.12311			0.943478
$58$		0			0
$59$	−1.43845	+	2.49146i	−0.187270	+	0.324361i	−0.944339	−	0.328974i	$-0.893297\pi$
$59$	−1.43845	+	2.49146i	−0.187270	+	0.324361i	0.757069	+	0.653335i	$0.226631\pi$
$60$		0			0
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	−0.963024	−	0.269414i	$-0.913170\pi$
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	0.714832	+	0.699297i	$0.246503\pi$
$62$		0			0
$63$	0.280776	+	0.486319i	0.0353745	+	0.0612704i
$64$		0			0
$65$	−1.78078	+	12.7173i	−0.220878	+	1.57739i
$66$		0			0
$67$	2.28078	+	3.95042i	0.278641	+	0.482621i	0.971047	−	0.238887i	$-0.0767826\pi$
$67$	2.28078	+	3.95042i	0.278641	+	0.482621i	−0.692406	+	0.721508i	$0.743449\pi$
$68$		0			0
$69$	−1.00000	+	1.73205i	−0.120386	+	0.208514i
$70$		0			0
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	−0.0666994	−	0.997773i	$-0.521247\pi$
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	0.897447	−	0.441123i	$-0.145420\pi$
$72$		0			0
$73$	−10.1231			−1.18482			−0.592410	−	0.805637i	$-0.701823\pi$
$73$	−10.1231			−1.18482			−0.592410	+	0.805637i	$0.701823\pi$
$74$		0			0
$75$	3.84233	+	6.65511i	0.443674	+	0.768466i
$76$		0			0
$77$	−1.12311			−0.127990
$78$		0			0
$79$	−5.43845			−0.611873			−0.305937	−	0.952052i	$-0.598970\pi$
$79$	−5.43845			−0.611873			−0.305937	+	0.952052i	$0.598970\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	0.876894			0.0962517			0.0481258	−	0.998841i	$-0.484675\pi$
$83$	0.876894			0.0962517			0.0481258	+	0.998841i	$0.484675\pi$
$84$		0			0
$85$	−2.78078	+	4.81645i	−0.301618	+	0.522417i
$86$		0			0
$87$	3.34233	−	5.78908i	0.358335	−	0.620655i
$88$		0			0
$89$	−2.43845	−	4.22351i	−0.258475	−	0.447692i	0.707359	−	0.706855i	$-0.249887\pi$
$89$	−2.43845	−	4.22351i	−0.258475	−	0.447692i	−0.965834	+	0.259163i	$0.916553\pi$
$90$		0			0
$91$	−1.59612	−	1.24573i	−0.167319	−	0.130588i
$92$		0			0
$93$	−1.28078	−	2.21837i	−0.132810	−	0.230034i
$94$		0			0
$95$	−12.6847	+	21.9705i	−1.30142	+	2.25412i
$96$		0			0
$97$	4.28078	−	7.41452i	0.434647	−	0.752831i	−0.562620	−	0.826716i	$-0.690206\pi$
$97$	4.28078	−	7.41452i	0.434647	−	0.752831i	0.997267	+	0.0738851i	$0.0235398\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$		0			0
$101$	3.78078	+	6.54850i	0.376201	+	0.651600i	0.990506	−	0.137469i	$-0.0438968\pi$
$101$	3.78078	+	6.54850i	0.376201	+	0.651600i	−0.614305	+	0.789069i	$0.710563\pi$
$102$		0			0
$103$	3.43845			0.338800			0.169400	−	0.985547i	$-0.445817\pi$
$103$	3.43845			0.338800			0.169400	+	0.985547i	$0.445817\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$		0			0
$107$	−4.12311	−	7.14143i	−0.398596	−	0.690388i	0.594957	−	0.803757i	$-0.297169\pi$
$107$	−4.12311	−	7.14143i	−0.398596	−	0.690388i	−0.993553	+	0.113369i	$0.963836\pi$
$108$		0			0
$109$	−2.80776			−0.268935			−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80776			−0.268935			−0.134468	+	0.990918i	$0.542932\pi$
$110$		0			0
$111$	3.78078	−	6.54850i	0.358855	−	0.621556i
$112$		0			0
$113$	−2.90388	+	5.02967i	−0.273174	+	0.473152i	−0.969673	−	0.244406i	$-0.921407\pi$
$113$	−2.90388	+	5.02967i	−0.273174	+	0.473152i	0.696499	+	0.717558i	$0.254740\pi$
$114$		0			0
$115$	−3.56155	−	6.16879i	−0.332117	−	0.575243i
$116$		0			0
$117$	2.84233	+	2.21837i	0.262773	+	0.205088i
$118$		0			0
$119$	−0.438447	−	0.759413i	−0.0401924	−	0.0696153i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−0.780776	+	1.35234i	−0.0704002	+	0.121937i
$124$		0			0
$125$	−9.56155			−0.855211
$126$		0			0
$127$	2.71922	+	4.70983i	0.241292	+	0.417930i	0.961083	−	0.276261i	$-0.0890955\pi$
$127$	2.71922	+	4.70983i	0.241292	+	0.417930i	−0.719791	+	0.694191i	$0.755762\pi$
$128$		0			0
$129$	4.56155			0.401622
$130$		0			0
$131$	−7.36932			−0.643860			−0.321930	−	0.946763i	$-0.604332\pi$
$131$	−7.36932			−0.643860			−0.321930	+	0.946763i	$0.604332\pi$
$132$		0			0
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$		0			0
$135$	3.56155			0.306530
$136$		0			0
$137$	2.78078	−	4.81645i	0.237578	−	0.411497i	−0.722441	−	0.691433i	$-0.756980\pi$
$137$	2.78078	−	4.81645i	0.237578	−	0.411497i	0.960019	+	0.279936i	$0.0903132\pi$
$138$		0			0
$139$	−8.96543	+	15.5286i	−0.760438	+	1.31712i	0.182187	+	0.983264i	$0.441682\pi$
$139$	−8.96543	+	15.5286i	−0.760438	+	1.31712i	−0.942625	+	0.333854i	$0.891651\pi$
$140$		0			0
$141$	−4.12311	−	7.14143i	−0.347228	−	0.601417i
$142$		0			0
$143$	−6.68466	+	2.70469i	−0.558999	+	0.226177i
$144$		0			0
$145$	11.9039	+	20.6181i	0.988564	+	1.71224i
$146$		0			0
$147$	−3.34233	+	5.78908i	−0.275671	+	0.477476i
$148$		0			0
$149$	1.21922	−	2.11176i	0.0998827	−	0.173002i	−0.811753	−	0.584001i	$-0.801487\pi$
$149$	1.21922	−	2.11176i	0.0998827	−	0.173002i	0.911636	+	0.410999i	$0.134820\pi$
$150$		0			0
$151$	9.36932			0.762464			0.381232	−	0.924479i	$-0.375500\pi$
$151$	9.36932			0.762464			0.381232	+	0.924479i	$0.375500\pi$
$152$		0			0
$153$	0.780776	+	1.35234i	0.0631220	+	0.109331i
$154$		0			0
$155$	9.12311			0.732785
$156$		0			0
$157$	20.3693			1.62565			0.812824	−	0.582509i	$-0.197929\pi$
$157$	20.3693			1.62565			0.812824	+	0.582509i	$0.197929\pi$
$158$		0			0
$159$	−0.342329	−	0.592932i	−0.0271485	−	0.0470225i
$160$		0			0
$161$	1.12311			0.0885131
$162$		0			0
$163$	−2.40388	+	4.16365i	−0.188287	+	0.326122i	−0.944679	−	0.327996i	$-0.893627\pi$
$163$	−2.40388	+	4.16365i	−0.188287	+	0.326122i	0.756393	+	0.654118i	$0.226960\pi$
$164$		0			0
$165$	−3.56155	+	6.16879i	−0.277267	+	0.480240i
$166$		0			0
$167$	5.12311	+	8.87348i	0.396438	+	0.686650i	0.993284	−	0.115706i	$-0.0369129\pi$
$167$	5.12311	+	8.87348i	0.396438	+	0.686650i	−0.596846	+	0.802356i	$0.703580\pi$
$168$		0			0
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$		0			0
$171$	3.56155	+	6.16879i	0.272359	+	0.471739i
$172$		0			0
$173$	−10.1231	+	17.5337i	−0.769645	+	1.33307i	0.168110	+	0.985768i	$0.446234\pi$
$173$	−10.1231	+	17.5337i	−0.769645	+	1.33307i	−0.937755	+	0.347297i	$0.887100\pi$
$174$		0			0
$175$	2.15767	−	3.73720i	0.163105	−	0.282505i
$176$		0			0
$177$	−2.87689			−0.216241
$178$		0			0
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	0.760391	−	0.649466i	$-0.225007\pi$
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	−0.942649	+	0.333785i	$0.891674\pi$
$180$		0			0
$181$	−2.68466			−0.199549			−0.0997745	−	0.995010i	$-0.531812\pi$
$181$	−2.68466			−0.199549			−0.0997745	+	0.995010i	$0.531812\pi$
$182$		0			0
$183$	−3.87689			−0.286588
$184$		0			0
$185$	13.4654	+	23.3228i	0.989998	+	1.71473i
$186$		0			0
$187$	−3.12311			−0.228384
$188$		0			0
$189$	−0.280776	+	0.486319i	−0.0204235	+	0.0353745i
$190$		0			0
$191$	−4.56155	+	7.90084i	−0.330062	+	0.571685i	−0.982524	−	0.186137i	$-0.940403\pi$
$191$	−4.56155	+	7.90084i	−0.330062	+	0.571685i	0.652461	+	0.757822i	$0.273736\pi$
$192$		0			0
$193$	6.74621	+	11.6848i	0.485603	+	0.841089i	0.999863	−	0.0165453i	$-0.00526677\pi$
$193$	6.74621	+	11.6848i	0.485603	+	0.841089i	−0.514260	+	0.857634i	$0.671933\pi$
$194$		0			0
$195$	−11.9039	+	4.81645i	−0.852455	+	0.344913i
$196$		0			0
$197$	−6.68466	−	11.5782i	−0.476262	−	0.824910i	0.523368	−	0.852107i	$-0.324675\pi$
$197$	−6.68466	−	11.5782i	−0.476262	−	0.824910i	−0.999630	+	0.0271965i	$0.991342\pi$
$198$		0			0
$199$	11.0885	−	19.2059i	0.786046	−	1.36147i	−0.142327	−	0.989820i	$-0.545458\pi$
$199$	11.0885	−	19.2059i	0.786046	−	1.36147i	0.928372	−	0.371651i	$-0.121208\pi$
$200$		0			0
$201$	−2.28078	+	3.95042i	−0.160874	+	0.278641i
$202$		0			0
$203$	−3.75379			−0.263464
$204$		0			0
$205$	−2.78078	−	4.81645i	−0.194218	−	0.336395i
$206$		0			0
$207$	−2.00000			−0.139010
$208$		0			0
$209$	−14.2462			−0.985431
$210$		0			0
$211$	9.84233	+	17.0474i	0.677574	+	1.17359i	0.975709	+	0.219069i	$0.0703019\pi$
$211$	9.84233	+	17.0474i	0.677574	+	1.17359i	−0.298136	+	0.954524i	$0.596365\pi$
$212$		0			0
$213$	14.0000			0.959264
$214$		0			0
$215$	−8.12311	+	14.0696i	−0.553991	+	0.959541i
$216$		0			0
$217$	−0.719224	+	1.24573i	−0.0488241	+	0.0845658i
$218$		0			0
$219$	−5.06155	−	8.76687i	−0.342028	−	0.592410i
$220$		0			0
$221$	−4.43845	−	3.46410i	−0.298562	−	0.233021i
$222$		0			0
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$		0			0
$225$	−3.84233	+	6.65511i	−0.256155	+	0.443674i
$226$		0			0
$227$	3.56155	−	6.16879i	0.236389	−	0.409437i	−0.723287	−	0.690548i	$-0.757370\pi$
$227$	3.56155	−	6.16879i	0.236389	−	0.409437i	0.959675	+	0.281111i	$0.0907028\pi$
$228$		0			0
$229$	−16.2462			−1.07358			−0.536790	−	0.843716i	$-0.680363\pi$
$229$	−16.2462			−1.07358			−0.536790	+	0.843716i	$0.680363\pi$
$230$		0			0
$231$	−0.561553	−	0.972638i	−0.0369475	−	0.0639949i
$232$		0			0
$233$	26.0000			1.70332			0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000			1.70332			0.851658	+	0.524097i	$0.175597\pi$
$234$		0			0
$235$	29.3693			1.91584
$236$		0			0
$237$	−2.71922	−	4.70983i	−0.176633	−	0.305937i
$238$		0			0
$239$	25.3693			1.64100			0.820502	−	0.571643i	$-0.193694\pi$
$239$	25.3693			1.64100			0.820502	+	0.571643i	$0.193694\pi$
$240$		0			0
$241$	8.90388	−	15.4220i	0.573549	−	0.993417i	−0.422648	−	0.906294i	$-0.638899\pi$
$241$	8.90388	−	15.4220i	0.573549	−	0.993417i	0.996198	−	0.0871229i	$-0.0277673\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−11.9039	−	20.6181i	−0.760511	−	1.31724i
$246$		0			0
$247$	−20.2462	−	15.8017i	−1.28824	−	1.00544i
$248$		0			0
$249$	0.438447	+	0.759413i	0.0277855	+	0.0481258i
$250$		0			0
$251$	9.36932	−	16.2281i	0.591386	−	1.02431i	−0.402660	−	0.915350i	$-0.631914\pi$
$251$	9.36932	−	16.2281i	0.591386	−	1.02431i	0.994046	−	0.108961i	$-0.0347524\pi$
$252$		0			0
$253$	2.00000	−	3.46410i	0.125739	−	0.217786i
$254$		0			0
$255$	−5.56155			−0.348278
$256$		0			0
$257$	−14.5885	−	25.2681i	−0.910008	−	1.57618i	−0.814050	−	0.580795i	$-0.802742\pi$
$257$	−14.5885	−	25.2681i	−0.910008	−	1.57618i	−0.0959583	−	0.995385i	$-0.530592\pi$
$258$		0			0
$259$	−4.24621			−0.263847
$260$		0			0
$261$	6.68466			0.413770
$262$		0			0
$263$	4.68466	+	8.11407i	0.288868	+	0.500335i	0.973540	−	0.228517i	$-0.0733877\pi$
$263$	4.68466	+	8.11407i	0.288868	+	0.500335i	−0.684672	+	0.728852i	$0.740054\pi$
$264$		0			0
$265$	2.43845			0.149793
$266$		0			0
$267$	2.43845	−	4.22351i	0.149231	−	0.258475i
$268$		0			0
$269$	10.6847	−	18.5064i	0.651455	−	1.12835i	−0.331315	−	0.943520i	$-0.607492\pi$
$269$	10.6847	−	18.5064i	0.651455	−	1.12835i	0.982770	−	0.184833i	$-0.0591745\pi$
$270$		0			0
$271$	−14.9654	−	25.9209i	−0.909085	−	1.57458i	−0.815337	−	0.578986i	$-0.803449\pi$
$271$	−14.9654	−	25.9209i	−0.909085	−	1.57458i	−0.0937481	−	0.995596i	$-0.529885\pi$
$272$		0			0
$273$	0.280776	−	2.00514i	0.0169934	−	0.121357i
$274$		0			0
$275$	−7.68466	−	13.3102i	−0.463402	−	0.802636i
$276$		0			0
$277$	−2.65767	+	4.60322i	−0.159684	+	0.276581i	−0.934755	−	0.355294i	$-0.884381\pi$
$277$	−2.65767	+	4.60322i	−0.159684	+	0.276581i	0.775071	+	0.631874i	$0.217714\pi$
$278$		0			0
$279$	1.28078	−	2.21837i	0.0766781	−	0.132810i
$280$		0			0
$281$	17.8078			1.06232			0.531161	−	0.847271i	$-0.321756\pi$
$281$	17.8078			1.06232			0.531161	+	0.847271i	$0.321756\pi$
$282$		0			0
$283$	−6.84233	−	11.8513i	−0.406734	−	0.704484i	0.587787	−	0.809015i	$-0.299999\pi$
$283$	−6.84233	−	11.8513i	−0.406734	−	0.704484i	−0.994522	+	0.104531i	$0.966666\pi$
$284$		0			0
$285$	−25.3693			−1.50275
$286$		0			0
$287$	0.876894			0.0517614
$288$		0			0
$289$	7.28078	+	12.6107i	0.428281	+	0.741804i
$290$		0			0
$291$	8.56155			0.501887
$292$		0			0
$293$	−10.2192	+	17.7002i	−0.597013	+	1.03406i	0.396246	+	0.918144i	$0.370313\pi$
$293$	−10.2192	+	17.7002i	−0.597013	+	1.03406i	−0.993259	+	0.115913i	$0.963021\pi$
$294$		0			0
$295$	5.12311	−	8.87348i	0.298279	−	0.516634i
$296$		0			0
$297$	1.00000	+	1.73205i	0.0580259	+	0.100504i
$298$		0			0
$299$	6.68466	−	2.70469i	0.386584	−	0.156416i
$300$		0			0
$301$	−1.28078	−	2.21837i	−0.0738227	−	0.127865i
$302$		0			0
$303$	−3.78078	+	6.54850i	−0.217200	+	0.376201i
$304$		0			0
$305$	6.90388	−	11.9579i	0.395315	−	0.684706i
$306$		0			0
$307$	−30.8078			−1.75829			−0.879146	−	0.476553i	$-0.841886\pi$
$307$	−30.8078			−1.75829			−0.879146	+	0.476553i	$0.841886\pi$
$308$		0			0
$309$	1.71922	+	2.97778i	0.0978032	+	0.169400i
$310$		0			0
$311$	19.1231			1.08437			0.542186	−	0.840259i	$-0.317597\pi$
$311$	19.1231			1.08437			0.542186	+	0.840259i	$0.317597\pi$
$312$		0			0
$313$	−13.6847			−0.773503			−0.386751	−	0.922184i	$-0.626403\pi$
$313$	−13.6847			−0.773503			−0.386751	+	0.922184i	$0.626403\pi$
$314$		0			0
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$		0			0
$317$	14.0540			0.789350			0.394675	−	0.918821i	$-0.370857\pi$
$317$	14.0540			0.789350			0.394675	+	0.918821i	$0.370857\pi$
$318$		0			0
$319$	−6.68466	+	11.5782i	−0.374269	+	0.648253i
$320$		0			0
$321$	4.12311	−	7.14143i	0.230129	−	0.398596i
$322$		0			0
$323$	−5.56155	−	9.63289i	−0.309453	−	0.535988i
$324$		0			0
$325$	3.84233	−	27.4397i	0.213134	−	1.52208i
$326$		0			0
$327$	−1.40388	−	2.43160i	−0.0776349	−	0.134468i
$328$		0			0
$329$	−2.31534	+	4.01029i	−0.127649	+	0.221094i
$330$		0			0
$331$	−1.59612	+	2.76456i	−0.0877306	+	0.151954i	−0.906552	−	0.422095i	$-0.861295\pi$
$331$	−1.59612	+	2.76456i	−0.0877306	+	0.151954i	0.818821	+	0.574049i	$0.194628\pi$
$332$		0			0
$333$	7.56155			0.414371
$334$		0			0
$335$	−8.12311	−	14.0696i	−0.443813	−	0.768706i
$336$		0			0
$337$	−6.12311			−0.333547			−0.166773	−	0.985995i	$-0.553335\pi$
$337$	−6.12311			−0.333547			−0.166773	+	0.985995i	$0.553335\pi$
$338$		0			0
$339$	−5.80776			−0.315434
$340$		0			0
$341$	2.56155	+	4.43674i	0.138716	+	0.240263i
$342$		0			0
$343$	7.68466			0.414933
$344$		0			0
$345$	3.56155	−	6.16879i	0.191748	−	0.332117i
$346$		0			0
$347$	13.8078	−	23.9157i	0.741240	−	1.28386i	−0.210692	−	0.977553i	$-0.567572\pi$
$347$	13.8078	−	23.9157i	0.741240	−	1.28386i	0.951931	−	0.306312i	$-0.0990951\pi$
$348$		0			0
$349$	−3.40388	−	5.89570i	−0.182206	−	0.315589i	0.760426	−	0.649425i	$-0.224990\pi$
$349$	−3.40388	−	5.89570i	−0.182206	−	0.315589i	−0.942631	+	0.333836i	$0.891657\pi$
$350$		0			0
$351$	−0.500000	+	3.57071i	−0.0266880	+	0.190591i
$352$		0			0
$353$	−2.65767	−	4.60322i	−0.141454	−	0.245005i	0.786591	−	0.617475i	$-0.211844\pi$
$353$	−2.65767	−	4.60322i	−0.141454	−	0.245005i	−0.928044	+	0.372470i	$0.878511\pi$
$354$		0			0
$355$	−24.9309	+	43.1815i	−1.32319	+	2.29184i
$356$		0			0
$357$	0.438447	−	0.759413i	0.0232051	−	0.0401924i
$358$		0			0
$359$	9.36932			0.494494			0.247247	−	0.968953i	$-0.420474\pi$
$359$	9.36932			0.494494			0.247247	+	0.968953i	$0.420474\pi$
$360$		0			0
$361$	−15.8693	−	27.4865i	−0.835227	−	1.44666i
$362$		0			0
$363$	7.00000			0.367405
$364$		0			0
$365$	36.0540			1.88715
$366$		0			0
$367$	−8.52699	−	14.7692i	−0.445105	−	0.770945i	0.552954	−	0.833212i	$-0.313500\pi$
$367$	−8.52699	−	14.7692i	−0.445105	−	0.770945i	−0.998060	+	0.0622668i	$0.980167\pi$
$368$		0			0
$369$	−1.56155			−0.0812912
$370$		0			0
$371$	−0.192236	+	0.332962i	−0.00998039	+	0.0172865i
$372$		0			0
$373$	−14.1847	+	24.5685i	−0.734454	+	1.27211i	0.220509	+	0.975385i	$0.429228\pi$
$373$	−14.1847	+	24.5685i	−0.734454	+	1.27211i	−0.954963	+	0.296726i	$0.904105\pi$
$374$		0			0
$375$	−4.78078	−	8.28055i	−0.246878	−	0.427606i
$376$		0			0
$377$	−22.3423	+	9.03996i	−1.15069	+	0.465582i
$378$		0			0
$379$	11.8423	+	20.5115i	0.608300	+	1.05361i	0.991521	+	0.129949i	$0.0414814\pi$
$379$	11.8423	+	20.5115i	0.608300	+	1.05361i	−0.383221	+	0.923657i	$0.625185\pi$
$380$		0			0
$381$	−2.71922	+	4.70983i	−0.139310	+	0.241292i
$382$		0			0
$383$	−11.3693	+	19.6922i	−0.580945	+	1.00623i	0.414423	+	0.910085i	$0.363984\pi$
$383$	−11.3693	+	19.6922i	−0.580945	+	1.00623i	−0.995368	+	0.0961417i	$0.969350\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$		0			0
$387$	2.28078	+	3.95042i	0.115938	+	0.200811i
$388$		0			0
$389$	34.0540			1.72661			0.863303	−	0.504687i	$-0.168392\pi$
$389$	34.0540			1.72661			0.863303	+	0.504687i	$0.168392\pi$
$390$		0			0
$391$	3.12311			0.157942
$392$		0			0
$393$	−3.68466	−	6.38202i	−0.185866	−	0.321930i
$394$		0			0
$395$	19.3693			0.974576
$396$		0			0
$397$	−12.5270	+	21.6974i	−0.628711	+	1.08896i	0.359099	+	0.933299i	$0.383084\pi$
$397$	−12.5270	+	21.6974i	−0.628711	+	1.08896i	−0.987811	+	0.155661i	$0.950249\pi$
$398$		0			0
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$		0			0
$401$	−7.21922	−	12.5041i	−0.360511	−	0.624423i	0.627534	−	0.778589i	$-0.284064\pi$
$401$	−7.21922	−	12.5041i	−0.360511	−	0.624423i	−0.988045	+	0.154166i	$0.950731\pi$
$402$		0			0
$403$	−1.28078	+	9.14657i	−0.0638000	+	0.455623i
$404$		0			0
$405$	1.78078	+	3.08440i	0.0884875	+	0.153265i
$406$		0			0
$407$	−7.56155	+	13.0970i	−0.374812	+	0.649194i
$408$		0			0
$409$	−3.18466	+	5.51599i	−0.157471	+	0.272748i	−0.933956	−	0.357388i	$-0.883667\pi$
$409$	−3.18466	+	5.51599i	−0.157471	+	0.272748i	0.776485	+	0.630136i	$0.217001\pi$
$410$		0			0
$411$	5.56155			0.274331
$412$		0			0
$413$	0.807764	+	1.39909i	0.0397475	+	0.0688446i
$414$		0			0
$415$	−3.12311			−0.153307
$416$		0			0
$417$	−17.9309			−0.878078
$418$		0			0
$419$	−17.1231	−	29.6581i	−0.836518	−	1.44889i	−0.892788	−	0.450477i	$-0.851254\pi$
$419$	−17.1231	−	29.6581i	−0.836518	−	1.44889i	0.0562697	−	0.998416i	$-0.482079\pi$
$420$		0			0
$421$	31.2462			1.52285			0.761424	−	0.648255i	$-0.224501\pi$
$421$	31.2462			1.52285			0.761424	+	0.648255i	$0.224501\pi$
$422$		0			0
$423$	4.12311	−	7.14143i	0.200472	−	0.347228i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	1.08854	+	1.88541i	0.0526782	+	0.0912413i
$428$		0			0
$429$	−5.68466	−	4.43674i	−0.274458	−	0.214208i
$430$		0			0
$431$	−5.56155	−	9.63289i	−0.267891	−	0.464000i	0.700426	−	0.713725i	$-0.252993\pi$
$431$	−5.56155	−	9.63289i	−0.267891	−	0.464000i	−0.968317	+	0.249725i	$0.919660\pi$
$432$		0			0
$433$	−4.37689	+	7.58100i	−0.210340	+	0.364320i	−0.951821	−	0.306654i	$-0.900790\pi$
$433$	−4.37689	+	7.58100i	−0.210340	+	0.364320i	0.741481	+	0.670974i	$0.234124\pi$
$434$		0			0
$435$	−11.9039	+	20.6181i	−0.570747	+	0.988564i
$436$		0			0
$437$	14.2462			0.681489
$438$		0			0
$439$	−6.84233	−	11.8513i	−0.326567	−	0.565630i	0.655262	−	0.755402i	$-0.272558\pi$
$439$	−6.84233	−	11.8513i	−0.326567	−	0.565630i	−0.981828	+	0.189772i	$0.939225\pi$
$440$		0			0
$441$	−6.68466			−0.318317
$442$		0			0
$443$	34.7386			1.65048			0.825241	−	0.564781i	$-0.191039\pi$
$443$	34.7386			1.65048			0.825241	+	0.564781i	$0.191039\pi$
$444$		0			0
$445$	8.68466	+	15.0423i	0.411692	+	0.713072i
$446$		0			0
$447$	2.43845			0.115335
$448$		0			0
$449$	4.12311	−	7.14143i	0.194581	−	0.337025i	−0.752182	−	0.658956i	$-0.770998\pi$
$449$	4.12311	−	7.14143i	0.194581	−	0.337025i	0.946763	+	0.321931i	$0.104332\pi$
$450$		0			0
$451$	1.56155	−	2.70469i	0.0735307	−	0.127359i
$452$		0			0
$453$	4.68466	+	8.11407i	0.220104	+	0.381232i
$454$		0			0
$455$	5.68466	+	4.43674i	0.266501	+	0.207998i
$456$		0			0
$457$	−6.30776	−	10.9254i	−0.295065	−	0.511067i	0.679935	−	0.733272i	$-0.262008\pi$
$457$	−6.30776	−	10.9254i	−0.295065	−	0.511067i	−0.975000	+	0.222205i	$0.928675\pi$
$458$		0			0
$459$	−0.780776	+	1.35234i	−0.0364435	+	0.0631220i
$460$		0			0
$461$	8.09612	−	14.0229i	0.377074	−	0.653111i	−0.613561	−	0.789647i	$-0.710264\pi$
$461$	8.09612	−	14.0229i	0.377074	−	0.653111i	0.990635	+	0.136536i	$0.0435970\pi$
$462$		0			0
$463$	14.3153			0.665290			0.332645	−	0.943052i	$-0.392059\pi$
$463$	14.3153			0.665290			0.332645	+	0.943052i	$0.392059\pi$
$464$		0			0
$465$	4.56155	+	7.90084i	0.211537	+	0.366393i
$466$		0			0
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$		0			0
$469$	2.56155			0.118282
$470$		0			0
$471$	10.1847	+	17.6403i	0.469284	+	0.812824i
$472$		0			0
$473$	−9.12311			−0.419481
$474$		0			0
$475$	27.3693	−	47.4050i	1.25579	−	2.17509i
$476$		0			0
$477$	0.342329	−	0.592932i	0.0156742	−	0.0271485i
$478$		0			0
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	0.959005	−	0.283389i	$-0.0914587\pi$
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	−0.724924	+	0.688828i	$0.758125\pi$
$480$		0			0
$481$	−25.2732	+	10.2258i	−1.15236	+	0.466257i
$482$		0			0
$483$	0.561553	+	0.972638i	0.0255515	+	0.0442566i
$484$		0			0
$485$	−15.2462	+	26.4072i	−0.692295	+	1.19909i
$486$		0			0
$487$	3.56155	−	6.16879i	0.161389	−	0.279535i	−0.773978	−	0.633213i	$-0.781736\pi$
$487$	3.56155	−	6.16879i	0.161389	−	0.279535i	0.935367	+	0.353678i	$0.115069\pi$
$488$		0			0
$489$	−4.80776			−0.217415
$490$		0			0
$491$	−18.1231	−	31.3901i	−0.817884	−	1.41662i	−0.907238	−	0.420617i	$-0.861814\pi$
$491$	−18.1231	−	31.3901i	−0.817884	−	1.41662i	0.0893539	−	0.996000i	$-0.471520\pi$
$492$		0			0
$493$	−10.4384			−0.470124
$494$		0			0
$495$	−7.12311			−0.320160
$496$		0			0
$497$	−3.93087	−	6.80847i	−0.176324	−	0.305401i
$498$		0			0
$499$	−4.49242			−0.201108			−0.100554	−	0.994932i	$-0.532062\pi$
$499$	−4.49242			−0.201108			−0.100554	+	0.994932i	$0.532062\pi$
$500$		0			0
$501$	−5.12311	+	8.87348i	−0.228883	+	0.396438i
$502$		0			0
$503$	−14.1231	+	24.4619i	−0.629718	+	1.09070i	0.357890	+	0.933764i	$0.383496\pi$
$503$	−14.1231	+	24.4619i	−0.629718	+	1.09070i	−0.987608	+	0.156940i	$0.949837\pi$
$504$		0			0
$505$	−13.4654	−	23.3228i	−0.599204	−	1.03785i
$506$		0			0
$507$	−3.15767	−	12.6107i	−0.140237	−	0.560060i
$508$		0			0
$509$	6.90388	+	11.9579i	0.306009	+	0.530023i	0.977486	−	0.211003i	$-0.0676728\pi$
$509$	6.90388	+	11.9579i	0.306009	+	0.530023i	−0.671476	+	0.741026i	$0.734340\pi$
$510$		0			0
$511$	−2.84233	+	4.92306i	−0.125737	+	0.217783i
$512$		0			0
$513$	−3.56155	+	6.16879i	−0.157246	+	0.272359i
$514$		0			0
$515$	−12.2462			−0.539633
$516$		0			0
$517$	8.24621	+	14.2829i	0.362668	+	0.628159i
$518$		0			0
$519$	−20.2462			−0.888710
$520$		0			0
$521$	−9.06913			−0.397326			−0.198663	−	0.980068i	$-0.563660\pi$
$521$	−9.06913			−0.397326			−0.198663	+	0.980068i	$0.563660\pi$
$522$		0			0
$523$	16.9309	+	29.3251i	0.740335	+	1.28230i	0.952343	+	0.305030i	$0.0986666\pi$
$523$	16.9309	+	29.3251i	0.740335	+	1.28230i	−0.212007	+	0.977268i	$0.568000\pi$
$524$		0			0
$525$	4.31534			0.188337
$526$		0			0
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	−1.43845	−	2.49146i	−0.0624233	−	0.108120i
$532$		0			0
$533$	5.21922	−	2.11176i	0.226070	−	0.0914704i
$534$		0			0
$535$	14.6847	+	25.4346i	0.634873	+	1.09963i
$536$		0			0
$537$	2.43845	−	4.22351i	0.105227	−	0.182258i
$538$		0			0
$539$	6.68466	−	11.5782i	0.287929	−	0.498707i
$540$		0			0
$541$	19.7386			0.848630			0.424315	−	0.905515i	$-0.360515\pi$
$541$	19.7386			0.848630			0.424315	+	0.905515i	$0.360515\pi$
$542$		0			0
$543$	−1.34233	−	2.32498i	−0.0576049	−	0.0997745i
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	−3.93087			−0.168072			−0.0840359	−	0.996463i	$-0.526781\pi$
$547$	−3.93087			−0.168072			−0.0840359	+	0.996463i	$0.526781\pi$
$548$		0			0
$549$	−1.93845	−	3.35749i	−0.0827309	−	0.143294i
$550$		0			0
$551$	−47.6155			−2.02849
$552$		0			0
$553$	−1.52699	+	2.64482i	−0.0649341	+	0.112469i
$554$		0			0
$555$	−13.4654	+	23.3228i	−0.571576	+	0.989998i
$556$		0			0
$557$	21.4654	+	37.1792i	0.909520	+	1.57533i	0.814733	+	0.579837i	$0.196884\pi$
$557$	21.4654	+	37.1792i	0.909520	+	1.57533i	0.0947869	+	0.995498i	$0.469783\pi$
$558$		0			0
$559$	−12.9654	−	10.1192i	−0.548379	−	0.427997i
$560$		0			0
$561$	−1.56155	−	2.70469i	−0.0659288	−	0.114192i
$562$		0			0
$563$	−11.6847	+	20.2384i	−0.492450	+	0.852948i	−0.999962	−	0.00869657i	$-0.997232\pi$
$563$	−11.6847	+	20.2384i	−0.492450	+	0.852948i	0.507513	+	0.861644i	$0.330565\pi$
$564$		0			0
$565$	10.3423	−	17.9134i	0.435105	−	0.753624i
$566$		0			0
$567$	−0.561553			−0.0235830
$568$		0			0
$569$	4.36932	+	7.56788i	0.183171	+	0.317262i	0.942959	−	0.332910i	$-0.108030\pi$
$569$	4.36932	+	7.56788i	0.183171	+	0.317262i	−0.759787	+	0.650171i	$0.774697\pi$
$570$		0			0
$571$	5.36932			0.224699			0.112349	−	0.993669i	$-0.464162\pi$
$571$	5.36932			0.224699			0.112349	+	0.993669i	$0.464162\pi$
$572$		0			0
$573$	−9.12311			−0.381123
$574$		0			0
$575$	7.68466	+	13.3102i	0.320472	+	0.555074i
$576$		0			0
$577$	−17.3153			−0.720847			−0.360424	−	0.932789i	$-0.617368\pi$
$577$	−17.3153			−0.720847			−0.360424	+	0.932789i	$0.617368\pi$
$578$		0			0
$579$	−6.74621	+	11.6848i	−0.280363	+	0.485603i
$580$		0			0
$581$	0.246211	−	0.426450i	0.0102146	−	0.0176921i
$582$		0			0
$583$	0.684658	+	1.18586i	0.0283557	+	0.0491134i
$584$		0			0
$585$	−10.1231	−	7.90084i	−0.418539	−	0.326660i
$586$		0			0
$587$	19.6847	+	34.0948i	0.812473	+	1.40724i	0.911128	+	0.412123i	$0.135212\pi$
$587$	19.6847	+	34.0948i	0.812473	+	1.40724i	−0.0986556	+	0.995122i	$0.531454\pi$
$588$		0			0
$589$	−9.12311	+	15.8017i	−0.375911	+	0.651097i
$590$		0			0
$591$	6.68466	−	11.5782i	0.274970	−	0.476262i
$592$		0			0
$593$	−17.4233			−0.715489			−0.357744	−	0.933820i	$-0.616454\pi$
$593$	−17.4233			−0.715489			−0.357744	+	0.933820i	$0.616454\pi$
$594$		0			0
$595$	1.56155	+	2.70469i	0.0640174	+	0.110881i
$596$		0			0
$597$	22.1771			0.907648
$598$		0			0
$599$	41.6155			1.70036			0.850182	−	0.526489i	$-0.176492\pi$
$599$	41.6155			1.70036			0.850182	+	0.526489i	$0.176492\pi$
$600$		0			0
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	0.929066	−	0.369914i	$-0.120613\pi$
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	−0.784888	+	0.619638i	$0.787280\pi$
$602$		0			0
$603$	−4.56155			−0.185761
$604$		0			0
$605$	−12.4654	+	21.5908i	−0.506792	+	0.877789i
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$		0			0
$609$	−1.87689	−	3.25088i	−0.0760556	−	0.131732i
$610$		0			0
$611$	−4.12311	+	29.4449i	−0.166803	+	1.19121i
$612$		0			0
$613$	17.4309	+	30.1912i	0.704026	+	1.21941i	0.967042	+	0.254618i	$0.0819496\pi$
$613$	17.4309	+	30.1912i	0.704026	+	1.21941i	−0.263016	+	0.964792i	$0.584717\pi$
$614$		0			0
$615$	2.78078	−	4.81645i	0.112132	−	0.194218i
$616$		0			0
$617$	−4.90388	+	8.49377i	−0.197423	+	0.341946i	−0.947692	−	0.319186i	$-0.896591\pi$
$617$	−4.90388	+	8.49377i	−0.197423	+	0.341946i	0.750269	+	0.661132i	$0.229924\pi$
$618$		0			0
$619$	−29.3002			−1.17767			−0.588837	−	0.808252i	$-0.700414\pi$
$619$	−29.3002			−1.17767			−0.588837	+	0.808252i	$0.700414\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$		0			0
$623$	−2.73863			−0.109721
$624$		0			0
$625$	−4.36932			−0.174773
$626$		0			0
$627$	−7.12311	−	12.3376i	−0.284469	−	0.492716i
$628$		0			0
$629$	−11.8078			−0.470806
$630$		0			0
$631$	−9.28078	+	16.0748i	−0.369462	+	0.639927i	−0.989481	−	0.144660i	$-0.953791\pi$
$631$	−9.28078	+	16.0748i	−0.369462	+	0.639927i	0.620020	+	0.784586i	$0.287125\pi$
$632$		0			0
$633$	−9.84233	+	17.0474i	−0.391197	+	0.677574i
$634$		0			0
$635$	−9.68466	−	16.7743i	−0.384324	−	0.665669i
$636$		0			0
$637$	22.3423	−	9.03996i	0.885235	−	0.358176i
$638$		0			0
$639$	7.00000	+	12.1244i	0.276916	+	0.479632i
$640$		0			0
$641$	9.58854	−	16.6078i	0.378725	−	0.655970i	−0.612152	−	0.790740i	$-0.709696\pi$
$641$	9.58854	−	16.6078i	0.378725	−	0.655970i	0.990877	+	0.134770i	$0.0430294\pi$
$642$		0			0
$643$	−15.7732	+	27.3200i	−0.622034	+	1.07739i	0.367072	+	0.930192i	$0.380360\pi$
$643$	−15.7732	+	27.3200i	−0.622034	+	1.07739i	−0.989106	+	0.147202i	$0.952973\pi$
$644$		0			0
$645$	−16.2462			−0.639694
$646$		0			0
$647$	−3.19224	−	5.52911i	−0.125500	−	0.217372i	0.796428	−	0.604733i	$-0.206720\pi$
$647$	−3.19224	−	5.52911i	−0.125500	−	0.217372i	−0.921928	+	0.387361i	$0.873387\pi$
$648$		0			0
$649$	5.75379			0.225856
$650$		0			0
$651$	−1.43845			−0.0563772
$652$		0			0
$653$	−11.5616	−	20.0252i	−0.452439	−	0.783647i	0.546098	−	0.837721i	$-0.316112\pi$
$653$	−11.5616	−	20.0252i	−0.452439	−	0.783647i	−0.998537	+	0.0540745i	$0.982779\pi$
$654$		0			0
$655$	26.2462			1.02552
$656$		0			0
$657$	5.06155	−	8.76687i	0.197470	−	0.342028i
$658$		0			0
$659$	−1.12311	+	1.94528i	−0.0437500	+	0.0757772i	−0.887071	−	0.461633i	$-0.847264\pi$
$659$	−1.12311	+	1.94528i	−0.0437500	+	0.0757772i	0.843321	+	0.537410i	$0.180597\pi$
$660$		0			0
$661$	−2.81534	−	4.87631i	−0.109504	−	0.189667i	0.806065	−	0.591827i	$-0.201593\pi$
$661$	−2.81534	−	4.87631i	−0.109504	−	0.189667i	−0.915569	+	0.402160i	$0.868260\pi$
$662$		0			0
$663$	0.780776	−	5.57586i	0.0303228	−	0.216548i
$664$		0			0
$665$	7.12311	+	12.3376i	0.276222	+	0.478431i
$666$		0			0
$667$	6.68466	−	11.5782i	0.258831	−	0.448308i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	7.75379			0.299332
$672$		0			0
$673$	11.6231	+	20.1318i	0.448038	+	0.776024i	0.998258	−	0.0589952i	$-0.0187897\pi$
$673$	11.6231	+	20.1318i	0.448038	+	0.776024i	−0.550220	+	0.835019i	$0.685456\pi$
$674$		0			0
$675$	−7.68466			−0.295783
$676$		0			0
$677$	−15.6155			−0.600153			−0.300077	−	0.953915i	$-0.597012\pi$
$677$	−15.6155			−0.600153			−0.300077	+	0.953915i	$0.597012\pi$
$678$		0			0
$679$	−2.40388	−	4.16365i	−0.0922525	−	0.159786i
$680$		0			0
$681$	7.12311			0.272958
$682$		0			0
$683$	−19.0540	+	33.0025i	−0.729080	+	1.26280i	0.228192	+	0.973616i	$0.426719\pi$
$683$	−19.0540	+	33.0025i	−0.729080	+	1.26280i	−0.957272	+	0.289188i	$0.906615\pi$
$684$		0			0
$685$	−9.90388	+	17.1540i	−0.378408	+	0.655422i
$686$		0			0
$687$	−8.12311	−	14.0696i	−0.309916	−	0.536790i
$688$		0			0
$689$	−0.342329	+	2.44472i	−0.0130417	+	0.0931364i
$690$		0			0
$691$	−25.6501	−	44.4273i	−0.975776	−	1.69009i	−0.677352	−	0.735659i	$-0.736872\pi$
$691$	−25.6501	−	44.4273i	−0.975776	−	1.69009i	−0.298424	−	0.954433i	$-0.596461\pi$
$692$		0			0
$693$	0.561553	−	0.972638i	0.0213316	−	0.0369475i
$694$		0			0
$695$	31.9309	−	55.3059i	1.21121	−	2.09787i
$696$		0			0
$697$	2.43845			0.0923628
$698$		0			0
$699$	13.0000	+	22.5167i	0.491705	+	0.851658i
$700$		0			0
$701$	−5.36932			−0.202796			−0.101398	−	0.994846i	$-0.532332\pi$
$701$	−5.36932			−0.202796			−0.101398	+	0.994846i	$0.532332\pi$
$702$		0			0
$703$	−53.8617			−2.03143
$704$		0			0
$705$	14.6847	+	25.4346i	0.553056	+	0.957921i
$706$		0			0
$707$	4.24621			0.159695
$708$		0			0
$709$	3.74621	−	6.48863i	0.140692	−	0.243686i	−0.787065	−	0.616869i	$-0.788401\pi$
$709$	3.74621	−	6.48863i	0.140692	−	0.243686i	0.927757	+	0.373184i	$0.121734\pi$
$710$		0			0
$711$	2.71922	−	4.70983i	0.101979	−	0.176633i
$712$		0			0
$713$	−2.56155	−	4.43674i	−0.0959309	−	0.166157i
$714$		0			0
$715$	23.8078	−	9.63289i	0.890360	−	0.360250i
$716$		0			0
$717$	12.6847	+	21.9705i	0.473717	+	0.820502i
$718$		0			0
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	−0.997358	−	0.0726475i	$-0.976855\pi$
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	0.561593	+	0.827413i	$0.310189\pi$
$720$		0			0
$721$	0.965435	−	1.67218i	0.0359547	−	0.0622753i
$722$		0			0
$723$	17.8078			0.662278
$724$		0			0
$725$	−25.6847	−	44.4871i	−0.953904	−	1.65221i
$726$		0			0
$727$	38.6695			1.43417			0.717086	−	0.696984i	$-0.245475\pi$
$727$	38.6695			1.43417			0.717086	+	0.696984i	$0.245475\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.56155	−	6.16879i	−0.131729	−	0.228161i
$732$		0			0
$733$	20.5076			0.757465			0.378732	−	0.925506i	$-0.376360\pi$
$733$	20.5076			0.757465			0.378732	+	0.925506i	$0.376360\pi$
$734$		0			0
$735$	11.9039	−	20.6181i	0.439081	−	0.760511i
$736$		0			0
$737$	4.56155	−	7.90084i	0.168027	−	0.291031i
$738$		0			0
$739$	5.12311	+	8.87348i	0.188456	+	0.326416i	0.944736	−	0.327833i	$-0.106318\pi$
$739$	5.12311	+	8.87348i	0.188456	+	0.326416i	−0.756279	+	0.654249i	$0.772985\pi$
$740$		0			0
$741$	3.56155	−	25.4346i	0.130837	−	0.934362i
$742$		0			0
$743$	−6.31534	−	10.9385i	−0.231687	−	0.401294i	0.726617	−	0.687042i	$-0.241091\pi$
$743$	−6.31534	−	10.9385i	−0.231687	−	0.401294i	−0.958305	+	0.285748i	$0.907758\pi$
$744$		0			0
$745$	−4.34233	+	7.52113i	−0.159091	+	0.275553i
$746$		0			0
$747$	−0.438447	+	0.759413i	−0.0160419	+	0.0277855i
$748$		0			0
$749$	−4.63068			−0.169201
$750$		0			0
$751$	22.0540	+	38.1986i	0.804761	+	1.39389i	0.916452	+	0.400144i	$0.131040\pi$
$751$	22.0540	+	38.1986i	0.804761	+	1.39389i	−0.111691	+	0.993743i	$0.535627\pi$
$752$		0			0
$753$	18.7386			0.682874
$754$		0			0
$755$	−33.3693			−1.21443
$756$		0			0
$757$	−15.0000	−	25.9808i	−0.545184	−	0.944287i	−0.998595	−	0.0529853i	$-0.983126\pi$
$757$	−15.0000	−	25.9808i	−0.545184	−	0.944287i	0.453411	−	0.891302i	$-0.350207\pi$
$758$		0			0
$759$	4.00000			0.145191
$760$		0			0
$761$	−4.68466	+	8.11407i	−0.169819	+	0.294135i	−0.938356	−	0.345670i	$-0.887652\pi$
$761$	−4.68466	+	8.11407i	−0.169819	+	0.294135i	0.768537	+	0.639805i	$0.220985\pi$
$762$		0			0
$763$	−0.788354	+	1.36547i	−0.0285403	+	0.0494333i
$764$		0			0
$765$	−2.78078	−	4.81645i	−0.100539	−	0.174139i
$766$		0			0
$767$	8.17708	+	6.38202i	0.295257	+	0.230441i
$768$		0			0
$769$	9.00000	+	15.5885i	0.324548	+	0.562134i	0.981421	−	0.191867i	$-0.0614544\pi$
$769$	9.00000	+	15.5885i	0.324548	+	0.562134i	−0.656873	+	0.754002i	$0.728121\pi$
$770$		0			0
$771$	14.5885	−	25.2681i	0.525393	−	0.910008i
$772$		0			0
$773$	12.1231	−	20.9978i	0.436038	−	0.755240i	−0.561342	−	0.827584i	$-0.689715\pi$
$773$	12.1231	−	20.9978i	0.436038	−	0.755240i	0.997380	+	0.0723444i	$0.0230481\pi$
$774$		0			0
$775$	−19.6847			−0.707094
$776$		0			0
$777$	−2.12311	−	3.67733i	−0.0761660	−	0.131923i
$778$		0			0
$779$	11.1231			0.398527
$780$		0			0
$781$	−28.0000			−1.00192
$782$		0			0
$783$	3.34233	+	5.78908i	0.119445	+	0.206885i
$784$		0			0
$785$	−72.5464			−2.58929
$786$		0			0
$787$	22.0885	−	38.2585i	0.787371	−	1.36377i	−0.140201	−	0.990123i	$-0.544775\pi$
$787$	22.0885	−	38.2585i	0.787371	−	1.36377i	0.927572	−	0.373644i	$-0.121892\pi$
$788$		0			0
$789$	−4.68466	+	8.11407i	−0.166778	+	0.288868i
$790$		0			0
$791$	1.63068	+	2.82443i	0.0579804	+	0.100425i
$792$		0			0
$793$	11.0194	+	8.60039i	0.391311	+	0.305409i
$794$		0			0
$795$	1.21922	+	2.11176i	0.0432414	+	0.0748963i
$796$		0			0
$797$	0.192236	−	0.332962i	0.00680935	−	0.0117941i	−0.862601	−	0.505885i	$-0.831166\pi$
$797$	0.192236	−	0.332962i	0.00680935	−	0.0117941i	0.869410	+	0.494091i	$0.164499\pi$
$798$		0			0
$799$	−6.43845	+	11.1517i	−0.227776	+	0.394519i
$800$		0			0
$801$	4.87689			0.172317
$802$		0			0
$803$	10.1231	+	17.5337i	0.357237	+	0.618752i
$804$		0			0
$805$	−4.00000			−0.140981
$806$		0			0
$807$	21.3693			0.752236
$808$		0			0
$809$	8.15009	+	14.1164i	0.286542	+	0.496305i	0.972982	−	0.230881i	$-0.0741609\pi$
$809$	8.15009	+	14.1164i	0.286542	+	0.496305i	−0.686440	+	0.727187i	$0.740828\pi$
$810$		0			0
$811$	−2.56155			−0.0899483			−0.0449741	−	0.998988i	$-0.514321\pi$
$811$	−2.56155			−0.0899483			−0.0449741	+	0.998988i	$0.514321\pi$
$812$		0			0
$813$	14.9654	−	25.9209i	0.524861	−	0.909085i
$814$		0			0
$815$	8.56155	−	14.8290i	0.299898	−	0.519439i
$816$		0			0
$817$	−16.2462	−	28.1393i	−0.568383	−	0.984468i
$818$		0			0
$819$	1.87689	−	0.759413i	0.0655840	−	0.0265360i
$820$		0			0
$821$	−3.24621	−	5.62260i	−0.113294	−	0.196230i	0.803803	−	0.594896i	$-0.202807\pi$
$821$	−3.24621	−	5.62260i	−0.113294	−	0.196230i	−0.917096	+	0.398666i	$0.869473\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$	7.68466	−	13.3102i	0.267545	−	0.463402i
$826$		0			0
$827$	14.7386			0.512513			0.256256	−	0.966609i	$-0.417511\pi$
$827$	14.7386			0.512513			0.256256	+	0.966609i	$0.417511\pi$
$828$		0			0
$829$	−6.74621	−	11.6848i	−0.234306	−	0.405829i	0.724765	−	0.688996i	$-0.241948\pi$
$829$	−6.74621	−	11.6848i	−0.234306	−	0.405829i	−0.959071	+	0.283167i	$0.908615\pi$
$830$		0			0
$831$	−5.31534			−0.184387
$832$		0			0
$833$	10.4384			0.361671
$834$		0			0
$835$	−18.2462	−	31.6034i	−0.631436	−	1.09368i
$836$		0			0
$837$	2.56155			0.0885402
$838$		0			0
$839$	10.8078	−	18.7196i	0.373125	−	0.646272i	−0.616919	−	0.787027i	$-0.711619\pi$
$839$	10.8078	−	18.7196i	0.373125	−	0.646272i	0.990045	+	0.140754i	$0.0449528\pi$
$840$		0			0
$841$	−7.84233	+	13.5833i	−0.270425	+	0.468390i
$842$		0			0
$843$	8.90388	+	15.4220i	0.306666	+	0.531161i
$844$		0			0
$845$	44.5194	+	12.7173i	1.53151	+	0.437488i
$846$		0			0
$847$	−1.96543	−	3.40423i	−0.0675331	−	0.116971i
$848$		0			0
$849$	6.84233	−	11.8513i	0.234828	−	0.406734i
$850$		0			0
$851$	7.56155	−	13.0970i	0.259207	−	0.448959i
$852$		0			0
$853$	2.12311			0.0726938			0.0363469	−	0.999339i	$-0.488428\pi$
$853$	2.12311			0.0726938			0.0363469	+	0.999339i	$0.488428\pi$
$854$		0			0
$855$	−12.6847	−	21.9705i	−0.433806	−	0.751374i
$856$		0			0
$857$	35.5616			1.21476			0.607380	−	0.794412i	$-0.292221\pi$
$857$	35.5616			1.21476			0.607380	+	0.794412i	$0.292221\pi$
$858$		0			0
$859$	−24.5616			−0.838029			−0.419015	−	0.907979i	$-0.637624\pi$
$859$	−24.5616			−0.838029			−0.419015	+	0.907979i	$0.637624\pi$
$860$		0			0
$861$	0.438447	+	0.759413i	0.0149422	+	0.0258807i
$862$		0			0
$863$	−30.4924			−1.03797			−0.518987	−	0.854782i	$-0.673691\pi$
$863$	−30.4924			−1.03797			−0.518987	+	0.854782i	$0.673691\pi$
$864$		0			0
$865$	36.0540	−	62.4473i	1.22587	−	2.12327i
$866$		0			0
$867$	−7.28078	+	12.6107i	−0.247268	+	0.428281i
$868$		0			0
$869$	5.43845	+	9.41967i	0.184487	+	0.319540i
$870$		0			0
$871$	15.2462	−	6.16879i	0.516598	−	0.209021i
$872$		0			0
$873$	4.28078	+	7.41452i	0.144882	+	0.250944i
$874$		0			0
$875$	−2.68466	+	4.64996i	−0.0907580	+	0.157198i
$876$		0			0
$877$	−11.7808	+	20.4049i	−0.397809	+	0.689025i	−0.993455	−	0.114222i	$-0.963563\pi$
$877$	−11.7808	+	20.4049i	−0.397809	+	0.689025i	0.595647	+	0.803247i	$0.296896\pi$
$878$		0			0
$879$	−20.4384			−0.689372
$880$		0			0
$881$	4.53457	+	7.85410i	0.152773	+	0.264611i	0.932246	−	0.361825i	$-0.117846\pi$
$881$	4.53457	+	7.85410i	0.152773	+	0.264611i	−0.779473	+	0.626436i	$0.784513\pi$
$882$		0			0
$883$	−8.80776			−0.296405			−0.148202	−	0.988957i	$-0.547349\pi$
$883$	−8.80776			−0.296405			−0.148202	+	0.988957i	$0.547349\pi$
$884$		0			0
$885$	10.2462			0.344423
$886$		0			0
$887$	12.3153	+	21.3308i	0.413509	+	0.716218i	0.995271	−	0.0971410i	$-0.0309698\pi$
$887$	12.3153	+	21.3308i	0.413509	+	0.716218i	−0.581762	+	0.813359i	$0.697636\pi$
$888$		0			0
$889$	3.05398			0.102427
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$		0			0
$893$	−29.3693	+	50.8691i	−0.982807	+	1.70227i
$894$		0			0
$895$	8.68466	+	15.0423i	0.290296	+	0.502808i
$896$		0			0
$897$	5.68466	+	4.43674i	0.189805	+	0.148138i
$898$		0			0
$899$	8.56155	+	14.8290i	0.285544	+	0.494576i
$900$		0			0
$901$	−0.534565	+	0.925894i	−0.0178089	+	0.0308460i
$902$		0			0
$903$	1.28078	−	2.21837i	0.0426216	−	0.0738227i
$904$		0			0
$905$	9.56155			0.317837
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$		0			0
$909$	−7.56155			−0.250801
$910$		0			0
$911$	−38.7386			−1.28347			−0.641734	−	0.766927i	$-0.721785\pi$
$911$	−38.7386			−1.28347			−0.641734	+	0.766927i	$0.721785\pi$
$912$		0			0
$913$	−0.876894	−	1.51883i	−0.0290210	−	0.0502658i
$914$		0			0
$915$	13.8078			0.456471
$916$		0			0
$917$	−2.06913	+	3.58384i	−0.0683287	+	0.118349i
$918$		0			0
$919$	5.75379	−	9.96585i	0.189800	−	0.328743i	−0.755383	−	0.655283i	$-0.772549\pi$
$919$	5.75379	−	9.96585i	0.189800	−	0.328743i	0.945183	+	0.326540i	$0.105883\pi$
$920$		0			0
$921$	−15.4039	−	26.6803i	−0.507575	−	0.879146i
$922$		0			0
$923$	−39.7926	−	31.0572i	−1.30979	−	1.02226i
$924$		0			0
$925$	−29.0540	−	50.3230i	−0.955289	−	1.65461i
$926$		0			0
$927$	−1.71922	+	2.97778i	−0.0564667	+	0.0978032i
$928$		0			0
$929$	3.90388	−	6.76172i	0.128082	−	0.221845i	−0.794851	−	0.606804i	$-0.792451\pi$
$929$	3.90388	−	6.76172i	0.128082	−	0.221845i	0.922934	+	0.384959i	$0.125785\pi$
$930$		0			0
$931$	47.6155			1.56054
$932$		0			0
$933$	9.56155	+	16.5611i	0.313031	+	0.542186i
$934$		0			0
$935$	11.1231			0.363764
$936$		0			0
$937$	−7.56155			−0.247025			−0.123513	−	0.992343i	$-0.539416\pi$
$937$	−7.56155			−0.247025			−0.123513	+	0.992343i	$0.539416\pi$
$938$		0			0
$939$	−6.84233	−	11.8513i	−0.223291	−	0.386751i
$940$		0			0
$941$	30.4924			0.994025			0.497012	−	0.867744i	$-0.334430\pi$
$941$	30.4924			0.994025			0.497012	+	0.867744i	$0.334430\pi$
$942$		0			0
$943$	−1.56155	+	2.70469i	−0.0508512	+	0.0880768i
$944$		0			0
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$		0			0
$947$	−19.3693	−	33.5486i	−0.629418	−	1.09018i	−0.987669	−	0.156559i	$-0.949960\pi$
$947$	−19.3693	−	33.5486i	−0.629418	−	1.09018i	0.358250	−	0.933626i	$-0.383373\pi$
$948$		0			0
$949$	−5.06155	+	36.1467i	−0.164305	+	1.17337i
$950$		0			0
$951$	7.02699	+	12.1711i	0.227866	+	0.394675i
$952$		0			0
$953$	−15.4924	+	26.8337i	−0.501849	+	0.869228i	0.498149	+	0.867091i	$0.334013\pi$
$953$	−15.4924	+	26.8337i	−0.501849	+	0.869228i	−0.999998	+	0.00213612i	$0.999320\pi$
$954$		0			0
$955$	16.2462	−	28.1393i	0.525715	−	0.910565i
$956$		0			0
$957$	−13.3693			−0.432169
$958$		0			0
$959$	−1.56155	−	2.70469i	−0.0504252	−	0.0873390i
$960$		0			0
$961$	−24.4384			−0.788337
$962$		0			0
$963$	8.24621			0.265730
$964$		0			0
$965$	−24.0270	−	41.6160i	−0.773456	−	1.33967i
$966$		0			0
$967$	0.876894			0.0281990			0.0140995	−	0.999901i	$-0.495512\pi$
$967$	0.876894			0.0281990			0.0140995	+	0.999901i	$0.495512\pi$
$968$		0			0
$969$	5.56155	−	9.63289i	0.178663	−	0.309453i
$970$		0			0
$971$	−6.49242	+	11.2452i	−0.208352	+	0.360876i	−0.951195	−	0.308589i	$-0.900143\pi$
$971$	−6.49242	+	11.2452i	−0.208352	+	0.360876i	0.742844	+	0.669465i	$0.233477\pi$
$972$		0			0
$973$	5.03457	+	8.72012i	0.161401	+	0.279554i
$974$		0			0
$975$	25.6847	−	10.3923i	0.822567	−	0.332820i
$976$		0			0
$977$	−30.5885	−	52.9809i	−0.978614	−	1.69501i	−0.667453	−	0.744652i	$-0.732615\pi$
$977$	−30.5885	−	52.9809i	−0.978614	−	1.69501i	−0.311162	−	0.950357i	$-0.600718\pi$
$978$		0			0
$979$	−4.87689	+	8.44703i	−0.155866	+	0.269968i
$980$		0			0
$981$	1.40388	−	2.43160i	0.0448225	−	0.0776349i
$982$		0			0
$983$	−13.6155			−0.434268			−0.217134	−	0.976142i	$-0.569671\pi$
$983$	−13.6155			−0.434268			−0.217134	+	0.976142i	$0.569671\pi$
$984$		0			0
$985$	23.8078	+	41.2363i	0.758578	+	1.31390i
$986$		0			0
$987$	−4.63068			−0.147396
$988$		0			0
$989$	9.12311			0.290098
$990$		0			0
$991$	−25.1771	−	43.6080i	−0.799776	−	1.38525i	−0.919762	−	0.392478i	$-0.871618\pi$
$991$	−25.1771	−	43.6080i	−0.799776	−	1.38525i	0.119985	−	0.992776i	$-0.461715\pi$
$992$		0			0
$993$	−3.19224			−0.101303
$994$		0			0
$995$	−39.4924	+	68.4029i	−1.25199	+	2.16852i
$996$		0			0
$997$	10.3078	−	17.8536i	0.326450	−	0.565428i	−0.655355	−	0.755321i	$-0.727481\pi$
$997$	10.3078	−	17.8536i	0.326450	−	0.565428i	0.981805	+	0.189893i	$0.0608141\pi$
$998$		0			0
$999$	3.78078	+	6.54850i	0.119618	+	0.207185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.q.h.289.1		4
3.2	odd	2		1872.2.t.r.289.2		4
4.3	odd	2		39.2.e.b.16.2	✓	4
12.11	even	2		117.2.g.c.55.1		4
13.3	even	3		8112.2.a.bk.1.1		2
13.9	even	3	inner	624.2.q.h.529.1		4
13.10	even	6		8112.2.a.bo.1.2		2
20.3	even	4		975.2.bb.i.874.3		8
20.7	even	4		975.2.bb.i.874.2		8
20.19	odd	2		975.2.i.k.601.1		4
39.35	odd	6		1872.2.t.r.1153.2		4
52.3	odd	6		507.2.a.g.1.1		2
52.7	even	12		507.2.j.g.316.3		8
52.11	even	12		507.2.b.d.337.2		4
52.15	even	12		507.2.b.d.337.3		4
52.19	even	12		507.2.j.g.316.2		8
52.23	odd	6		507.2.a.d.1.2		2
52.31	even	4		507.2.j.g.361.3		8
52.35	odd	6		39.2.e.b.22.2	yes	4
52.43	odd	6		507.2.e.g.22.1		4
52.47	even	4		507.2.j.g.361.2		8
52.51	odd	2		507.2.e.g.484.1		4
156.11	odd	12		1521.2.b.h.1351.3		4
156.23	even	6		1521.2.a.m.1.1		2
156.35	even	6		117.2.g.c.100.1		4
156.107	even	6		1521.2.a.g.1.2		2
156.119	odd	12		1521.2.b.h.1351.2		4
260.87	even	12		975.2.bb.i.724.3		8
260.139	odd	6		975.2.i.k.451.1		4
260.243	even	12		975.2.bb.i.724.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.2	✓	4	4.3	odd	2
39.2.e.b.22.2	yes	4	52.35	odd	6
117.2.g.c.55.1		4	12.11	even	2
117.2.g.c.100.1		4	156.35	even	6
507.2.a.d.1.2		2	52.23	odd	6
507.2.a.g.1.1		2	52.3	odd	6
507.2.b.d.337.2		4	52.11	even	12
507.2.b.d.337.3		4	52.15	even	12
507.2.e.g.22.1		4	52.43	odd	6
507.2.e.g.484.1		4	52.51	odd	2
507.2.j.g.316.2		8	52.19	even	12
507.2.j.g.316.3		8	52.7	even	12
507.2.j.g.361.2		8	52.47	even	4
507.2.j.g.361.3		8	52.31	even	4
624.2.q.h.289.1		4	1.1	even	1	trivial
624.2.q.h.529.1		4	13.9	even	3	inner
975.2.i.k.451.1		4	260.139	odd	6
975.2.i.k.601.1		4	20.19	odd	2
975.2.bb.i.724.2		8	260.243	even	12
975.2.bb.i.724.3		8	260.87	even	12
975.2.bb.i.874.2		8	20.7	even	4
975.2.bb.i.874.3		8	20.3	even	4
1521.2.a.g.1.2		2	156.107	even	6
1521.2.a.m.1.1		2	156.23	even	6
1521.2.b.h.1351.2		4	156.119	odd	12
1521.2.b.h.1351.3		4	156.11	odd	12
1872.2.t.r.289.2		4	3.2	odd	2
1872.2.t.r.1153.2		4	39.35	odd	6
8112.2.a.bk.1.1		2	13.3	even	3
8112.2.a.bo.1.2		2	13.10	even	6

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} -3.56155 q^{5} +(0.280776 - 0.486319i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} -3.56155 q^{5} +(0.280776 - 0.486319i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 3.57071i) q^{13} +(-1.78078 - 3.08440i) q^{15} +(0.780776 - 1.35234i) q^{17} +(3.56155 - 6.16879i) q^{19} +0.561553 q^{21} +(1.00000 + 1.73205i) q^{23} +7.68466 q^{25} -1.00000 q^{27} +(-3.34233 - 5.78908i) q^{29} -2.56155 q^{31} +(1.00000 - 1.73205i) q^{33} +(-1.00000 + 1.73205i) q^{35} +(-3.78078 - 6.54850i) q^{37} +(3.34233 - 1.35234i) q^{39} +(0.780776 + 1.35234i) q^{41} +(2.28078 - 3.95042i) q^{43} +(1.78078 - 3.08440i) q^{45} -8.24621 q^{47} +(3.34233 + 5.78908i) q^{49} +1.56155 q^{51} -0.684658 q^{53} +(3.56155 + 6.16879i) q^{55} +7.12311 q^{57} +(-1.43845 + 2.49146i) q^{59} +(-1.93845 + 3.35749i) q^{61} +(0.280776 + 0.486319i) q^{63} +(-1.78078 + 12.7173i) q^{65} +(2.28078 + 3.95042i) q^{67} +(-1.00000 + 1.73205i) q^{69} +(7.00000 - 12.1244i) q^{71} -10.1231 q^{73} +(3.84233 + 6.65511i) q^{75} -1.12311 q^{77} -5.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +0.876894 q^{83} +(-2.78078 + 4.81645i) q^{85} +(3.34233 - 5.78908i) q^{87} +(-2.43845 - 4.22351i) q^{89} +(-1.59612 - 1.24573i) q^{91} +(-1.28078 - 2.21837i) q^{93} +(-12.6847 + 21.9705i) q^{95} +(4.28078 - 7.41452i) q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 6 q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 6 * q^5 - 3 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} - 6 q^{5} - 3 q^{7} - 2 q^{9} - 4 q^{11} + 2 q^{13} - 3 q^{15} - q^{17} + 6 q^{19} - 6 q^{21} + 4 q^{23} + 6 q^{25} - 4 q^{27} - q^{29} - 2 q^{31} + 4 q^{33} - 4 q^{35} - 11 q^{37} + q^{39} - q^{41} + 5 q^{43} + 3 q^{45} + q^{49} - 2 q^{51} + 22 q^{53} + 6 q^{55} + 12 q^{57} - 14 q^{59} - 16 q^{61} - 3 q^{63} - 3 q^{65} + 5 q^{67} - 4 q^{69} + 28 q^{71} - 24 q^{73} + 3 q^{75} + 12 q^{77} - 30 q^{79} - 2 q^{81} + 20 q^{83} - 7 q^{85} + q^{87} - 18 q^{89} - 27 q^{91} - q^{93} - 26 q^{95} + 13 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^5 - 3 * q^7 - 2 * q^9 - 4 * q^11 + 2 * q^13 - 3 * q^15 - q^17 + 6 * q^19 - 6 * q^21 + 4 * q^23 + 6 * q^25 - 4 * q^27 - q^29 - 2 * q^31 + 4 * q^33 - 4 * q^35 - 11 * q^37 + q^39 - q^41 + 5 * q^43 + 3 * q^45 + q^49 - 2 * q^51 + 22 * q^53 + 6 * q^55 + 12 * q^57 - 14 * q^59 - 16 * q^61 - 3 * q^63 - 3 * q^65 + 5 * q^67 - 4 * q^69 + 28 * q^71 - 24 * q^73 + 3 * q^75 + 12 * q^77 - 30 * q^79 - 2 * q^81 + 20 * q^83 - 7 * q^85 + q^87 - 18 * q^89 - 27 * q^91 - q^93 - 26 * q^95 + 13 * q^97 + 8 * q^99

Introduction

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