LMFDB - Embedded newform 783.2.k.a.487.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(82,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-2,0,-2,-8,0,-8,-7,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			487.1
Root			$0.222521 + 0.974928i$ of defining polynomial
Character	$\chi$	$=$	783.487
Dual form			783.2.k.a.82.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12349 + 1.40881i) q^{2} +(-0.277479 - 1.21572i) q^{4} +(-1.27748 + 1.60191i) q^{5} +(-0.599031 + 2.62453i) q^{7} +(-1.22252 - 0.588735i) q^{8} +(-0.821552 - 3.59945i) q^{10} +(-3.82640 + 1.84270i) q^{11} +(-0.0990311 + 0.0476909i) q^{13} +(-3.02446 - 3.79255i) q^{14} +(4.44989 - 2.14295i) q^{16} +1.10992 q^{17} +(-0.291053 - 1.27518i) q^{19} +(2.30194 + 1.10855i) q^{20} +(1.70291 - 7.46092i) q^{22} +(-1.74698 - 2.19064i) q^{23} +(0.178448 + 0.781831i) q^{25} +(0.0440730 - 0.193096i) q^{26} +3.35690 q^{28} +(2.97554 + 4.48845i) q^{29} +(2.77748 - 3.48285i) q^{31} +(-1.37651 + 6.03089i) q^{32} +(-1.24698 + 1.56366i) q^{34} +(-3.43900 - 4.31237i) q^{35} +(-8.32036 - 4.00687i) q^{37} +(2.12349 + 1.02262i) q^{38} +(2.50484 - 1.20627i) q^{40} -6.19806 q^{41} +(-2.28836 - 2.86952i) q^{43} +(3.30194 + 4.14050i) q^{44} +5.04892 q^{46} +(6.49396 - 3.12733i) q^{47} +(-0.222521 - 0.107160i) q^{49} +(-1.30194 - 0.626980i) q^{50} +(0.0854576 + 0.107160i) q^{52} +(7.09783 - 8.90040i) q^{53} +(1.93631 - 8.48354i) q^{55} +(2.27748 - 2.85587i) q^{56} +(-9.66637 - 0.850747i) q^{58} -6.10992 q^{59} +(-2.02446 + 8.86973i) q^{61} +(1.78621 + 7.82589i) q^{62} +(-0.791053 - 0.991949i) q^{64} +(0.0501138 - 0.219563i) q^{65} +(-1.96950 - 0.948461i) q^{67} +(-0.307979 - 1.34934i) q^{68} +9.93900 q^{70} +(4.57338 - 2.20242i) q^{71} +(-5.57942 - 6.99637i) q^{73} +(14.9928 - 7.22013i) q^{74} +(-1.46950 + 0.707674i) q^{76} +(-2.54407 - 11.1463i) q^{77} +(-7.70560 - 3.71082i) q^{79} +(-2.25182 + 9.86589i) q^{80} +(6.96346 - 8.73190i) q^{82} +(-0.900969 - 3.94740i) q^{83} +(-1.41789 + 1.77798i) q^{85} +6.61356 q^{86} +5.76271 q^{88} +(-6.64526 + 8.33289i) q^{89} +(-0.0658433 - 0.288478i) q^{91} +(-2.17845 + 2.73169i) q^{92} +(-2.89008 + 12.6623i) q^{94} +(2.41454 + 1.16278i) q^{95} +(2.53588 + 11.1104i) q^{97} +(0.400969 - 0.193096i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 8 q^{7} - 7 q^{8} - 9 q^{10} - 5 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} + 8 q^{17} + 4 q^{19} + 5 q^{20} - 3 q^{22} - q^{23} - 3 q^{25} + 4 q^{26} + 12 q^{28} + 27 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 - 8 * q^5 - 8 * q^7 - 7 * q^8 - 9 * q^10 - 5 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 + 8 * q^17 + 4 * q^19 + 5 * q^20 - 3 * q^22 - q^23 - 3 * q^25 + 4 * q^26 + 12 * q^28 + 27 * q^29 + 17 * q^31 - 13 * q^32 + 2 * q^34 - q^35 - 13 * q^37 + 8 * q^38 - 7 * q^40 - 46 * q^41 - 11 * q^43 + 11 * q^44 + 12 * q^46 + 20 * q^47 - q^49 + q^50 + 11 * q^52 + 6 * q^53 - 5 * q^55 + 14 * q^56 - 16 * q^58 - 38 * q^59 - 3 * q^61 + 27 * q^62 + q^64 + 23 * q^65 - 2 * q^67 - 12 * q^68 + 40 * q^70 - 25 * q^73 + 30 * q^74 + q^76 - 19 * q^77 - 30 * q^79 + 18 * q^80 + 13 * q^82 - q^83 - 20 * q^85 - 22 * q^86 - 29 * q^89 + 2 * q^91 - 9 * q^92 - 16 * q^94 + 4 * q^95 + 19 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−1.12349	+	1.40881i	−0.794427	+	0.996180i	0.205419	+	0.978674i	$0.434144\pi$
$2$	−1.12349	+	1.40881i	−0.794427	+	0.996180i	−0.999847	+	0.0175063i	$0.994427\pi$
$3$		0			0
$3$		0			0
$4$	−0.277479	−	1.21572i	−0.138740	−	0.607858i
$5$	−1.27748	+	1.60191i	−0.571306	+	0.716395i	−0.980603	−	0.196006i	$-0.937203\pi$
$5$	−1.27748	+	1.60191i	−0.571306	+	0.716395i	0.409297	+	0.912401i	$0.365774\pi$
$6$		0			0
$7$	−0.599031	+	2.62453i	−0.226412	+	0.991978i	0.726126	+	0.687561i	$0.241319\pi$
$7$	−0.599031	+	2.62453i	−0.226412	+	0.991978i	−0.952539	+	0.304417i	$0.901538\pi$
$8$	−1.22252	−	0.588735i	−0.432226	−	0.208149i
$9$		0			0
$10$	−0.821552	−	3.59945i	−0.259798	−	1.13825i
$11$	−3.82640	+	1.84270i	−1.15370	+	0.555594i	−0.910144	−	0.414293i	$-0.864029\pi$
$11$	−3.82640	+	1.84270i	−1.15370	+	0.555594i	−0.243558	+	0.969886i	$0.578315\pi$
$12$		0			0
$13$	−0.0990311	+	0.0476909i	−0.0274663	+	0.0132271i	−0.447566	−	0.894251i	$-0.647709\pi$
$13$	−0.0990311	+	0.0476909i	−0.0274663	+	0.0132271i	0.420100	+	0.907478i	$0.361995\pi$
$14$	−3.02446	−	3.79255i	−0.808321	−	1.01360i
$15$		0			0
$16$	4.44989	−	2.14295i	1.11247	−	0.535738i
$17$	1.10992			0.269194			0.134597	−	0.990900i	$-0.457026\pi$
$17$	1.10992			0.269194			0.134597	+	0.990900i	$0.457026\pi$
$18$		0			0
$19$	−0.291053	−	1.27518i	−0.0667720	−	0.292547i	0.930506	−	0.366276i	$-0.119367\pi$
$19$	−0.291053	−	1.27518i	−0.0667720	−	0.292547i	−0.997278	+	0.0737284i	$0.976510\pi$
$20$	2.30194	+	1.10855i	0.514729	+	0.247880i
$21$		0			0
$22$	1.70291	−	7.46092i	0.363061	−	1.59067i
$23$	−1.74698	−	2.19064i	−0.364270	−	0.456781i	0.565594	−	0.824684i	$-0.308647\pi$
$23$	−1.74698	−	2.19064i	−0.364270	−	0.456781i	−0.929864	+	0.367903i	$0.880076\pi$
$24$		0			0
$25$	0.178448	+	0.781831i	0.0356896	+	0.156366i
$26$	0.0440730	−	0.193096i	0.00864343	−	0.0378693i
$27$		0			0
$28$	3.35690			0.634394
$29$	2.97554	+	4.48845i	0.552544	+	0.833484i
$29$	2.97554	+	4.48845i	0.552544	+	0.833484i
$30$		0			0
$31$	2.77748	−	3.48285i	0.498850	−	0.625538i	−0.467120	−	0.884194i	$-0.654708\pi$
$31$	2.77748	−	3.48285i	0.498850	−	0.625538i	0.965969	+	0.258656i	$0.0832796\pi$
$32$	−1.37651	+	6.03089i	−0.243335	+	1.06612i
$33$		0			0
$34$	−1.24698	+	1.56366i	−0.213855	+	0.268166i
$35$	−3.43900	−	4.31237i	−0.581297	−	0.728924i
$36$		0			0
$37$	−8.32036	−	4.00687i	−1.36786	−	0.658726i	−0.401484	−	0.915866i	$-0.631505\pi$
$37$	−8.32036	−	4.00687i	−1.36786	−	0.658726i	−0.966374	+	0.257140i	$0.917220\pi$
$38$	2.12349	+	1.02262i	0.344476	+	0.165891i
$39$		0			0
$40$	2.50484	−	1.20627i	0.396051	−	0.190728i
$41$	−6.19806			−0.967975			−0.483987	−	0.875075i	$-0.660812\pi$
$41$	−6.19806			−0.967975			−0.483987	+	0.875075i	$0.660812\pi$
$42$		0			0
$43$	−2.28836	−	2.86952i	−0.348972	−	0.437597i	0.576105	−	0.817375i	$-0.304572\pi$
$43$	−2.28836	−	2.86952i	−0.348972	−	0.437597i	−0.925078	+	0.379778i	$0.876000\pi$
$44$	3.30194	+	4.14050i	0.497786	+	0.624204i
$45$		0			0
$46$	5.04892			0.744422
$47$	6.49396	−	3.12733i	0.947241	−	0.456167i	0.104523	−	0.994522i	$-0.466668\pi$
$47$	6.49396	−	3.12733i	0.947241	−	0.456167i	0.842718	+	0.538355i	$0.180954\pi$
$48$		0			0
$49$	−0.222521	−	0.107160i	−0.0317887	−	0.0153086i
$50$	−1.30194	−	0.626980i	−0.184122	−	0.0886684i
$51$		0			0
$52$	0.0854576	+	0.107160i	0.0118508	+	0.0148605i
$53$	7.09783	−	8.90040i	0.974963	−	1.22256i	4.45840e−5	−	1.00000i	$-0.499986\pi$
$53$	7.09783	−	8.90040i	0.974963	−	1.22256i	0.974918	−	0.222564i	$-0.0714428\pi$
$54$		0			0
$55$	1.93631	−	8.48354i	0.261092	−	1.14392i
$56$	2.27748	−	2.85587i	0.304341	−	0.381631i
$57$		0			0
$58$	−9.66637	−	0.850747i	−1.26926	−	0.111709i
$59$	−6.10992			−0.795443			−0.397722	−	0.917506i	$-0.630199\pi$
$59$	−6.10992			−0.795443			−0.397722	+	0.917506i	$0.630199\pi$
$60$		0			0
$61$	−2.02446	+	8.86973i	−0.259205	+	1.13565i	0.662898	+	0.748710i	$0.269326\pi$
$61$	−2.02446	+	8.86973i	−0.259205	+	1.13565i	−0.922103	+	0.386943i	$0.873531\pi$
$62$	1.78621	+	7.82589i	0.226849	+	0.993889i
$63$		0			0
$64$	−0.791053	−	0.991949i	−0.0988816	−	0.123994i
$65$	0.0501138	−	0.219563i	0.00621585	−	0.0272334i
$66$		0			0
$67$	−1.96950	−	0.948461i	−0.240613	−	0.115873i	0.309692	−	0.950837i	$-0.399774\pi$
$67$	−1.96950	−	0.948461i	−0.240613	−	0.115873i	−0.550305	+	0.834964i	$0.685488\pi$
$68$	−0.307979	−	1.34934i	−0.0373479	−	0.163632i
$69$		0			0
$70$	9.93900			1.18794
$71$	4.57338	−	2.20242i	0.542760	−	0.261379i	−0.142353	−	0.989816i	$-0.545467\pi$
$71$	4.57338	−	2.20242i	0.542760	−	0.261379i	0.685113	+	0.728437i	$0.259753\pi$
$72$		0			0
$73$	−5.57942	−	6.99637i	−0.653021	−	0.818863i	0.339542	−	0.940591i	$-0.389728\pi$
$73$	−5.57942	−	6.99637i	−0.653021	−	0.818863i	−0.992563	+	0.121728i	$0.961156\pi$
$74$	14.9928	−	7.22013i	1.74287	−	0.839324i
$75$		0			0
$76$	−1.46950	+	0.707674i	−0.168563	+	0.0811758i
$77$	−2.54407	−	11.1463i	−0.289924	−	1.27024i
$78$		0			0
$79$	−7.70560	−	3.71082i	−0.866947	−	0.417500i	−0.0531072	−	0.998589i	$-0.516913\pi$
$79$	−7.70560	−	3.71082i	−0.866947	−	0.417500i	−0.813840	+	0.581089i	$0.802627\pi$
$80$	−2.25182	+	9.86589i	−0.251762	+	1.10304i
$81$		0			0
$82$	6.96346	−	8.73190i	0.768985	−	0.964277i
$83$	−0.900969	−	3.94740i	−0.0988942	−	0.433284i	0.901106	−	0.433599i	$-0.142757\pi$
$83$	−0.900969	−	3.94740i	−0.0988942	−	0.433284i	−1.00000		0.000315629i	$0.999900\pi$
$84$		0			0
$85$	−1.41789	+	1.77798i	−0.153792	+	0.192849i
$86$	6.61356			0.713159
$87$		0			0
$88$	5.76271			0.614307
$89$	−6.64526	+	8.33289i	−0.704396	+	0.883285i	−0.997343	−	0.0728438i	$-0.976793\pi$
$89$	−6.64526	+	8.33289i	−0.704396	+	0.883285i	0.292947	+	0.956129i	$0.405364\pi$
$90$		0			0
$91$	−0.0658433	−	0.288478i	−0.00690225	−	0.0302407i
$92$	−2.17845	+	2.73169i	−0.227119	+	0.284798i
$93$		0			0
$94$	−2.89008	+	12.6623i	−0.298089	+	1.30601i
$95$	2.41454	+	1.16278i	0.247727	+	0.119299i
$96$		0			0
$97$	2.53588	+	11.1104i	0.257479	+	1.12809i	0.923936	+	0.382547i	$0.124953\pi$
$97$	2.53588	+	11.1104i	0.257479	+	1.12809i	−0.666457	+	0.745544i	$0.732190\pi$
$98$	0.400969	−	0.193096i	0.0405040	−	0.0195057i
$99$		0			0
$100$	0.900969	−	0.433884i	0.0900969	−	0.0433884i
$101$	−0.507533	−	0.636426i	−0.0505014	−	0.0633267i	0.755939	−	0.654642i	$-0.227180\pi$
$101$	−0.507533	−	0.636426i	−0.0505014	−	0.0633267i	−0.806441	+	0.591315i	$0.798609\pi$
$102$		0			0
$103$	13.6114	−	6.55491i	1.34117	−	0.645874i	0.380816	−	0.924651i	$-0.375643\pi$
$103$	13.6114	−	6.55491i	1.34117	−	0.645874i	0.960356	+	0.278777i	$0.0899289\pi$
$104$	0.149145			0.0146249
$105$		0			0
$106$	4.56465	+	19.9990i	0.443358	+	1.94248i
$107$	4.48039	+	2.15764i	0.433135	+	0.208587i	0.637730	−	0.770260i	$-0.279873\pi$
$107$	4.48039	+	2.15764i	0.433135	+	0.208587i	−0.204595	+	0.978847i	$0.565588\pi$
$108$		0			0
$109$	−1.99731	+	8.75079i	−0.191308	+	0.838174i	0.784602	+	0.620000i	$0.212867\pi$
$109$	−1.99731	+	8.75079i	−0.191308	+	0.838174i	−0.975910	+	0.218174i	$0.929990\pi$
$110$	9.77628	+	12.2591i	0.932132	+	1.16886i
$111$		0			0
$112$	2.95862	+	12.9625i	0.279563	+	1.22484i
$113$	2.84817	−	12.4786i	0.267933	−	1.17389i	−0.644480	−	0.764621i	$-0.722926\pi$
$113$	2.84817	−	12.4786i	0.267933	−	1.17389i	0.912413	−	0.409270i	$-0.134217\pi$
$114$		0			0
$115$	5.74094			0.535345
$116$	4.63102	−	4.86286i	0.429980	−	0.451505i
$117$		0			0
$118$	6.86443	−	8.60772i	0.631922	−	0.792405i
$119$	−0.664874	+	2.91301i	−0.0609489	+	0.267035i
$120$		0			0
$121$	4.38740	−	5.50162i	0.398854	−	0.500147i
$122$	−10.2213	−	12.8171i	−0.925395	−	1.16041i
$123$		0			0
$124$	−5.00484	−	2.41021i	−0.449448	−	0.216443i
$125$	−10.7104	−	5.15788i	−0.957971	−	0.461334i
$126$		0			0
$127$	−13.7702	+	6.63140i	−1.22191	+	0.588442i	−0.929843	−	0.367956i	$-0.880058\pi$
$127$	−13.7702	+	6.63140i	−1.22191	+	0.588442i	−0.292068	+	0.956398i	$0.594343\pi$
$128$	−10.0858			−0.891463
$129$		0			0
$130$	0.253020	+	0.317278i	0.0221914	+	0.0278271i
$131$	−5.89493	−	7.39201i	−0.515042	−	0.645843i	0.454506	−	0.890744i	$-0.349816\pi$
$131$	−5.89493	−	7.39201i	−0.515042	−	0.645843i	−0.969548	+	0.244901i	$0.921244\pi$
$132$		0			0
$133$	3.52111			0.305319
$134$	3.54892	−	1.70907i	0.306580	−	0.147641i
$135$		0			0
$136$	−1.35690	−	0.653447i	−0.116353	−	0.0560326i
$137$	17.2615	+	8.31271i	1.47475	+	0.710202i	0.986691	−	0.162608i	$-0.0519905\pi$
$137$	17.2615	+	8.31271i	1.47475	+	0.710202i	0.488060	+	0.872810i	$0.337705\pi$
$138$		0			0
$139$	2.96197	+	3.71419i	0.251231	+	0.315033i	0.891415	−	0.453188i	$-0.149713\pi$
$139$	2.96197	+	3.71419i	0.251231	+	0.315033i	−0.640184	+	0.768222i	$0.721142\pi$
$140$	−4.28836	+	5.37744i	−0.362433	+	0.454477i
$141$		0			0
$142$	−2.03534	+	8.91742i	−0.170802	+	0.748334i
$143$	0.291053	−	0.364968i	0.0243390	−	0.0305202i
$144$		0			0
$145$	−10.9913	−	0.967353i	−0.912775	−	0.0803343i
$146$	16.1250			1.33451
$147$		0			0
$148$	−2.56249	+	11.2270i	−0.210635	+	0.922854i
$149$	−0.826396	−	3.62068i	−0.0677010	−	0.296618i	0.929731	−	0.368240i	$-0.120040\pi$
$149$	−0.826396	−	3.62068i	−0.0677010	−	0.296618i	−0.997432	+	0.0716223i	$0.977182\pi$
$150$		0			0
$151$	−11.6298	−	14.5833i	−0.946422	−	1.18678i	−0.982280	−	0.187419i	$-0.939988\pi$
$151$	−11.6298	−	14.5833i	−0.946422	−	1.18678i	0.0358583	−	0.999357i	$-0.488583\pi$
$152$	−0.394928	+	1.73029i	−0.0320329	+	0.140345i
$153$		0			0
$154$	18.5613	+	8.93865i	1.49571	+	0.720297i
$155$	2.03103	+	8.89853i	0.163136	+	0.714747i
$156$		0			0
$157$	−20.5743			−1.64201			−0.821005	−	0.570920i	$-0.806586\pi$
$157$	−20.5743			−1.64201			−0.821005	+	0.570920i	$0.806586\pi$
$158$	13.8850	−	6.68666i	1.10463	−	0.531962i
$159$		0			0
$160$	−7.90246	−	9.90937i	−0.624744	−	0.783405i
$161$	6.79590	−	3.27273i	0.535592	−	0.257927i
$162$		0			0
$163$	−11.6516	+	5.61111i	−0.912623	+	0.439496i	−0.830432	−	0.557120i	$-0.811906\pi$
$163$	−11.6516	+	5.61111i	−0.912623	+	0.439496i	−0.0821916	+	0.996617i	$0.526192\pi$
$164$	1.71983	+	7.53508i	0.134296	+	0.588391i
$165$		0			0
$166$	6.57338	+	3.16557i	0.510193	+	0.245696i
$167$	−3.73945	+	16.3836i	−0.289367	+	1.26780i	0.596029	+	0.802963i	$0.296744\pi$
$167$	−3.73945	+	16.3836i	−0.289367	+	1.26780i	−0.885396	+	0.464837i	$0.846113\pi$
$168$		0			0
$169$	−8.09783	+	10.1544i	−0.622910	+	0.781105i
$170$	−0.911854	−	3.99509i	−0.0699360	−	0.306410i
$171$		0			0
$172$	−2.85354	+	3.57823i	−0.217581	+	0.272838i
$173$	−20.3381			−1.54628			−0.773139	−	0.634237i	$-0.781314\pi$
$173$	−20.3381			−1.54628			−0.773139	+	0.634237i	$0.781314\pi$
$174$		0			0
$175$	−2.15883			−0.163192
$176$	−13.0782	+	16.3996i	−0.985808	+	1.23616i
$177$		0			0
$178$	−4.27359	−	18.7238i	−0.320319	−	1.40341i
$179$	−3.20895	+	4.02389i	−0.239848	+	0.300760i	−0.887157	−	0.461468i	$-0.847323\pi$
$179$	−3.20895	+	4.02389i	−0.239848	+	0.300760i	0.647309	+	0.762228i	$0.275894\pi$
$180$		0			0
$181$	−5.85743	+	25.6631i	−0.435379	+	1.90752i	−0.0156368	+	0.999878i	$0.504978\pi$
$181$	−5.85743	+	25.6631i	−0.435379	+	1.90752i	−0.419742	+	0.907643i	$0.637880\pi$
$182$	0.480386	+	0.231342i	0.0356086	+	0.0171482i
$183$		0			0
$184$	0.846011	+	3.70662i	0.0623687	+	0.273255i
$185$	17.0477	−	8.20975i	1.25337	−	0.603593i
$186$		0			0
$187$	−4.24698	+	2.04524i	−0.310570	+	0.149563i
$188$	−5.60388	−	7.02704i	−0.408705	−	0.512499i
$189$		0			0
$190$	−4.35086	+	2.09526i	−0.315644	+	0.152006i
$191$	−19.6993			−1.42539			−0.712696	−	0.701473i	$-0.752526\pi$
$191$	−19.6993			−1.42539			−0.712696	+	0.701473i	$0.752526\pi$
$192$		0			0
$193$	−1.80529	−	7.90949i	−0.129948	−	0.569338i	−0.997416	−	0.0718451i	$-0.977111\pi$
$193$	−1.80529	−	7.90949i	−0.129948	−	0.569338i	0.867468	−	0.497493i	$-0.165746\pi$
$194$	−18.5015	−	8.90985i	−1.32833	−	0.639690i
$195$		0			0
$196$	−0.0685317	+	0.300257i	−0.00489512	+	0.0214469i
$197$	−6.44049	−	8.07612i	−0.458866	−	0.575400i	0.497540	−	0.867441i	$-0.334237\pi$
$197$	−6.44049	−	8.07612i	−0.458866	−	0.575400i	−0.956406	+	0.292041i	$0.905666\pi$
$198$		0			0
$199$	2.69441	+	11.8050i	0.191002	+	0.836834i	0.976076	+	0.217432i	$0.0697680\pi$
$199$	2.69441	+	11.8050i	0.191002	+	0.836834i	−0.785074	+	0.619403i	$0.787375\pi$
$200$	0.242135	−	1.06086i	0.0171215	−	0.0750144i
$201$		0			0
$202$	1.46681			0.103205
$203$	−13.5625	+	5.12067i	−0.951900	+	0.359400i
$204$		0			0
$205$	7.91789	−	9.92873i	0.553010	−	0.693452i
$206$	−6.05765	+	26.5403i	−0.422056	+	1.84915i
$207$		0			0
$208$	−0.338478	+	0.424438i	−0.0234692	+	0.0294295i
$209$	3.46346	+	4.34304i	0.239573	+	0.300414i
$210$		0			0
$211$	12.4330	+	5.98740i	0.855920	+	0.412189i	0.809772	−	0.586745i	$-0.199591\pi$
$211$	12.4330	+	5.98740i	0.855920	+	0.412189i	0.0461486	+	0.998935i	$0.485305\pi$
$212$	−12.7899	−	6.15927i	−0.878411	−	0.423020i
$213$		0			0
$214$	−8.07338	+	3.88793i	−0.551885	+	0.265774i
$215$	7.52004			0.512863
$216$		0			0
$217$	7.47703	+	9.37590i	0.507574	+	0.636478i
$218$	−10.0843	−	12.6453i	−0.682992	−	0.856445i
$219$		0			0
$220$	−10.8509			−0.731564
$221$	−0.109916	+	0.0529329i	−0.00739377	+	0.00356065i
$222$		0			0
$223$	−17.1516	−	8.25977i	−1.14856	−	0.553115i	−0.239956	−	0.970784i	$-0.577133\pi$
$223$	−17.1516	−	8.25977i	−1.14856	−	0.553115i	−0.908600	+	0.417668i	$0.862847\pi$
$224$	−15.0036	−	7.22538i	−1.00247	−	0.482766i
$225$		0			0
$226$	14.3802	+	18.0321i	0.956554	+	1.19948i
$227$	−1.17092	+	1.46828i	−0.0777164	+	0.0974532i	−0.819170	−	0.573551i	$-0.805565\pi$
$227$	−1.17092	+	1.46828i	−0.0777164	+	0.0974532i	0.741453	+	0.671004i	$0.234137\pi$
$228$		0			0
$229$	0.769282	−	3.37045i	0.0508356	−	0.222725i	−0.943129	−	0.332427i	$-0.892132\pi$
$229$	0.769282	−	3.37045i	0.0508356	−	0.222725i	0.993965	+	0.109702i	$0.0349896\pi$
$230$	−6.44989	+	8.08790i	−0.425293	+	0.533300i
$231$		0			0
$232$	−0.995156	−	7.23903i	−0.0653352	−	0.475265i
$233$	−0.567040			−0.0371480			−0.0185740	−	0.999827i	$-0.505913\pi$
$233$	−0.567040			−0.0371480			−0.0185740	+	0.999827i	$0.505913\pi$
$234$		0			0
$235$	−3.28621	+	14.3978i	−0.214369	+	0.939210i
$236$	1.69537	+	7.42792i	0.110359	+	0.483516i
$237$		0			0
$238$	−3.35690	−	4.20941i	−0.217595	−	0.272856i
$239$	−2.05161	+	8.98867i	−0.132707	+	0.581429i	0.864221	+	0.503112i	$0.167812\pi$
$239$	−2.05161	+	8.98867i	−0.132707	+	0.581429i	−0.996929	+	0.0783168i	$0.975045\pi$
$240$		0			0
$241$	11.9025	+	5.73192i	0.766705	+	0.369226i	0.776001	−	0.630731i	$-0.217245\pi$
$241$	11.9025	+	5.73192i	0.766705	+	0.369226i	−0.00929651	+	0.999957i	$0.502959\pi$
$242$	2.82155	+	12.3620i	0.181376	+	0.794661i
$243$		0			0
$244$	11.3448			0.726277
$245$	0.455927	−	0.219563i	0.0291281	−	0.0140274i
$246$		0			0
$247$	0.0896380	+	0.112402i	0.00570353	+	0.00715200i
$248$	−5.44600	+	2.62266i	−0.345821	+	0.166539i
$249$		0			0
$250$	19.2995	−	9.29417i	1.22061	−	0.587815i
$251$	−0.0864171	−	0.378618i	−0.00545460	−	0.0238982i	0.972127	−	0.234453i	$-0.0753300\pi$
$251$	−0.0864171	−	0.378618i	−0.00545460	−	0.0238982i	−0.977582	+	0.210555i	$0.932473\pi$
$252$		0			0
$253$	10.7213	+	5.16312i	0.674044	+	0.324602i
$254$	6.12833	−	26.8500i	0.384526	−	1.68472i
$255$		0			0
$256$	12.9133	−	16.1928i	0.807084	−	1.01205i
$257$	2.32520	+	10.1874i	0.145042	+	0.635470i	0.994220	+	0.107363i	$0.0342409\pi$
$257$	2.32520	+	10.1874i	0.145042	+	0.635470i	−0.849178	+	0.528107i	$0.822902\pi$
$258$		0			0
$259$	15.5003	−	19.4368i	0.963141	−	1.20774i
$260$	−0.280831			−0.0174164
$261$		0			0
$262$	17.0368			1.05254
$263$	−7.31886	+	9.17756i	−0.451300	+	0.565913i	−0.954482	−	0.298268i	$-0.903591\pi$
$263$	−7.31886	+	9.17756i	−0.451300	+	0.565913i	0.503182	+	0.864181i	$0.332163\pi$
$264$		0			0
$265$	5.19029	+	22.7402i	0.318837	+	1.39692i
$266$	−3.95593	+	4.96058i	−0.242553	+	0.304152i
$267$		0			0
$268$	−0.606564	+	2.65753i	−0.0370518	+	0.162334i
$269$	18.0673	+	8.70077i	1.10158	+	0.530495i	0.894156	−	0.447755i	$-0.147776\pi$
$269$	18.0673	+	8.70077i	1.10158	+	0.530495i	0.207429	+	0.978250i	$0.433491\pi$
$270$		0			0
$271$	−4.62445	−	20.2610i	−0.280915	−	1.23077i	−0.896623	−	0.442795i	$-0.853987\pi$
$271$	−4.62445	−	20.2610i	−0.280915	−	1.23077i	0.615707	−	0.787975i	$-0.288870\pi$
$272$	4.93900	−	2.37850i	0.299471	−	0.144218i
$273$		0			0
$274$	−31.1042	+	14.9790i	−1.87907	+	0.904913i
$275$	−2.12349	−	2.66277i	−0.128051	−	0.160571i
$276$		0			0
$277$	−7.87047	+	3.79022i	−0.472891	+	0.227732i	−0.655121	−	0.755524i	$-0.727383\pi$
$277$	−7.87047	+	3.79022i	−0.472891	+	0.227732i	0.182231	+	0.983256i	$0.441668\pi$
$278$	−8.56033			−0.513415
$279$		0			0
$280$	1.66541	+	7.29662i	0.0995271	+	0.436057i
$281$	11.2349	+	5.41044i	0.670218	+	0.322760i	0.737864	−	0.674949i	$-0.235835\pi$
$281$	11.2349	+	5.41044i	0.670218	+	0.322760i	−0.0676461	+	0.997709i	$0.521549\pi$
$282$		0			0
$283$	2.52930	−	11.0816i	0.150351	−	0.658733i	−0.842431	−	0.538804i	$-0.818876\pi$
$283$	2.52930	−	11.0816i	0.150351	−	0.658733i	0.992783	−	0.119929i	$-0.0382666\pi$
$284$	−3.94653	−	4.94880i	−0.234184	−	0.293657i
$285$		0			0
$286$	0.187177	+	0.820077i	0.0110680	+	0.0484921i
$287$	3.71283	−	16.2670i	0.219162	−	0.960210i
$288$		0			0
$289$	−15.7681			−0.927534
$290$	13.7114	−	14.3978i	0.805161	−	0.845469i
$291$		0			0
$292$	−6.95742	+	8.72433i	−0.407152	+	0.510553i
$293$	1.50053	−	6.57426i	0.0876620	−	0.384073i	−0.911997	−	0.410198i	$-0.865460\pi$
$293$	1.50053	−	6.57426i	0.0876620	−	0.384073i	0.999659	+	0.0261252i	$0.00831685\pi$
$294$		0			0
$295$	7.80529	−	9.78752i	0.454442	−	0.569852i
$296$	7.81282	+	9.79697i	0.454111	+	0.569437i
$297$		0			0
$298$	6.02930	+	2.90356i	0.349268	+	0.168199i
$299$	0.277479	+	0.133627i	0.0160470	+	0.00772784i
$300$		0			0
$301$	8.90193	−	4.28694i	0.513099	−	0.247095i
$302$	33.6112			1.93411
$303$		0			0
$304$	−4.02781	−	5.05072i	−0.231011	−	0.289678i
$305$	−11.6223	−	14.5739i	−0.665491	−	0.834499i
$306$		0			0
$307$	−4.59956			−0.262511			−0.131255	−	0.991349i	$-0.541901\pi$
$307$	−4.59956			−0.262511			−0.131255	+	0.991349i	$0.541901\pi$
$308$	−12.8448	+	6.18574i	−0.731901	+	0.352465i
$309$		0			0
$310$	−14.8182	−	7.13607i	−0.841617	−	0.405301i
$311$	26.2838	+	12.6576i	1.49042	+	0.717748i	0.989063	−	0.147494i	$-0.0471206\pi$
$311$	26.2838	+	12.6576i	1.49042	+	0.717748i	0.501355	+	0.865241i	$0.332835\pi$
$312$		0			0
$313$	−8.12833	−	10.1926i	−0.459441	−	0.576120i	0.497110	−	0.867688i	$-0.334395\pi$
$313$	−8.12833	−	10.1926i	−0.459441	−	0.576120i	−0.956550	+	0.291567i	$0.905823\pi$
$314$	23.1151	−	28.9854i	1.30446	−	1.63574i
$315$		0			0
$316$	−2.37316	+	10.3975i	−0.133501	+	0.584904i
$317$	−18.9494	+	23.7617i	−1.06430	+	1.33459i	−0.124749	+	0.992188i	$0.539813\pi$
$317$	−18.9494	+	23.7617i	−1.06430	+	1.33459i	−0.939553	+	0.342404i	$0.888759\pi$
$318$		0			0
$319$	−19.6564	−	11.6916i	−1.10055	−	0.654602i
$320$	2.59956			0.145320
$321$		0			0
$322$	−3.02446	+	13.2510i	−0.168546	+	0.738450i
$323$	−0.323044	−	1.41535i	−0.0179747	−	0.0787521i
$324$		0			0
$325$	−0.0549581	−	0.0689153i	−0.00304853	−	0.00382273i
$326$	5.18545	−	22.7189i	0.287195	−	1.25829i
$327$		0			0
$328$	7.57726	+	3.64902i	0.418384	+	0.201483i
$329$	4.31767	+	18.9169i	0.238041	+	1.04292i
$330$		0			0
$331$	−18.4655			−1.01495			−0.507477	−	0.861665i	$-0.669422\pi$
$331$	−18.4655			−1.01495			−0.507477	+	0.861665i	$0.669422\pi$
$332$	−4.54892	+	2.19064i	−0.249654	+	0.120227i
$333$		0			0
$334$	−18.8802	−	23.6750i	−1.03308	−	1.29544i
$335$	4.03534	−	1.94332i	0.220474	−	0.106175i
$336$		0			0
$337$	29.3904	−	14.1537i	1.60100	−	0.770999i	0.601387	−	0.798958i	$-0.294615\pi$
$337$	29.3904	−	14.1537i	1.60100	−	0.770999i	0.999609	+	0.0279589i	$0.00890076\pi$
$338$	−5.20775	−	22.8166i	−0.283264	−	1.24106i
$339$		0			0
$340$	2.55496	+	1.23040i	0.138562	+	0.0667280i
$341$	−4.20991	+	18.4448i	−0.227979	+	0.998842i
$342$		0			0
$343$	−11.3346	+	14.2131i	−0.612011	+	0.767437i
$344$	1.10819	+	4.85529i	0.0597495	+	0.261779i
$345$		0			0
$346$	22.8497	−	28.6526i	1.22841	−	1.54037i
$347$	8.29829			0.445476			0.222738	−	0.974878i	$-0.428501\pi$
$347$	8.29829			0.445476			0.222738	+	0.974878i	$0.428501\pi$
$348$		0			0
$349$	28.0127			1.49948			0.749742	−	0.661730i	$-0.230178\pi$
$349$	28.0127			1.49948			0.749742	+	0.661730i	$0.230178\pi$
$350$	2.42543	−	3.04139i	0.129645	−	0.162569i
$351$		0			0
$352$	−5.84601	−	25.6130i	−0.311593	−	1.36518i
$353$	5.14340	−	6.44962i	0.273756	−	0.343279i	−0.625881	−	0.779919i	$-0.715260\pi$
$353$	5.14340	−	6.44962i	0.273756	−	0.343279i	0.899636	+	0.436640i	$0.143832\pi$
$354$		0			0
$355$	−2.31431	+	10.1397i	−0.122831	+	0.538158i
$356$	11.9743	+	5.76654i	0.634639	+	0.305626i
$357$		0			0
$358$	−2.06369	−	9.04160i	−0.109069	−	0.477864i
$359$	13.1489	−	6.33218i	0.693973	−	0.334200i	−0.0534293	−	0.998572i	$-0.517015\pi$
$359$	13.1489	−	6.33218i	0.693973	−	0.334200i	0.747402	+	0.664372i	$0.231301\pi$
$360$		0			0
$361$	15.5770	−	7.50150i	0.819843	−	0.394816i
$362$	−29.5737	−	37.0842i	−1.55436	−	1.94910i
$363$		0			0
$364$	−0.332437	+	0.160093i	−0.0174244	+	0.00839117i
$365$	18.3351			0.959704
$366$		0			0
$367$	−6.44869	−	28.2536i	−0.336619	−	1.47482i	−0.806046	−	0.591853i	$-0.798397\pi$
$367$	−6.44869	−	28.2536i	−0.336619	−	1.47482i	0.469427	−	0.882971i	$-0.344460\pi$
$368$	−12.4683	−	6.00442i	−0.649955	−	0.313002i
$369$		0			0
$370$	−7.58695	+	33.2406i	−0.394427	+	1.72810i
$371$	19.1075	+	23.9601i	0.992013	+	1.24395i
$372$		0			0
$373$	4.77844	+	20.9357i	0.247418	+	1.08401i	0.934089	+	0.357041i	$0.116214\pi$
$373$	4.77844	+	20.9357i	0.247418	+	1.08401i	−0.686671	+	0.726969i	$0.740928\pi$
$374$	1.89008	−	8.28100i	0.0977339	−	0.428200i
$375$		0			0
$376$	−9.78017			−0.504374
$377$	−0.508729	−	0.302590i	−0.0262009	−	0.0155842i
$378$		0			0
$379$	14.1746	−	17.7743i	0.728098	−	0.913007i	−0.270667	−	0.962673i	$-0.587244\pi$
$379$	14.1746	−	17.7743i	0.728098	−	0.913007i	0.998766	+	0.0496664i	$0.0158158\pi$
$380$	0.743627	−	3.25804i	0.0381473	−	0.167134i
$381$		0			0
$382$	22.1320	−	27.7526i	1.13237	−	1.41995i
$383$	−2.16003	−	2.70859i	−0.110372	−	0.138403i	0.723577	−	0.690244i	$-0.242497\pi$
$383$	−2.16003	−	2.70859i	−0.110372	−	0.138403i	−0.833949	+	0.551841i	$0.813925\pi$
$384$		0			0
$385$	21.1054	+	10.1638i	1.07563	+	0.517996i
$386$	13.1712	+	6.34292i	0.670397	+	0.322846i
$387$		0			0
$388$	12.8034	−	6.16581i	0.649996	−	0.313021i
$389$	8.49635			0.430782			0.215391	−	0.976528i	$-0.430897\pi$
$389$	8.49635			0.430782			0.215391	+	0.976528i	$0.430897\pi$
$390$		0			0
$391$	−1.93900	−	2.43143i	−0.0980595	−	0.122963i
$392$	0.208947	+	0.262012i	0.0105534	+	0.0132336i
$393$		0			0
$394$	18.6136			0.937738
$395$	15.7881	−	7.60316i	0.794387	−	0.382557i
$396$		0			0
$397$	−25.1356	−	12.1047i	−1.26152	−	0.607517i	−0.320944	−	0.947098i	$-0.604000\pi$
$397$	−25.1356	−	12.1047i	−1.26152	−	0.607517i	−0.940577	+	0.339581i	$0.889715\pi$
$398$	−19.6582	−	9.46688i	−0.985375	−	0.474532i
$399$		0			0
$400$	2.46950	+	3.09666i	0.123475	+	0.154833i
$401$	11.5565	−	14.4913i	0.577102	−	0.723662i	−0.404514	−	0.914532i	$-0.632559\pi$
$401$	11.5565	−	14.4913i	0.577102	−	0.723662i	0.981615	+	0.190869i	$0.0611307\pi$
$402$		0			0
$403$	−0.108957	+	0.477371i	−0.00542752	+	0.0237795i
$404$	−0.632883	+	0.793610i	−0.0314871	+	0.0394836i
$405$		0			0
$406$	8.02326	−	24.8600i	0.398188	−	1.23378i
$407$	39.2204			1.94408
$408$		0			0
$409$	−7.90485	+	34.6334i	−0.390870	+	1.71251i	0.270730	+	0.962655i	$0.412735\pi$
$409$	−7.90485	+	34.6334i	−0.390870	+	1.71251i	−0.661600	+	0.749857i	$0.730122\pi$
$410$	5.09203	+	22.3096i	0.251477	+	1.10179i
$411$		0			0
$412$	−11.7458	−	14.7287i	−0.578673	−	0.725633i
$413$	3.66003	−	16.0356i	0.180098	−	0.789062i
$414$		0			0
$415$	7.47434	+	3.59945i	0.366901	+	0.176690i
$416$	−0.151301	−	0.662892i	−0.00741813	−	0.0325010i
$417$		0			0
$418$	−10.0097			−0.489590
$419$	0.825437	−	0.397509i	0.0403252	−	0.0194196i	−0.413612	−	0.910453i	$-0.635733\pi$
$419$	0.825437	−	0.397509i	0.0403252	−	0.0194196i	0.453938	+	0.891033i	$0.350019\pi$
$420$		0			0
$421$	−11.5395	−	14.4701i	−0.562402	−	0.705230i	0.416598	−	0.909091i	$-0.363222\pi$
$421$	−11.5395	−	14.4701i	−0.562402	−	0.705230i	−0.979000	+	0.203861i	$0.934651\pi$
$422$	−22.4034	+	10.7889i	−1.09058	+	0.525196i
$423$		0			0
$424$	−13.9172	+	6.70219i	−0.675880	+	0.325487i
$425$	0.198062	+	0.867767i	0.00960743	+	0.0420929i
$426$		0			0
$427$	−22.0661	−	10.6265i	−1.06786	−	0.514252i
$428$	1.37986	−	6.04557i	0.0666982	−	0.292224i
$429$		0			0
$430$	−8.44869	+	10.5943i	−0.407432	+	0.510904i
$431$	7.08844	+	31.0565i	0.341438	+	1.49594i	0.796040	+	0.605244i	$0.206924\pi$
$431$	7.08844	+	31.0565i	0.341438	+	1.49594i	−0.454602	+	0.890695i	$0.650218\pi$
$432$		0			0
$433$	10.9227	−	13.6967i	0.524913	−	0.658221i	−0.446731	−	0.894668i	$-0.647412\pi$
$433$	10.9227	−	13.6967i	0.524913	−	0.658221i	0.971644	+	0.236448i	$0.0759833\pi$
$434$	−21.6093			−1.03728
$435$		0			0
$436$	11.1927			0.536032
$437$	−2.28501	+	2.86531i	−0.109307	+	0.137067i
$438$		0			0
$439$	−2.20828	−	9.67512i	−0.105396	−	0.461768i	−0.999892	−	0.0146933i	$-0.995323\pi$
$439$	−2.20828	−	9.67512i	−0.105396	−	0.461768i	0.894496	−	0.447075i	$-0.147534\pi$
$440$	−7.36174	+	9.23133i	−0.350957	+	0.440086i
$441$		0			0
$442$	0.0489173	−	0.214321i	0.00232676	−	0.0101942i
$443$	−29.0819	−	14.0051i	−1.38172	−	0.665402i	−0.412355	−	0.911023i	$-0.635294\pi$
$443$	−29.0819	−	14.0051i	−1.38172	−	0.665402i	−0.969366	+	0.245621i	$0.921008\pi$
$444$		0			0
$445$	−4.85935	−	21.2902i	−0.230355	−	1.00925i
$446$	30.9061	−	14.8836i	1.46345	−	0.704759i
$447$		0			0
$448$	3.07726	−	1.48193i	0.145387	−	0.0700146i
$449$	3.09568	+	3.88186i	0.146094	+	0.183196i	0.849494	−	0.527598i	$-0.176907\pi$
$449$	3.09568	+	3.88186i	0.146094	+	0.183196i	−0.703400	+	0.710794i	$0.748336\pi$
$450$		0			0
$451$	23.7162	−	11.4211i	1.11675	−	0.537801i
$452$	−15.9608			−0.750732
$453$		0			0
$454$	−0.753020	−	3.29920i	−0.0353410	−	0.154839i
$455$	0.546229	+	0.263050i	0.0256076	+	0.0123320i
$456$		0			0
$457$	−8.19806	+	35.9181i	−0.383489	+	1.68018i	0.302964	+	0.953002i	$0.402024\pi$
$457$	−8.19806	+	35.9181i	−0.383489	+	1.68018i	−0.686453	+	0.727174i	$0.740833\pi$
$458$	3.88404	+	4.87044i	0.181489	+	0.227581i
$459$		0			0
$460$	−1.59299	−	6.97935i	−0.0742736	−	0.325414i
$461$	−2.78783	+	12.2143i	−0.129842	+	0.568876i	0.867591	+	0.497278i	$0.165667\pi$
$461$	−2.78783	+	12.2143i	−0.129842	+	0.568876i	−0.997434	+	0.0715982i	$0.977190\pi$
$462$		0			0
$463$	20.6396			0.959206			0.479603	−	0.877486i	$-0.340781\pi$
$463$	20.6396			0.959206			0.479603	+	0.877486i	$0.340781\pi$
$464$	22.8593	+	13.5966i	1.06122	+	0.631208i
$465$		0			0
$466$	0.637063	−	0.798852i	0.0295114	−	0.0370061i
$467$	3.59664	−	15.7579i	0.166433	−	0.729189i	−0.820971	−	0.570969i	$-0.806568\pi$
$467$	3.59664	−	15.7579i	0.166433	−	0.729189i	0.987404	−	0.158219i	$-0.0505753\pi$
$468$		0			0
$469$	3.66905	−	4.60085i	0.169421	−	0.212447i
$470$	−16.5918	−	20.8055i	−0.765322	−	0.959684i
$471$		0			0
$472$	7.46950	+	3.59712i	0.343812	+	0.165571i
$473$	14.0438	+	6.76315i	0.645736	+	0.310970i
$474$		0			0
$475$	0.945042	−	0.455108i	0.0433615	−	0.0208818i
$476$	3.72587			0.170775
$477$		0			0
$478$	−10.3584	−	12.9890i	−0.473782	−	0.594103i
$479$	−15.8014	−	19.8143i	−0.721985	−	0.905340i	0.276464	−	0.961024i	$-0.410837\pi$
$479$	−15.8014	−	19.8143i	−0.721985	−	0.905340i	−0.998448	+	0.0556842i	$0.982266\pi$
$480$		0			0
$481$	1.01507			0.0462830
$482$	−21.4475	+	10.3286i	−0.976907	+	0.470453i
$483$		0			0
$484$	−7.90581	−	3.80724i	−0.359355	−	0.173056i
$485$	−21.0374	−	10.1311i	−0.955258	−	0.460028i
$486$		0			0
$487$	−13.9973	−	17.5521i	−0.634279	−	0.795360i	0.355996	−	0.934488i	$-0.384142\pi$
$487$	−13.9973	−	17.5521i	−0.634279	−	0.795360i	−0.990275	+	0.139127i	$0.955570\pi$
$488$	7.69687	−	9.65156i	0.348421	−	0.436906i
$489$		0			0
$490$	−0.202907	+	0.888992i	−0.00916639	+	0.0401606i
$491$	−0.682628	+	0.855989i	−0.0308066	+	0.0386302i	−0.796996	−	0.603984i	$-0.793579\pi$
$491$	−0.682628	+	0.855989i	−0.0308066	+	0.0386302i	0.766190	+	0.642615i	$0.222150\pi$
$492$		0			0
$493$	3.30260	+	4.98180i	0.148742	+	0.224369i
$494$	−0.259061			−0.0116557
$495$		0			0
$496$	4.89589	−	21.4503i	0.219832	−	0.963146i
$497$	3.04072	+	13.3223i	0.136395	+	0.597585i
$498$		0			0
$499$	−7.16786	−	8.98821i	−0.320877	−	0.402368i	0.595065	−	0.803678i	$-0.297126\pi$
$499$	−7.16786	−	8.98821i	−0.320877	−	0.402368i	−0.915942	+	0.401310i	$0.868555\pi$
$500$	−3.29859	+	14.4520i	−0.147517	+	0.646315i
$501$		0			0
$502$	0.630490	+	0.303628i	0.0281401	+	0.0135516i
$503$	−5.67898	−	24.8812i	−0.253213	−	1.10940i	−0.928350	−	0.371707i	$-0.878773\pi$
$503$	−5.67898	−	24.8812i	−0.253213	−	1.10940i	0.675137	−	0.737693i	$-0.264085\pi$
$504$		0			0
$505$	1.66786			0.0742187
$506$	−19.3192	+	9.30362i	−0.858841	+	0.413596i
$507$		0			0
$508$	11.8828	+	14.9006i	0.527216	+	0.661108i
$509$	−35.2923	+	16.9959i	−1.56430	+	0.753329i	−0.997510	−	0.0705302i	$-0.977531\pi$
$509$	−35.2923	+	16.9959i	−1.56430	+	0.753329i	−0.566794	+	0.823859i	$0.691817\pi$
$510$		0			0
$511$	21.7044	−	10.4523i	0.960146	−	0.462382i
$512$	3.81604	+	16.7192i	0.168647	+	0.738890i
$513$		0			0
$514$	−16.9644	−	8.16963i	−0.748268	−	0.360347i
$515$	−6.88793	+	30.1780i	−0.303518	+	1.32980i
$516$		0			0
$517$	−19.0858	+	23.9328i	−0.839390	+	1.05256i
$518$	9.96830	+	43.6740i	0.437982	+	1.91893i
$519$		0			0
$520$	−0.190530	+	0.238916i	−0.00835527	+	0.0104772i
$521$	−20.1142			−0.881220			−0.440610	−	0.897699i	$-0.645238\pi$
$521$	−20.1142			−0.881220			−0.440610	+	0.897699i	$0.645238\pi$
$522$		0			0
$523$	22.2295			0.972029			0.486015	−	0.873951i	$-0.338450\pi$
$523$	22.2295			0.972029			0.486015	+	0.873951i	$0.338450\pi$
$524$	−7.35086	+	9.21768i	−0.321124	+	0.402676i
$525$		0			0
$526$	−4.70679	−	20.6218i	−0.205226	−	0.899153i
$527$	3.08277	−	3.86567i	0.134288	−	0.168391i
$528$		0			0
$529$	3.37100	−	14.7693i	0.146565	−	0.642145i
$530$	−37.8678	−	18.2362i	−1.64487	−	0.792129i
$531$		0			0
$532$	−0.977033	−	4.28066i	−0.0423598	−	0.185590i
$533$	0.613801	−	0.295591i	0.0265867	−	0.0128035i
$534$		0			0
$535$	−9.17994	+	4.42083i	−0.396883	+	0.191129i
$536$	1.84936	+	2.31903i	0.0798803	+	0.100167i
$537$		0			0
$538$	−32.5562	+	15.6782i	−1.40360	+	0.675937i
$539$	1.04892			0.0451801
$540$		0			0
$541$	5.05161	+	22.1325i	0.217185	+	0.951552i	0.959546	+	0.281551i	$0.0908490\pi$
$541$	5.05161	+	22.1325i	0.217185	+	0.951552i	−0.742361	+	0.670000i	$0.766294\pi$
$542$	33.7395	+	16.2481i	1.44924	+	0.697915i
$543$		0			0
$544$	−1.52781	+	6.69378i	−0.0655044	+	0.286993i
$545$	−11.4664	−	14.3785i	−0.491168	−	0.615906i
$546$		0			0
$547$	2.30367	+	10.0930i	0.0984977	+	0.431547i	0.999999	−	0.00122932i	$-0.000391306\pi$
$547$	2.30367	+	10.0930i	0.0984977	+	0.431547i	−0.901502	+	0.432776i	$0.857534\pi$
$548$	5.31618	−	23.2917i	0.227096	−	0.994971i
$549$		0			0
$550$	6.13706			0.261685
$551$	4.85756	−	5.10074i	0.206939	−	0.217299i
$552$		0			0
$553$	14.3550	−	18.0006i	0.610438	−	0.765465i
$554$	3.50269	−	15.3463i	0.148815	−	0.652001i
$555$		0			0
$556$	3.69351	−	4.63152i	0.156640	−	0.196420i
$557$	−1.89948	−	2.38187i	−0.0804834	−	0.100923i	0.739960	−	0.672651i	$-0.234845\pi$
$557$	−1.89948	−	2.38187i	−0.0804834	−	0.100923i	−0.820443	+	0.571728i	$0.806273\pi$
$558$		0			0
$559$	0.363469	+	0.175038i	0.0153731	+	0.00740330i
$560$	−24.5444	−	11.8199i	−1.03719	−	0.499484i
$561$		0			0
$562$	−20.2446	+	9.74928i	−0.853966	+	0.411249i
$563$	−6.08144			−0.256302			−0.128151	−	0.991755i	$-0.540904\pi$
$563$	−6.08144			−0.256302			−0.128151	+	0.991755i	$0.540904\pi$
$564$		0			0
$565$	16.3512	+	20.5037i	0.687898	+	0.862597i
$566$	12.7702	+	16.0134i	0.536773	+	0.673092i
$567$		0			0
$568$	−6.88769			−0.289001
$569$	−31.3245	+	15.0851i	−1.31319	+	0.632400i	−0.953703	−	0.300749i	$-0.902763\pi$
$569$	−31.3245	+	15.0851i	−1.31319	+	0.632400i	−0.359489	+	0.933149i	$0.617049\pi$
$570$		0			0
$571$	−1.53534	−	0.739383i	−0.0642521	−	0.0309422i	0.401482	−	0.915867i	$-0.368495\pi$
$571$	−1.53534	−	0.739383i	−0.0642521	−	0.0309422i	−0.465734	+	0.884925i	$0.654210\pi$
$572$	−0.524459	−	0.252566i	−0.0219287	−	0.0105603i
$573$		0			0
$574$	18.7458	+	23.5065i	0.782434	+	0.981141i
$575$	1.40097	−	1.75676i	0.0584244	−	0.0732619i
$576$		0			0
$577$	5.98374	−	26.2165i	0.249106	−	1.09141i	−0.683341	−	0.730099i	$-0.739474\pi$
$577$	5.98374	−	26.2165i	0.249106	−	1.09141i	0.932447	−	0.361306i	$-0.117669\pi$
$578$	17.7153	−	22.2143i	0.736859	−	0.923992i
$579$		0			0
$580$	1.87382	+	13.6307i	0.0778062	+	0.565983i
$581$	10.8998			0.452199
$582$		0			0
$583$	−10.7584	+	47.1356i	−0.445567	+	1.95216i
$584$	2.70195	+	11.8380i	0.111807	+	0.489860i
$585$		0			0
$586$	7.57606	+	9.50008i	0.312964	+	0.392445i
$587$	2.24794	−	9.84886i	0.0927824	−	0.406506i	−0.907114	−	0.420884i	$-0.861720\pi$
$587$	2.24794	−	9.84886i	0.0927824	−	0.406506i	0.999897	+	0.0143783i	$0.00457692\pi$
$588$		0			0
$589$	−5.24967	−	2.52811i	−0.216309	−	0.104169i
$590$	5.01961	+	21.9924i	0.206654	+	0.905411i
$591$		0			0
$592$	−45.6112			−1.87461
$593$	−29.7681	+	14.3356i	−1.22243	+	0.588691i	−0.929987	−	0.367593i	$-0.880182\pi$
$593$	−29.7681	+	14.3356i	−1.22243	+	0.588691i	−0.292442	+	0.956283i	$0.594468\pi$
$594$		0			0
$595$	−3.81700	−	4.78637i	−0.156482	−	0.196222i
$596$	−4.17241	+	2.00933i	−0.170908	+	0.0823052i
$597$		0			0
$598$	−0.500000	+	0.240787i	−0.0204465	+	0.00984653i
$599$	−1.70267	−	7.45988i	−0.0695692	−	0.304803i	0.928158	−	0.372187i	$-0.121392\pi$
$599$	−1.70267	−	7.45988i	−0.0695692	−	0.304803i	−0.997727	+	0.0673841i	$0.978535\pi$
$600$		0			0
$601$	26.5698	+	12.7953i	1.08380	+	0.521933i	0.888531	−	0.458816i	$-0.151726\pi$
$601$	26.5698	+	12.7953i	1.08380	+	0.521933i	0.195273	+	0.980749i	$0.437441\pi$
$602$	−3.96173	+	17.3575i	−0.161468	+	0.707438i
$603$		0			0
$604$	−14.5022	+	18.1851i	−0.590084	+	0.739942i
$605$	3.20828	+	14.0564i	0.130435	+	0.571474i
$606$		0			0
$607$	9.38703	−	11.7710i	0.381008	−	0.477769i	−0.553939	−	0.832557i	$-0.686876\pi$
$607$	9.38703	−	11.7710i	0.381008	−	0.477769i	0.934946	+	0.354789i	$0.115447\pi$
$608$	8.09113			0.328139
$609$		0			0
$610$	33.5894			1.36000
$611$	−0.493959	+	0.619405i	−0.0199835	+	0.0250585i
$612$		0			0
$613$	3.26122	+	14.2883i	0.131719	+	0.577100i	0.997108	+	0.0759987i	$0.0242145\pi$
$613$	3.26122	+	14.2883i	0.131719	+	0.577100i	−0.865389	+	0.501101i	$0.832928\pi$
$614$	5.16756	−	6.47992i	0.208546	−	0.261508i
$615$		0			0
$616$	−3.45204	+	15.1244i	−0.139087	+	0.609379i
$617$	31.6521	+	15.2429i	1.27427	+	0.613655i	0.943910	−	0.330202i	$-0.107117\pi$
$617$	31.6521	+	15.2429i	1.27427	+	0.613655i	0.330356	+	0.943856i	$0.392831\pi$
$618$		0			0
$619$	8.46668	+	37.0950i	0.340305	+	1.49097i	0.798432	+	0.602085i	$0.205663\pi$
$619$	8.46668	+	37.0950i	0.340305	+	1.49097i	−0.458127	+	0.888887i	$0.651480\pi$
$620$	10.2545	−	4.93831i	0.411831	−	0.198327i
$621$		0			0
$622$	−47.3618	+	22.8082i	−1.89904	+	0.914527i
$623$	−17.8892	−	22.4323i	−0.716715	−	0.898732i
$624$		0			0
$625$	18.3322	−	8.82832i	0.733288	−	0.353133i
$626$	23.4916			0.938912
$627$		0			0
$628$	5.70895	+	25.0125i	0.227812	+	0.998109i
$629$	−9.23490	−	4.44729i	−0.368219	−	0.177325i
$630$		0			0
$631$	5.09269	−	22.3126i	0.202737	−	0.888249i	−0.766524	−	0.642215i	$-0.778016\pi$
$631$	5.09269	−	22.3126i	0.202737	−	0.888249i	0.969261	−	0.246033i	$-0.0791273\pi$
$632$	7.23556	+	9.07311i	0.287815	+	0.360909i
$633$		0			0
$634$	−12.1864	−	53.3921i	−0.483984	−	2.12047i
$635$	6.96830	−	30.5301i	0.276529	−	1.21155i
$636$		0			0
$637$	0.0271471			0.00107561
$638$	38.5550	−	14.5569i	1.52641	−	0.576312i
$639$		0			0
$640$	12.8843	−	16.1564i	0.509298	−	0.638640i
$641$	−6.10358	+	26.7415i	−0.241077	+	1.05623i	0.698962	+	0.715159i	$0.253646\pi$
$641$	−6.10358	+	26.7415i	−0.241077	+	1.05623i	−0.940039	+	0.341068i	$0.889211\pi$
$642$		0			0
$643$	7.56853	−	9.49064i	0.298474	−	0.374274i	−0.609868	−	0.792503i	$-0.708778\pi$
$643$	7.56853	−	9.49064i	0.298474	−	0.374274i	0.908342	+	0.418229i	$0.137349\pi$
$644$	−5.86443	−	7.35376i	−0.231091	−	0.289779i
$645$		0			0
$646$	2.35690	+	1.13502i	0.0927308	+	0.0446568i
$647$	−33.9502	−	16.3495i	−1.33472	−	0.642767i	−0.375867	−	0.926673i	$-0.622655\pi$
$647$	−33.9502	−	16.3495i	−1.33472	−	0.642767i	−0.958852	+	0.283906i	$0.908369\pi$
$648$		0			0
$649$	23.3790	−	11.2587i	0.917705	−	0.441943i
$650$	0.158834			0.00622997
$651$		0			0
$652$	10.0546	+	12.6081i	0.393768	+	0.493770i
$653$	−1.12498	−	1.41068i	−0.0440239	−	0.0552043i	0.759332	−	0.650703i	$-0.225526\pi$
$653$	−1.12498	−	1.41068i	−0.0440239	−	0.0552043i	−0.803356	+	0.595499i	$0.796954\pi$
$654$		0			0
$655$	19.3720			0.756925
$656$	−27.5807	+	13.2822i	−1.07684	+	0.518581i
$657$		0			0
$658$	−31.5013	−	15.1702i	−1.22805	−	0.591396i
$659$	−38.1863	−	18.3895i	−1.48753	−	0.716355i	−0.498888	−	0.866667i	$-0.666258\pi$
$659$	−38.1863	−	18.3895i	−1.48753	−	0.716355i	−0.988639	+	0.150312i	$0.951972\pi$
$660$		0			0
$661$	23.8391	+	29.8932i	0.927232	+	1.16271i	0.986383	+	0.164463i	$0.0525893\pi$
$661$	23.8391	+	29.8932i	0.927232	+	1.16271i	−0.0591509	+	0.998249i	$0.518839\pi$
$662$	20.7458	−	26.0144i	0.806308	−	1.01108i
$663$		0			0
$664$	−1.22252	+	5.35621i	−0.0474430	+	0.207861i
$665$	−4.49814	+	5.64049i	−0.174430	+	0.218729i
$666$		0			0
$667$	4.63437	−	14.3596i	0.179444	−	0.556005i
$668$	20.9554			0.810789
$669$		0			0
$670$	−1.79590	+	7.86834i	−0.0693816	+	0.303980i
$671$	−8.59783	−	37.6696i	−0.331916	−	1.45422i
$672$		0			0
$673$	17.0843	+	21.4230i	0.658550	+	0.825795i	0.993185	−	0.116553i	$-0.0371843\pi$
$673$	17.0843	+	21.4230i	0.658550	+	0.825795i	−0.334635	+	0.942348i	$0.608613\pi$
$674$	−13.0799	+	57.3070i	−0.503821	+	2.20738i
$675$		0			0
$676$	14.5918	+	7.02704i	0.561223	+	0.270271i
$677$	−7.06920	−	30.9722i	−0.271691	−	1.19036i	−0.908016	−	0.418936i	$-0.862403\pi$
$677$	−7.06920	−	30.9722i	−0.271691	−	1.19036i	0.636325	−	0.771421i	$-0.280454\pi$
$678$		0			0
$679$	−30.6786			−1.17734
$680$	2.78017	−	1.33886i	0.106615	−	0.0513429i
$681$		0			0
$682$	−21.2555	−	26.6535i	−0.813914	−	1.02062i
$683$	12.3509	−	5.94786i	0.472592	−	0.227588i	−0.182399	−	0.983225i	$-0.558386\pi$
$683$	12.3509	−	5.94786i	0.472592	−	0.227588i	0.654992	+	0.755636i	$0.272672\pi$
$684$		0			0
$685$	−35.3674	+	17.0320i	−1.35132	+	0.650761i
$686$	−7.28932	−	31.9366i	−0.278308	−	1.21935i
$687$		0			0
$688$	−16.3322	−	7.86517i	−0.622659	−	0.299857i
$689$	−0.278439	+	1.21992i	−0.0106077	+	0.0464752i
$690$		0			0
$691$	−1.38822	+	1.74078i	−0.0528105	+	0.0662223i	−0.807535	−	0.589819i	$-0.799199\pi$
$691$	−1.38822	+	1.74078i	−0.0528105	+	0.0662223i	0.754725	+	0.656042i	$0.227770\pi$
$692$	5.64340	+	24.7253i	0.214530	+	0.939917i
$693$		0			0
$694$	−9.32304	+	11.6907i	−0.353898	+	0.443774i
$695$	−9.73364			−0.369218
$696$		0			0
$697$	−6.87933			−0.260573
$698$	−31.4720	+	39.4646i	−1.19123	+	1.49376i
$699$		0			0
$700$	0.599031	+	2.62453i	0.0226412	+	0.0991978i
$701$	10.4426	−	13.0947i	0.394413	−	0.494579i	−0.544486	−	0.838770i	$-0.683275\pi$
$701$	10.4426	−	13.0947i	0.394413	−	0.494579i	0.938900	+	0.344191i	$0.111847\pi$
$702$		0			0
$703$	−2.68784	+	11.7762i	−0.101374	+	0.444148i
$704$	4.85474	+	2.33792i	0.182970	+	0.0881137i
$705$		0			0
$706$	3.30774	+	14.4922i	0.124488	+	0.545420i
$707$	1.97434	−	0.950794i	0.0742529	−	0.0357583i
$708$		0			0
$709$	−27.0824	+	13.0422i	−1.01710	+	0.489810i	−0.866708	−	0.498816i	$-0.833768\pi$
$709$	−27.0824	+	13.0422i	−1.01710	+	0.489810i	−0.150393	+	0.988626i	$0.548054\pi$
$710$	−11.6848	−	14.6523i	−0.438522	−	0.549889i
$711$		0			0
$712$	13.0298	−	6.27484i	0.488314	−	0.235159i
$713$	−12.4819			−0.467450
$714$		0			0
$715$	0.212832	+	0.932479i	0.00795948	+	0.0348727i
$716$	5.78232	+	2.78462i	0.216096	+	0.104066i
$717$		0			0
$718$	−5.85181	+	25.6385i	−0.218388	+	0.956819i
$719$	25.1719	+	31.5645i	0.938753	+	1.17716i	0.983997	+	0.178183i	$0.0570217\pi$
$719$	25.1719	+	31.5645i	0.938753	+	1.17716i	−0.0452449	+	0.998976i	$0.514407\pi$
$720$		0			0
$721$	9.04988	+	39.6501i	0.337035	+	1.47665i
$722$	−6.93243	+	30.3730i	−0.257998	+	1.13036i
$723$		0			0
$724$	32.8243			1.21991
$725$	−2.97823	+	3.12733i	−0.110609	+	0.116146i
$726$		0			0
$727$	17.4291	−	21.8554i	0.646409	−	0.810571i	−0.345379	−	0.938463i	$-0.612250\pi$
$727$	17.4291	−	21.8554i	0.646409	−	0.810571i	0.991788	+	0.127892i	$0.0408212\pi$
$728$	−0.0893425	+	0.391435i	−0.00331125	+	0.0145075i
$729$		0			0
$730$	−20.5993	+	25.8307i	−0.762415	+	0.956039i
$731$	−2.53989	−	3.18492i	−0.0939413	−	0.117799i
$732$		0			0
$733$	−1.28932	−	0.620906i	−0.0476223	−	0.0229337i	0.409921	−	0.912121i	$-0.365556\pi$
$733$	−1.28932	−	0.620906i	−0.0476223	−	0.0229337i	−0.457543	+	0.889187i	$0.651271\pi$
$734$	47.0490	+	22.6576i	1.73661	+	0.836307i
$735$		0			0
$736$	15.6163	−	7.52039i	0.575623	−	0.277205i
$737$	9.28382			0.341974
$738$		0			0
$739$	−20.9483	−	26.2684i	−0.770596	−	0.966297i	0.229379	−	0.973337i	$-0.426331\pi$
$739$	−20.9483	−	26.2684i	−0.770596	−	0.966297i	−0.999975	+	0.00703985i	$0.997759\pi$
$740$	−14.7111	−	18.4471i	−0.540791	−	0.678130i
$741$		0			0
$742$	−55.2223			−2.02728
$743$	−23.2150	+	11.1798i	−0.851677	+	0.410146i	−0.808200	−	0.588908i	$-0.799558\pi$
$743$	−23.2150	+	11.1798i	−0.851677	+	0.410146i	−0.0434775	+	0.999054i	$0.513844\pi$
$744$		0			0
$745$	6.85570	+	3.30153i	0.251173	+	0.120959i
$746$	−34.8630	−	16.7891i	−1.27642	−	0.614694i
$747$		0			0
$748$	3.66487	+	4.59561i	0.134001	+	0.168032i
$749$	−8.34667	+	10.4664i	−0.304981	+	0.382434i
$750$		0			0
$751$	5.88955	−	25.8038i	0.214913	−	0.941594i	−0.746262	−	0.665653i	$-0.768153\pi$
$751$	5.88955	−	25.8038i	0.214913	−	0.941594i	0.961174	−	0.275942i	$-0.0889897\pi$
$752$	22.1957	−	27.8325i	0.809393	−	1.01495i
$753$		0			0
$754$	0.997844	−	0.376747i	0.0363393	−	0.0137203i
$755$	38.2180			1.39090
$756$		0			0
$757$	−4.67187	+	20.4688i	−0.169802	+	0.743952i	0.816275	+	0.577664i	$0.196035\pi$
$757$	−4.67187	+	20.4688i	−0.169802	+	0.743952i	−0.986077	+	0.166288i	$0.946822\pi$
$758$	9.11572	+	39.9386i	0.331098	+	1.45063i
$759$		0			0
$760$	−2.26726	−	2.84305i	−0.0822421	−	0.103128i
$761$	−7.85019	+	34.3939i	−0.284569	+	1.24678i	0.607295	+	0.794476i	$0.292255\pi$
$761$	−7.85019	+	34.3939i	−0.284569	+	1.24678i	−0.891864	+	0.452303i	$0.850603\pi$
$762$		0			0
$763$	−21.7702	−	10.4840i	−0.788136	−	0.379546i
$764$	5.46615	+	23.9488i	0.197758	+	0.866436i
$765$		0			0
$766$	6.24267			0.225557
$767$	0.605072	−	0.291387i	0.0218479	−	0.0105214i
$768$		0			0
$769$	−15.7860	−	19.7950i	−0.569257	−	0.713825i	0.410982	−	0.911643i	$-0.365186\pi$
$769$	−15.7860	−	19.7950i	−0.569257	−	0.713825i	−0.980239	+	0.197818i	$0.936614\pi$
$770$	−38.0306	+	18.3146i	−1.37053	+	0.660011i
$771$		0			0
$772$	−9.11476	+	4.38944i	−0.328047	+	0.157979i
$773$	−5.06949	−	22.2109i	−0.182337	−	0.798870i	−0.980514	−	0.196448i	$-0.937059\pi$
$773$	−5.06949	−	22.2109i	−0.182337	−	0.798870i	0.798177	−	0.602423i	$-0.205798\pi$
$774$		0			0
$775$	3.21864	+	1.55001i	0.115617	+	0.0556781i
$776$	3.44092	−	15.0757i	0.123522	−	0.541185i
$777$		0			0
$778$	−9.54556	+	11.9698i	−0.342225	+	0.429137i
$779$	1.80396	+	7.90367i	0.0646337	+	0.283179i
$780$		0			0
$781$	−13.4412	+	16.8547i	−0.480962	+	0.603108i
$782$	5.60388			0.200394
$783$		0			0
$784$	−1.21983			−0.0435654
$785$	26.2833	−	32.9582i	0.938091	−	1.17633i
$786$		0			0
$787$	3.15010	+	13.8015i	0.112289	+	0.491971i	0.999530	+	0.0306638i	$0.00976213\pi$
$787$	3.15010	+	13.8015i	0.112289	+	0.491971i	−0.887241	+	0.461307i	$0.847381\pi$
$788$	−8.03116	+	10.0708i	−0.286098	+	0.358756i
$789$		0			0
$790$	−7.02638	+	30.7846i	−0.249987	+	1.09527i
$791$	31.0444	+	14.9502i	1.10381	+	0.531567i
$792$		0			0
$793$	−0.222521	−	0.974928i	−0.00790195	−	0.0346207i
$794$	45.2928	−	21.8119i	1.60738	−	0.774075i
$795$		0			0
$796$	13.6039	−	6.55128i	0.482177	−	0.232204i
$797$	−1.79523	−	2.25115i	−0.0635904	−	0.0797399i	0.749019	−	0.662548i	$-0.230525\pi$
$797$	−1.79523	−	2.25115i	−0.0635904	−	0.0797399i	−0.812609	+	0.582809i	$0.801954\pi$
$798$		0			0
$799$	7.20775	−	3.47107i	0.254992	−	0.122798i
$800$	−4.96077			−0.175390
$801$		0			0
$802$	7.43200	+	32.5617i	0.262433	+	1.14979i
$803$	34.2412	+	16.4897i	1.20835	+	0.581909i
$804$		0			0
$805$	−3.43900	+	15.0672i	−0.121209	+	0.531051i
$806$	−0.550114	−	0.689821i	−0.0193769	−	0.0242979i
$807$		0			0
$808$	0.245783	+	1.07685i	0.00864662	+	0.0378833i
$809$	0.254749	−	1.11613i	0.00895651	−	0.0392410i	−0.970252	−	0.242096i	$-0.922165\pi$
$809$	0.254749	−	1.11613i	0.00895651	−	0.0392410i	0.979209	+	0.202855i	$0.0650221\pi$
$810$		0			0
$811$	40.1021			1.40818			0.704088	−	0.710112i	$-0.251356\pi$
$811$	40.1021			1.40818			0.704088	+	0.710112i	$0.251356\pi$
$812$	9.98858	+	15.0672i	0.350531	+	0.528757i
$813$		0			0
$814$	−44.0637	+	55.2542i	−1.54443	+	1.93666i
$815$	5.89618	−	25.8329i	0.206534	−	0.904886i
$816$		0			0
$817$	−2.99313	+	3.75327i	−0.104716	+	0.131310i
$818$	−39.9110	−	50.0468i	−1.39545	−	1.74984i
$819$		0			0
$820$	−14.2676	−	6.87089i	−0.498245	−	0.239942i
$821$	−31.4654	−	15.1529i	−1.09815	−	0.528841i	−0.205073	−	0.978747i	$-0.565743\pi$
$821$	−31.4654	−	15.1529i	−1.09815	−	0.528841i	−0.893076	+	0.449906i	$0.851458\pi$
$822$		0			0
$823$	40.4834	−	19.4958i	1.41116	−	0.679580i	0.435770	−	0.900058i	$-0.356476\pi$
$823$	40.4834	−	19.4958i	1.41116	−	0.679580i	0.975392	+	0.220479i	$0.0707619\pi$
$824$	−20.4993			−0.714128
$825$		0			0
$826$	18.4792	+	23.1722i	0.642973	+	0.806263i
$827$	5.62751	+	7.05667i	0.195688	+	0.245384i	0.869988	−	0.493072i	$-0.164126\pi$
$827$	5.62751	+	7.05667i	0.195688	+	0.245384i	−0.674301	+	0.738457i	$0.735555\pi$
$828$		0			0
$829$	41.5362			1.44261			0.721305	−	0.692617i	$-0.243542\pi$
$829$	41.5362			1.44261			0.721305	+	0.692617i	$0.243542\pi$
$830$	−13.4683	+	6.48599i	−0.467492	+	0.225132i
$831$		0			0
$832$	0.125646	+	0.0605078i	0.00435598	+	0.00209773i
$833$	−0.246980	−	0.118939i	−0.00855734	−	0.00412100i
$834$		0			0
$835$	−21.4679	−	26.9199i	−0.742929	−	0.931603i
$836$	4.31886	−	5.41568i	0.149371	−	0.187305i
$837$		0			0
$838$	−0.367354	+	1.60948i	−0.0126900	+	0.0555987i
$839$	−30.5604	+	38.3215i	−1.05506	+	1.32301i	−0.110788	+	0.993844i	$0.535338\pi$
$839$	−30.5604	+	38.3215i	−1.05506	+	1.32301i	−0.944274	+	0.329162i	$0.893234\pi$
$840$		0			0
$841$	−11.2923	+	26.7111i	−0.389390	+	0.921073i
$842$	33.3502			1.14932
$843$		0			0
$844$	3.82908	−	16.7763i	0.131803	−	0.577465i
$845$	−5.92154	−	25.9440i	−0.203707	−	0.892500i
$846$		0			0
$847$	11.8110	+	14.8105i	0.405829	+	0.508894i
$848$	12.5114	−	54.8161i	0.429644	−	1.88239i
$849$		0			0
$850$	−1.44504	−	0.695895i	−0.0495645	−	0.0238690i
$851$	5.75786	+	25.2269i	0.197377	+	0.864765i
$852$		0			0
$853$	−57.0974			−1.95498			−0.977488	−	0.210990i	$-0.932331\pi$
$853$	−57.0974			−1.95498			−0.977488	+	0.210990i	$0.932331\pi$
$854$	39.7618	−	19.1483i	1.36062	−	0.655241i
$855$		0			0
$856$	−4.20709	−	5.27552i	−0.143795	−	0.180314i
$857$	50.5250	−	24.3316i	1.72590	−	0.831151i	0.738243	−	0.674534i	$-0.235656\pi$
$857$	50.5250	−	24.3316i	1.72590	−	0.831151i	0.987659	−	0.156616i	$-0.0500587\pi$
$858$		0			0
$859$	−5.70506	+	2.74741i	−0.194654	+	0.0937405i	−0.528672	−	0.848826i	$-0.677310\pi$
$859$	−5.70506	+	2.74741i	−0.194654	+	0.0937405i	0.334018	+	0.942567i	$0.391595\pi$
$860$	−2.08665	−	9.14223i	−0.0711543	−	0.311747i
$861$		0			0
$862$	−51.7165	−	24.9054i	−1.76147	−	0.848280i
$863$	12.6667	−	55.4963i	0.431178	−	1.88912i	−0.0258555	−	0.999666i	$-0.508231\pi$
$863$	12.6667	−	55.4963i	0.431178	−	1.88912i	0.457034	−	0.889449i	$-0.348912\pi$
$864$		0			0
$865$	25.9815	−	32.5798i	0.883398	−	1.10775i
$866$	7.02446	+	30.7762i	0.238701	+	1.04582i
$867$		0			0
$868$	9.32371	−	11.6916i	0.316467	−	0.396837i
$869$	36.3226			1.23216
$870$		0			0
$871$	0.240275			0.00814140
$872$	7.59365	−	9.52214i	0.257154	−	0.322460i
$873$		0			0
$874$	−1.46950	−	6.43830i	−0.0497066	−	0.217779i
$875$	19.9529	−	25.0201i	0.674530	−	0.845834i
$876$		0			0
$877$	−9.94414	+	43.5681i	−0.335790	+	1.47119i	0.471936	+	0.881633i	$0.343555\pi$
$877$	−9.94414	+	43.5681i	−0.335790	+	1.47119i	−0.807726	+	0.589558i	$0.799302\pi$
$878$	16.1114	+	7.75885i	0.543734	+	0.261848i
$879$		0			0
$880$	−9.56345	−	41.9002i	−0.322384	−	1.41246i
$881$	−5.57218	+	2.68342i	−0.187731	+	0.0904067i	−0.525388	−	0.850863i	$-0.676080\pi$
$881$	−5.57218	+	2.68342i	−0.187731	+	0.0904067i	0.337657	+	0.941269i	$0.390366\pi$
$882$		0			0
$883$	−33.5100	+	16.1376i	−1.12770	+	0.543072i	−0.902263	−	0.431186i	$-0.858095\pi$
$883$	−33.5100	+	16.1376i	−1.12770	+	0.543072i	−0.225437	+	0.974258i	$0.572381\pi$
$884$	0.0948508	+	0.118939i	0.00319018	+	0.00400036i
$885$		0			0
$886$	52.4037	−	25.2363i	1.76054	−	0.847830i
$887$	−58.1651			−1.95299			−0.976496	−	0.215536i	$-0.930850\pi$
$887$	−58.1651			−1.95299			−0.976496	+	0.215536i	$0.930850\pi$
$888$		0			0
$889$	−9.15548	−	40.1128i	−0.307065	−	1.34534i
$890$	35.4533	+	17.0734i	1.18840	+	0.572302i
$891$		0			0
$892$	−5.28232	+	23.1434i	−0.176865	+	0.774897i
$893$	−5.87800	−	7.37078i	−0.196700	−	0.246654i
$894$		0			0
$895$	−2.34654	−	10.2809i	−0.0784363	−	0.343652i
$896$	6.04168	−	26.4703i	0.201838	−	0.884312i
$897$		0			0
$898$	−8.94677			−0.298558
$899$	23.8971	+	2.10321i	0.797012	+	0.0701459i
$900$		0			0
$901$	7.87800	−	9.87870i	0.262454	−	0.329107i
$902$	−10.5547	+	46.2433i	−0.351434	+	1.53973i
$903$		0			0
$904$	−10.8286	+	13.5786i	−0.360152	+	0.451617i
$905$	−33.6271	−	42.1671i	−1.11780	−	1.40168i
$906$		0			0
$907$	39.8935	+	19.2117i	1.32464	+	0.637914i	0.956466	−	0.291843i	$-0.0942683\pi$
$907$	39.8935	+	19.2117i	1.32464	+	0.637914i	0.368175	+	0.929756i	$0.379983\pi$
$908$	2.10992	+	1.01608i	0.0700200	+	0.0337199i
$909$		0			0
$910$	−0.984271	+	0.474000i	−0.0326283	+	0.0157129i
$911$	50.6886			1.67939			0.839694	−	0.543061i	$-0.182735\pi$
$911$	50.6886			1.67939			0.839694	+	0.543061i	$0.182735\pi$
$912$		0			0
$913$	10.7213	+	13.4441i	0.354824	+	0.444935i
$914$	−41.3913	−	51.9031i	−1.36910	−	1.71680i
$915$		0			0
$916$	−4.31096			−0.142438
$917$	22.9318	−	11.0434i	0.757274	−	0.364684i
$918$		0			0
$919$	11.8029	+	5.68398i	0.389342	+	0.187497i	0.618305	−	0.785938i	$-0.287819\pi$
$919$	11.8029	+	5.68398i	0.389342	+	0.187497i	−0.228964	+	0.973435i	$0.573534\pi$
$920$	−7.01842	−	3.37989i	−0.231390	−	0.111432i
$921$		0			0
$922$	−14.0755	−	17.6502i	−0.463553	−	0.581277i
$923$	−0.347871	+	0.436217i	−0.0114503	+	0.0143582i
$924$		0			0
$925$	1.64795	−	7.22013i	0.0541842	−	0.237397i
$926$	−23.1884	+	29.0774i	−0.762019	+	0.955542i
$927$		0			0
$928$	−31.1652	+	11.7668i	−1.02305	+	0.386263i
$929$	−8.04759			−0.264033			−0.132016	−	0.991248i	$-0.542145\pi$
$929$	−8.04759			−0.264033			−0.132016	+	0.991248i	$0.542145\pi$
$930$		0			0
$931$	−0.0718841	+	0.314945i	−0.00235590	+	0.0103219i
$932$	0.157342	+	0.689359i	0.00515390	+	0.0225807i
$933$		0			0
$934$	18.1591	+	22.7708i	0.594185	+	0.745084i
$935$	2.14914	−	9.41602i	0.0702846	−	0.307937i
$936$		0			0
$937$	−2.46585	−	1.18749i	−0.0805559	−	0.0387937i	0.393172	−	0.919465i	$-0.371378\pi$
$937$	−2.46585	−	1.18749i	−0.0805559	−	0.0387937i	−0.473728	+	0.880671i	$0.657092\pi$
$938$	2.35958	+	10.3380i	0.0770432	+	0.337548i
$939$		0			0
$940$	18.4155			0.600647
$941$	38.9816	−	18.7726i	1.27077	−	0.611968i	0.327765	−	0.944759i	$-0.393705\pi$
$941$	38.9816	−	18.7726i	1.27077	−	0.611968i	0.943001	+	0.332791i	$0.107990\pi$
$942$		0			0
$943$	10.8279	+	13.5777i	0.352605	+	0.442152i
$944$	−27.1884	+	13.0933i	−0.884908	+	0.426149i
$945$		0			0
$946$	−25.3061	+	12.1868i	−0.822773	+	0.396227i
$947$	2.63946	+	11.5642i	0.0857708	+	0.375786i	0.999536	−	0.0304561i	$-0.00969596\pi$
$947$	2.63946	+	11.5642i	0.0857708	+	0.375786i	−0.913765	+	0.406243i	$0.866839\pi$
$948$		0			0
$949$	0.886199	+	0.426771i	0.0287672	+	0.0138536i
$950$	−0.420583	+	1.84270i	−0.0136455	+	0.0597849i
$951$		0			0
$952$	2.52781	−	3.16977i	0.0819268	−	0.102733i
$953$	2.81647	+	12.3398i	0.0912344	+	0.399724i	0.999839	−	0.0179328i	$-0.00570851\pi$
$953$	2.81647	+	12.3398i	0.0912344	+	0.399724i	−0.908605	+	0.417657i	$0.862851\pi$
$954$		0			0
$955$	25.1655	−	31.5565i	0.814335	−	1.02114i
$956$	11.4969			0.371838
$957$		0			0
$958$	45.6674			1.47545
$959$	−32.1571	+	40.3237i	−1.03841	+	1.30212i
$960$		0			0
$961$	2.48230	+	10.8757i	0.0800743	+	0.350829i
$962$	−1.14042	+	1.43004i	−0.0367685	+	0.0461062i
$963$		0			0
$964$	3.66570	−	16.0605i	0.118064	−	0.517274i
$965$	14.9765	+	7.21230i	0.482111	+	0.232172i
$966$		0			0
$967$	−2.42357	−	10.6183i	−0.0779367	−	0.341463i	0.920894	−	0.389814i	$-0.127461\pi$
$967$	−2.42357	−	10.6183i	−0.0779367	−	0.341463i	−0.998830	+	0.0483508i	$0.984603\pi$
$968$	−8.60268	+	4.14283i	−0.276501	+	0.133156i
$969$		0			0
$970$	37.9080	−	18.2555i	1.21715	−	0.586150i
$971$	6.70626	+	8.40938i	0.215214	+	0.269870i	0.877706	−	0.479199i	$-0.159073\pi$
$971$	6.70626	+	8.40938i	0.215214	+	0.269870i	−0.662492	+	0.749069i	$0.730501\pi$
$972$		0			0
$973$	−11.5223	+	5.54885i	−0.369388	+	0.177888i
$974$	40.4534			1.29621
$975$		0			0
$976$	9.99880	+	43.8076i	0.320054	+	1.40225i
$977$	37.5388	+	18.0777i	1.20097	+	0.578357i	0.923952	−	0.382507i	$-0.124939\pi$
$977$	37.5388	+	18.0777i	1.20097	+	0.578357i	0.277019	+	0.960865i	$0.410654\pi$
$978$		0			0
$979$	10.0724	−	44.1301i	0.321916	−	1.41041i
$980$	−0.393436	−	0.493353i	−0.0125679	−	0.0157596i
$981$		0			0
$982$	−0.439001	−	1.92339i	−0.0140091	−	0.0613778i
$983$	−5.82616	+	25.5261i	−0.185826	+	0.814155i	0.792961	+	0.609273i	$0.208538\pi$
$983$	−5.82616	+	25.5261i	−0.185826	+	0.814155i	−0.978787	+	0.204883i	$0.934319\pi$
$984$		0			0
$985$	21.1648			0.674367
$986$	−10.7289	−	0.944258i	−0.341676	−	0.0300713i
$987$		0			0
$988$	0.111777	−	0.140164i	0.00355609	−	0.00445920i
$989$	−2.28836	+	10.0260i	−0.0727657	+	0.318808i
$990$		0			0
$991$	−28.4983	+	35.7357i	−0.905277	+	1.13518i	0.0850424	+	0.996377i	$0.472897\pi$
$991$	−28.4983	+	35.7357i	−0.905277	+	1.13518i	−0.990320	+	0.138805i	$0.955674\pi$
$992$	17.1814	+	21.5448i	0.545511	+	0.684049i
$993$		0			0
$994$	−22.1848	−	10.6836i	−0.703659	−	0.338864i
$995$	−22.3526	−	10.7644i	−0.708625	−	0.341256i
$996$		0			0
$997$	−14.4753	+	6.97094i	−0.458437	+	0.220772i	−0.648826	−	0.760937i	$-0.724740\pi$
$997$	−14.4753	+	6.97094i	−0.458437	+	0.220772i	0.190388	+	0.981709i	$0.439025\pi$
$998$	20.7157			0.655744
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.k.a.487.1	yes	6
3.2	odd	2		783.2.k.b.487.1	yes	6
29.24	even	7	inner	783.2.k.a.82.1	✓	6
87.53	odd	14		783.2.k.b.82.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.k.a.82.1	✓	6	29.24	even	7	inner
783.2.k.a.487.1	yes	6	1.1	even	1	trivial
783.2.k.b.82.1	yes	6	87.53	odd	14
783.2.k.b.487.1	yes	6	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12349 + 1.40881i) q^{2} +(-0.277479 - 1.21572i) q^{4} +(-1.27748 + 1.60191i) q^{5} +(-0.599031 + 2.62453i) q^{7} +(-1.22252 - 0.588735i) q^{8} +(-0.821552 - 3.59945i) q^{10} +(-3.82640 + 1.84270i) q^{11} +(-0.0990311 + 0.0476909i) q^{13} +(-3.02446 - 3.79255i) q^{14} +(4.44989 - 2.14295i) q^{16} +1.10992 q^{17} +(-0.291053 - 1.27518i) q^{19} +(2.30194 + 1.10855i) q^{20} +(1.70291 - 7.46092i) q^{22} +(-1.74698 - 2.19064i) q^{23} +(0.178448 + 0.781831i) q^{25} +(0.0440730 - 0.193096i) q^{26} +3.35690 q^{28} +(2.97554 + 4.48845i) q^{29} +(2.77748 - 3.48285i) q^{31} +(-1.37651 + 6.03089i) q^{32} +(-1.24698 + 1.56366i) q^{34} +(-3.43900 - 4.31237i) q^{35} +(-8.32036 - 4.00687i) q^{37} +(2.12349 + 1.02262i) q^{38} +(2.50484 - 1.20627i) q^{40} -6.19806 q^{41} +(-2.28836 - 2.86952i) q^{43} +(3.30194 + 4.14050i) q^{44} +5.04892 q^{46} +(6.49396 - 3.12733i) q^{47} +(-0.222521 - 0.107160i) q^{49} +(-1.30194 - 0.626980i) q^{50} +(0.0854576 + 0.107160i) q^{52} +(7.09783 - 8.90040i) q^{53} +(1.93631 - 8.48354i) q^{55} +(2.27748 - 2.85587i) q^{56} +(-9.66637 - 0.850747i) q^{58} -6.10992 q^{59} +(-2.02446 + 8.86973i) q^{61} +(1.78621 + 7.82589i) q^{62} +(-0.791053 - 0.991949i) q^{64} +(0.0501138 - 0.219563i) q^{65} +(-1.96950 - 0.948461i) q^{67} +(-0.307979 - 1.34934i) q^{68} +9.93900 q^{70} +(4.57338 - 2.20242i) q^{71} +(-5.57942 - 6.99637i) q^{73} +(14.9928 - 7.22013i) q^{74} +(-1.46950 + 0.707674i) q^{76} +(-2.54407 - 11.1463i) q^{77} +(-7.70560 - 3.71082i) q^{79} +(-2.25182 + 9.86589i) q^{80} +(6.96346 - 8.73190i) q^{82} +(-0.900969 - 3.94740i) q^{83} +(-1.41789 + 1.77798i) q^{85} +6.61356 q^{86} +5.76271 q^{88} +(-6.64526 + 8.33289i) q^{89} +(-0.0658433 - 0.288478i) q^{91} +(-2.17845 + 2.73169i) q^{92} +(-2.89008 + 12.6623i) q^{94} +(2.41454 + 1.16278i) q^{95} +(2.53588 + 11.1104i) q^{97} +(0.400969 - 0.193096i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 8 q^{7} - 7 q^{8} - 9 q^{10} - 5 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} + 8 q^{17} + 4 q^{19} + 5 q^{20} - 3 q^{22} - q^{23} - 3 q^{25} + 4 q^{26} + 12 q^{28} + 27 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 - 8 * q^5 - 8 * q^7 - 7 * q^8 - 9 * q^10 - 5 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 + 8 * q^17 + 4 * q^19 + 5 * q^20 - 3 * q^22 - q^23 - 3 * q^25 + 4 * q^26 + 12 * q^28 + 27 * q^29 + 17 * q^31 - 13 * q^32 + 2 * q^34 - q^35 - 13 * q^37 + 8 * q^38 - 7 * q^40 - 46 * q^41 - 11 * q^43 + 11 * q^44 + 12 * q^46 + 20 * q^47 - q^49 + q^50 + 11 * q^52 + 6 * q^53 - 5 * q^55 + 14 * q^56 - 16 * q^58 - 38 * q^59 - 3 * q^61 + 27 * q^62 + q^64 + 23 * q^65 - 2 * q^67 - 12 * q^68 + 40 * q^70 - 25 * q^73 + 30 * q^74 + q^76 - 19 * q^77 - 30 * q^79 + 18 * q^80 + 13 * q^82 - q^83 - 20 * q^85 - 22 * q^86 - 29 * q^89 + 2 * q^91 - 9 * q^92 - 16 * q^94 + 4 * q^95 + 19 * q^97 - 2 * q^98

Introduction

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