LMFDB - Embedded newform 1170.2.bj.c.829.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.2
Root			$1.75374 + 1.62986i$ of defining polynomial
Character	$\chi$	$=$	1170.829
Dual form			1170.2.bj.c.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(-0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(-0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(-0.809179 + 2.08452i) q^{10} +(1.14057 - 0.658509i) q^{11} +(2.41225 + 2.67975i) q^{13} +1.52767 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.35904 - 0.784645i) q^{17} +(-4.18063 - 2.41369i) q^{19} +(2.20984 - 0.341491i) q^{20} +(-1.14057 - 0.658509i) q^{22} +(-7.31172 + 4.22143i) q^{23} +(-1.07631 + 4.88278i) q^{25} +(1.11461 - 3.42894i) q^{26} +(-0.763837 - 1.32301i) q^{28} +(2.21438 + 3.83543i) q^{29} -1.62745i q^{31} +(-0.500000 + 0.866025i) q^{32} +1.56929i q^{34} +(3.37591 - 0.521687i) q^{35} +(1.40148 + 2.42743i) q^{37} +4.82738i q^{38} +(-1.40066 - 1.74303i) q^{40} +(-1.35904 + 0.784645i) q^{41} +(4.58006 + 2.64430i) q^{43} +1.31702i q^{44} +(7.31172 + 4.22143i) q^{46} +4.94552 q^{47} +(2.33310 + 4.04106i) q^{49} +(4.76677 - 1.50928i) q^{50} +(-3.52686 + 0.749192i) q^{52} +13.9161i q^{53} +(-2.74535 - 1.06570i) q^{55} +(-0.763837 + 1.32301i) q^{56} +(2.21438 - 3.83543i) q^{58} +(9.07005 + 5.23660i) q^{59} +(2.49134 - 4.31513i) q^{61} +(-1.40941 + 0.813725i) q^{62} +1.00000 q^{64} +(1.29215 - 7.95804i) q^{65} +(-1.38628 - 2.40112i) q^{67} +(1.35904 - 0.784645i) q^{68} +(-2.13975 - 2.66278i) q^{70} +(12.8513 + 7.41968i) q^{71} -5.98944 q^{73} +(1.40148 - 2.42743i) q^{74} +(4.18063 - 2.41369i) q^{76} +2.01198i q^{77} +4.87632 q^{79} +(-0.809179 + 2.08452i) q^{80} +(1.35904 + 0.784645i) q^{82} -6.39020 q^{83} +(0.535898 + 3.46788i) q^{85} -5.28860i q^{86} +(1.14057 - 0.658509i) q^{88} +(-15.9738 + 9.22251i) q^{89} +(-5.38789 + 1.14452i) q^{91} -8.44285i q^{92} +(-2.47276 - 4.28295i) q^{94} +(1.64851 + 10.6677i) q^{95} +(-0.963028 + 1.66801i) q^{97} +(2.33310 - 4.04106i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.40066	−	1.74303i	−0.626394	−	0.779507i
$5$	−1.40066	−	1.74303i	−0.626394	−	0.779507i
$6$		0			0
$7$	−0.763837	+	1.32301i	−0.288703	+	0.500049i	−0.973501	−	0.228685i	$-0.926557\pi$
$7$	−0.763837	+	1.32301i	−0.288703	+	0.500049i	0.684797	+	0.728734i	$0.259891\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.809179	+	2.08452i	−0.255885	+	0.659184i
$11$	1.14057	−	0.658509i	0.343895	−	0.198548i	−0.318098	−	0.948058i	$-0.603044\pi$
$11$	1.14057	−	0.658509i	0.343895	−	0.198548i	0.661993	+	0.749510i	$0.269711\pi$
$12$		0			0
$13$	2.41225	+	2.67975i	0.669037	+	0.743229i
$13$	2.41225	+	2.67975i	0.669037	+	0.743229i
$14$	1.52767			0.408288
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.35904	−	0.784645i	−0.329617	−	0.190304i	0.326054	−	0.945351i	$-0.394281\pi$
$17$	−1.35904	−	0.784645i	−0.329617	−	0.190304i	−0.655671	+	0.755047i	$0.727614\pi$
$18$		0			0
$19$	−4.18063	−	2.41369i	−0.959103	−	0.553738i	−0.0632058	−	0.998001i	$-0.520132\pi$
$19$	−4.18063	−	2.41369i	−0.959103	−	0.553738i	−0.895897	+	0.444262i	$0.853466\pi$
$20$	2.20984	−	0.341491i	0.494135	−	0.0763597i
$21$		0			0
$22$	−1.14057	−	0.658509i	−0.243171	−	0.140395i
$23$	−7.31172	+	4.22143i	−1.52460	+	0.880228i	−0.525025	+	0.851087i	$0.675944\pi$
$23$	−7.31172	+	4.22143i	−1.52460	+	0.880228i	−0.999575	+	0.0291412i	$0.990723\pi$
$24$		0			0
$25$	−1.07631	+	4.88278i	−0.215262	+	0.976556i
$26$	1.11461	−	3.42894i	0.218593	−	0.672471i
$27$		0			0
$28$	−0.763837	−	1.32301i	−0.144352	−	0.250025i
$29$	2.21438	+	3.83543i	0.411201	+	0.712221i	0.995021	−	0.0996620i	$-0.0317762\pi$
$29$	2.21438	+	3.83543i	0.411201	+	0.712221i	−0.583821	+	0.811883i	$0.698443\pi$
$30$		0			0
$31$		−	1.62745i		−	0.292299i	−0.989263	−	0.146149i	$-0.953312\pi$
$31$		−	1.62745i		−	0.292299i	0.989263	−	0.146149i	$-0.0466880\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			1.56929i			0.269131i
$35$	3.37591	−	0.521687i	0.570634	−	0.0881813i
$36$		0			0
$37$	1.40148	+	2.42743i	0.230402	+	0.399067i	0.957926	−	0.287014i	$-0.0926627\pi$
$37$	1.40148	+	2.42743i	0.230402	+	0.399067i	−0.727525	+	0.686081i	$0.759329\pi$
$38$			4.82738i			0.783104i
$39$		0			0
$40$	−1.40066	−	1.74303i	−0.221464	−	0.275597i
$41$	−1.35904	+	0.784645i	−0.212247	+	0.122541i	−0.602355	−	0.798228i	$-0.705771\pi$
$41$	−1.35904	+	0.784645i	−0.212247	+	0.122541i	0.390108	+	0.920769i	$0.372438\pi$
$42$		0			0
$43$	4.58006	+	2.64430i	0.698452	+	0.403252i	0.806771	−	0.590865i	$-0.201213\pi$
$43$	4.58006	+	2.64430i	0.698452	+	0.403252i	−0.108318	+	0.994116i	$0.534547\pi$
$44$			1.31702i			0.198548i
$45$		0			0
$46$	7.31172	+	4.22143i	1.07805	+	0.622415i
$47$	4.94552			0.721378			0.360689	−	0.932686i	$-0.382542\pi$
$47$	4.94552			0.721378			0.360689	+	0.932686i	$0.382542\pi$
$48$		0			0
$49$	2.33310	+	4.04106i	0.333301	+	0.577294i
$50$	4.76677	−	1.50928i	0.674123	−	0.213444i
$51$		0			0
$52$	−3.52686	+	0.749192i	−0.489087	+	0.103894i
$53$			13.9161i			1.91152i	0.294148	+	0.955760i	$0.404964\pi$
$53$			13.9161i			1.91152i	−0.294148	+	0.955760i	$0.595036\pi$
$54$		0			0
$55$	−2.74535	−	1.06570i	−0.370183	−	0.143699i
$56$	−0.763837	+	1.32301i	−0.102072	+	0.176794i
$57$		0			0
$58$	2.21438	−	3.83543i	0.290763	−	0.503616i
$59$	9.07005	+	5.23660i	1.18082	+	0.681747i	0.956204	−	0.292700i	$-0.0945539\pi$
$59$	9.07005	+	5.23660i	1.18082	+	0.681747i	0.224616	+	0.974447i	$0.427887\pi$
$60$		0			0
$61$	2.49134	−	4.31513i	0.318984	−	0.552496i	−0.661293	−	0.750128i	$-0.729992\pi$
$61$	2.49134	−	4.31513i	0.318984	−	0.552496i	0.980276	+	0.197632i	$0.0633252\pi$
$62$	−1.40941	+	0.813725i	−0.178996	+	0.103343i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.29215	−	7.95804i	0.160272	−	0.987073i
$66$		0			0
$67$	−1.38628	−	2.40112i	−0.169362	−	0.293343i	0.768834	−	0.639448i	$-0.220837\pi$
$67$	−1.38628	−	2.40112i	−0.169362	−	0.293343i	−0.938196	+	0.346105i	$0.887504\pi$
$68$	1.35904	−	0.784645i	0.164808	−	0.0951521i
$69$		0			0
$70$	−2.13975	−	2.66278i	−0.255749	−	0.318264i
$71$	12.8513	+	7.41968i	1.52516	+	0.880554i	0.999555	+	0.0298269i	$0.00949560\pi$
$71$	12.8513	+	7.41968i	1.52516	+	0.880554i	0.525608	+	0.850727i	$0.323838\pi$
$72$		0			0
$73$	−5.98944			−0.701011			−0.350505	−	0.936561i	$-0.613990\pi$
$73$	−5.98944			−0.701011			−0.350505	+	0.936561i	$0.613990\pi$
$74$	1.40148	−	2.42743i	0.162919	−	0.282183i
$75$		0			0
$76$	4.18063	−	2.41369i	0.479551	−	0.276869i
$77$			2.01198i			0.229286i
$78$		0			0
$79$	4.87632			0.548629			0.274315	−	0.961640i	$-0.411549\pi$
$79$	4.87632			0.548629			0.274315	+	0.961640i	$0.411549\pi$
$80$	−0.809179	+	2.08452i	−0.0904690	+	0.233057i
$81$		0			0
$82$	1.35904	+	0.784645i	0.150081	+	0.0866495i
$83$	−6.39020			−0.701416			−0.350708	−	0.936485i	$-0.614059\pi$
$83$	−6.39020			−0.701416			−0.350708	+	0.936485i	$0.614059\pi$
$84$		0			0
$85$	0.535898	+	3.46788i	0.0581263	+	0.376144i
$86$		−	5.28860i		−	0.570284i
$87$		0			0
$88$	1.14057	−	0.658509i	0.121585	−	0.0701973i
$89$	−15.9738	+	9.22251i	−1.69322	+	0.977584i	−0.741338	+	0.671131i	$0.765809\pi$
$89$	−15.9738	+	9.22251i	−1.69322	+	0.977584i	−0.951886	+	0.306452i	$0.900858\pi$
$90$		0			0
$91$	−5.38789	+	1.14452i	−0.564804	+	0.119978i
$92$		−	8.44285i		−	0.880228i
$93$		0			0
$94$	−2.47276	−	4.28295i	−0.255046	−	0.441752i
$95$	1.64851	+	10.6677i	0.169133	+	1.09449i
$96$		0			0
$97$	−0.963028	+	1.66801i	−0.0977807	+	0.169361i	−0.910766	−	0.412923i	$-0.864508\pi$
$97$	−0.963028	+	1.66801i	−0.0977807	+	0.169361i	0.812985	+	0.582285i	$0.197841\pi$
$98$	2.33310	−	4.04106i	0.235679	−	0.408208i
$99$		0			0
$100$	−3.69046	−	3.37350i	−0.369046	−	0.337350i
$101$	−1.21929	−	2.11188i	−0.121324	−	0.210140i	0.798966	−	0.601376i	$-0.205381\pi$
$101$	−1.21929	−	2.11188i	−0.121324	−	0.210140i	−0.920290	+	0.391237i	$0.872047\pi$
$102$		0			0
$103$		−	12.4300i		−	1.22477i	−0.790561	−	0.612383i	$-0.790211\pi$
$103$		−	12.4300i		−	1.22477i	0.790561	−	0.612383i	$-0.209789\pi$
$104$	2.41225	+	2.67975i	0.236540	+	0.262771i
$105$		0			0
$106$	12.0517	−	6.95804i	1.17056	−	0.675824i
$107$	−9.07302	+	5.23831i	−0.877122	+	0.506407i	−0.869708	−	0.493566i	$-0.835693\pi$
$107$	−9.07302	+	5.23831i	−0.877122	+	0.506407i	−0.00741349	+	0.999973i	$0.502360\pi$
$108$		0			0
$109$			17.1799i			1.64553i	0.568379	+	0.822767i	$0.307571\pi$
$109$			17.1799i			1.64553i	−0.568379	+	0.822767i	$0.692429\pi$
$110$	0.449750	+	2.91040i	0.0428820	+	0.277495i
$111$		0			0
$112$	1.52767			0.144352
$113$	2.25151	+	1.29991i	0.211805	+	0.122285i	0.602150	−	0.798383i	$-0.294311\pi$
$113$	2.25151	+	1.29991i	0.211805	+	0.122285i	−0.390345	+	0.920669i	$0.627644\pi$
$114$		0			0
$115$	17.5993	+	6.83178i	1.64114	+	0.637067i
$116$	−4.42877			−0.411201
$117$		0			0
$118$		−	10.4732i		−	0.964136i
$119$	2.07618	−	1.19868i	0.190323	−	0.109883i
$120$		0			0
$121$	−4.63273	+	8.02413i	−0.421157	+	0.729466i
$122$	−4.98268			−0.451111
$123$		0			0
$124$	1.40941	+	0.813725i	0.126569	+	0.0730747i
$125$	10.0184	−	4.96307i	0.896071	−	0.443911i
$126$		0			0
$127$	−7.01552	+	4.05041i	−0.622527	+	0.359416i	−0.777852	−	0.628447i	$-0.783691\pi$
$127$	−7.01552	+	4.05041i	−0.622527	+	0.359416i	0.155325	+	0.987863i	$0.450357\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−7.53794	+	2.85998i	−0.661121	+	0.250837i
$131$	2.32506			0.203141			0.101571	−	0.994828i	$-0.467613\pi$
$131$	2.32506			0.203141			0.101571	+	0.994828i	$0.467613\pi$
$132$		0			0
$133$	6.38665	−	3.68733i	0.553792	−	0.319732i
$134$	−1.38628	+	2.40112i	−0.119757	+	0.207425i
$135$		0			0
$136$	−1.35904	−	0.784645i	−0.116537	−	0.0672827i
$137$	6.14192	−	10.6381i	0.524740	−	0.908876i	−0.474845	−	0.880069i	$-0.657496\pi$
$137$	6.14192	−	10.6381i	0.524740	−	0.908876i	0.999585	−	0.0288066i	$-0.00917069\pi$
$138$		0			0
$139$	−3.32861	+	5.76531i	−0.282329	+	0.489008i	−0.971958	−	0.235155i	$-0.924440\pi$
$139$	−3.32861	+	5.76531i	−0.282329	+	0.489008i	0.689629	+	0.724163i	$0.257774\pi$
$140$	−1.23616	+	3.18447i	−0.104475	+	0.269137i
$141$		0			0
$142$		−	14.8394i		−	1.24529i
$143$	4.51598	+	1.46796i	0.377645	+	0.122757i
$144$		0			0
$145$	3.58367	−	9.23186i	0.297607	−	0.766664i
$146$	2.99472	+	5.18700i	0.247845	+	0.429280i
$147$		0			0
$148$	−2.80296			−0.230402
$149$	2.60768	+	1.50554i	0.213629	+	0.123339i	0.602997	−	0.797744i	$-0.293973\pi$
$149$	2.60768	+	1.50554i	0.213629	+	0.123339i	−0.389368	+	0.921082i	$0.627306\pi$
$150$		0			0
$151$		−	12.0149i		−	0.977759i	−0.872351	−	0.488880i	$-0.837406\pi$
$151$		−	12.0149i		−	0.977759i	0.872351	−	0.488880i	$-0.162594\pi$
$152$	−4.18063	−	2.41369i	−0.339094	−	0.195776i
$153$		0			0
$154$	1.74242	−	1.00599i	0.140408	−	0.0810648i
$155$	−2.83670	+	2.27950i	−0.227849	+	0.183094i
$156$		0			0
$157$			3.01556i			0.240668i	0.992733	+	0.120334i	$0.0383965\pi$
$157$			3.01556i			0.240668i	−0.992733	+	0.120334i	$0.961604\pi$
$158$	−2.43816	−	4.22302i	−0.193970	−	0.335965i
$159$		0			0
$160$	2.20984	−	0.341491i	0.174703	−	0.0269972i
$161$		−	12.8979i		−	1.01650i
$162$		0			0
$163$	4.95812	−	8.58772i	0.388350	−	0.672642i	−0.603878	−	0.797077i	$-0.706379\pi$
$163$	4.95812	−	8.58772i	0.388350	−	0.672642i	0.992228	+	0.124435i	$0.0397119\pi$
$164$		−	1.56929i		−	0.122541i
$165$		0			0
$166$	3.19510	+	5.53408i	0.247988	+	0.429528i
$167$	−6.49472	−	11.2492i	−0.502576	−	0.870488i	−0.999996	−	0.00297754i	$-0.999052\pi$
$167$	−6.49472	−	11.2492i	−0.502576	−	0.870488i	0.497419	−	0.867510i	$-0.334281\pi$
$168$		0			0
$169$	−1.36213	+	12.9284i	−0.104779	+	0.994496i
$170$	2.73532	−	2.19804i	0.209789	−	0.168582i
$171$		0			0
$172$	−4.58006	+	2.64430i	−0.349226	+	0.201626i
$173$	3.35755	+	1.93848i	0.255270	+	0.147380i	0.622175	−	0.782878i	$-0.286249\pi$
$173$	3.35755	+	1.93848i	0.255270	+	0.147380i	−0.366905	+	0.930258i	$0.619583\pi$
$174$		0			0
$175$	−5.63782	−	5.15361i	−0.426179	−	0.389577i
$176$	−1.14057	−	0.658509i	−0.0859738	−	0.0496370i
$177$		0			0
$178$	15.9738	+	9.22251i	1.19729	+	0.691256i
$179$	−7.05325	−	12.2166i	−0.527185	−	0.913111i	−0.999498	−	0.0316802i	$-0.989914\pi$
$179$	−7.05325	−	12.2166i	−0.527185	−	0.913111i	0.472313	−	0.881431i	$-0.343419\pi$
$180$		0			0
$181$	−26.1472			−1.94351			−0.971753	−	0.236001i	$-0.924163\pi$
$181$	−26.1472			−1.94351			−0.971753	+	0.236001i	$0.924163\pi$
$182$	3.68513	+	4.09379i	0.273160	+	0.303452i
$183$		0			0
$184$	−7.31172	+	4.22143i	−0.539027	+	0.311208i
$185$	2.26809	−	5.84282i	0.166754	−	0.429573i
$186$		0			0
$187$	−2.06678			−0.151138
$188$	−2.47276	+	4.28295i	−0.180345	+	0.312366i
$189$		0			0
$190$	8.41426	−	6.76151i	0.610435	−	0.490531i
$191$	9.42713	−	16.3283i	0.682123	−	1.18147i	−0.292208	−	0.956355i	$-0.594390\pi$
$191$	9.42713	−	16.3283i	0.682123	−	1.18147i	0.974332	−	0.225117i	$-0.0722766\pi$
$192$		0			0
$193$	8.94600	+	15.4949i	0.643947	+	1.11535i	0.984544	+	0.175140i	$0.0560378\pi$
$193$	8.94600	+	15.4949i	0.643947	+	1.11535i	−0.340596	+	0.940210i	$0.610629\pi$
$194$	1.92606			0.138283
$195$		0			0
$196$	−4.66621			−0.333301
$197$	0.312928	+	0.542008i	0.0222952	+	0.0386165i	0.876958	−	0.480567i	$-0.159569\pi$
$197$	0.312928	+	0.542008i	0.0222952	+	0.0386165i	−0.854663	+	0.519184i	$0.826236\pi$
$198$		0			0
$199$	−8.84057	+	15.3123i	−0.626691	+	1.08546i	0.361520	+	0.932364i	$0.382258\pi$
$199$	−8.84057	+	15.3123i	−0.626691	+	1.08546i	−0.988211	+	0.153097i	$0.951075\pi$
$200$	−1.07631	+	4.88278i	−0.0761065	+	0.345265i
$201$		0			0
$202$	−1.21929	+	2.11188i	−0.0857891	+	0.148591i
$203$	−6.76572			−0.474860
$204$		0			0
$205$	3.27122	+	1.26984i	0.228472	+	0.0886892i
$206$	−10.7647	+	6.21501i	−0.750013	+	0.433020i
$207$		0			0
$208$	1.11461	−	3.42894i	0.0772842	−	0.237754i
$209$	−6.35774			−0.439774
$210$		0			0
$211$	−8.62227	−	14.9342i	−0.593581	−	1.02811i	−0.993745	−	0.111669i	$-0.964380\pi$
$211$	−8.62227	−	14.9342i	−0.593581	−	1.02811i	0.400164	−	0.916443i	$-0.368953\pi$
$212$	−12.0517	−	6.95804i	−0.827712	−	0.477880i
$213$		0			0
$214$	9.07302	+	5.23831i	0.620219	+	0.358083i
$215$	−1.80601	−	11.6869i	−0.123169	−	0.797043i
$216$		0			0
$217$	2.15313	+	1.24311i	0.146164	+	0.0843877i
$218$	14.8782	−	8.58994i	1.00768	−	0.581784i
$219$		0			0
$220$	2.29560	−	1.84469i	0.154769	−	0.124369i
$221$	−1.17570	−	5.53466i	−0.0790861	−	0.372301i
$222$		0			0
$223$	2.44858	+	4.24107i	0.163969	+	0.284003i	0.936289	−	0.351231i	$-0.114237\pi$
$223$	2.44858	+	4.24107i	0.163969	+	0.284003i	−0.772320	+	0.635234i	$0.780904\pi$
$224$	−0.763837	−	1.32301i	−0.0510360	−	0.0883970i
$225$		0			0
$226$		−	2.59982i		−	0.172938i
$227$	5.07567	−	8.79132i	0.336884	−	0.583500i	−0.646961	−	0.762523i	$-0.723960\pi$
$227$	5.07567	−	8.79132i	0.336884	−	0.583500i	0.983845	+	0.179023i	$0.0572936\pi$
$228$		0			0
$229$			15.3959i			1.01739i	0.860947	+	0.508694i	$0.169871\pi$
$229$			15.3959i			1.01739i	−0.860947	+	0.508694i	$0.830129\pi$
$230$	−2.88316	−	18.6573i	−0.190110	−	1.23023i
$231$		0			0
$232$	2.21438	+	3.83543i	0.145381	+	0.251808i
$233$		−	9.91624i		−	0.649634i	−0.945777	−	0.324817i	$-0.894697\pi$
$233$		−	9.91624i		−	0.649634i	0.945777	−	0.324817i	$-0.105303\pi$
$234$		0			0
$235$	−6.92699	−	8.62019i	−0.451867	−	0.562319i
$236$	−9.07005	+	5.23660i	−0.590410	+	0.340873i
$237$		0			0
$238$	−2.07618	−	1.19868i	−0.134579	−	0.0776990i
$239$		−	9.46167i		−	0.612024i	−0.952028	−	0.306012i	$-0.901005\pi$
$239$		−	9.46167i		−	0.612024i	0.952028	−	0.306012i	$-0.0989948\pi$
$240$		0			0
$241$	11.3482	+	6.55189i	0.731002	+	0.422044i	0.818789	−	0.574095i	$-0.194646\pi$
$241$	11.3482	+	6.55189i	0.731002	+	0.422044i	−0.0877865	+	0.996139i	$0.527979\pi$
$242$	9.26546			0.595607
$243$		0			0
$244$	2.49134	+	4.31513i	0.159492	+	0.276248i
$245$	3.77580	−	9.72681i	0.241227	−	0.621423i
$246$		0			0
$247$	−3.61663	−	17.0255i	−0.230121	−	1.08330i
$248$		−	1.62745i		−	0.103343i
$249$		0			0
$250$	−9.30734	−	6.19463i	−0.588648	−	0.391783i
$251$	−11.5822	+	20.0610i	−0.731062	+	1.26624i	0.225367	+	0.974274i	$0.427642\pi$
$251$	−11.5822	+	20.0610i	−0.731062	+	1.26624i	−0.956430	+	0.291963i	$0.905692\pi$
$252$		0			0
$253$	−5.55969	+	9.62967i	−0.349535	+	0.605412i
$254$	7.01552	+	4.05041i	0.440193	+	0.254146i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.32895	−	1.92197i	0.207654	−	0.119889i	−0.392566	−	0.919724i	$-0.628413\pi$
$257$	3.32895	−	1.92197i	0.207654	−	0.119889i	0.600221	+	0.799834i	$0.295079\pi$
$258$		0			0
$259$	−4.28201			−0.266071
$260$	6.24579	+	5.09805i	0.387347	+	0.316168i
$261$		0			0
$262$	−1.16253	−	2.01356i	−0.0718213	−	0.124398i
$263$	−26.5060	+	15.3032i	−1.63443	+	0.943638i	−0.651726	+	0.758455i	$0.725955\pi$
$263$	−26.5060	+	15.3032i	−1.63443	+	0.943638i	−0.982704	+	0.185184i	$0.940712\pi$
$264$		0			0
$265$	24.2561	−	19.4917i	1.49004	−	1.19736i
$266$	−6.38665	−	3.68733i	−0.391590	−	0.226085i
$267$		0			0
$268$	2.77257			0.169362
$269$	−9.04370	+	15.6641i	−0.551404	+	0.955060i	0.446769	+	0.894649i	$0.352574\pi$
$269$	−9.04370	+	15.6641i	−0.551404	+	0.955060i	−0.998174	+	0.0604109i	$0.980759\pi$
$270$		0			0
$271$	12.2869	−	7.09382i	0.746373	−	0.430919i	−0.0780089	−	0.996953i	$-0.524856\pi$
$271$	12.2869	−	7.09382i	0.746373	−	0.430919i	0.824382	+	0.566034i	$0.191523\pi$
$272$			1.56929i			0.0951521i
$273$		0			0
$274$	−12.2838			−0.742094
$275$	1.98775	+	6.27792i	0.119866	+	0.378573i
$276$		0			0
$277$	14.5855	+	8.42097i	0.876360	+	0.505967i	0.869457	−	0.494009i	$-0.164469\pi$
$277$	14.5855	+	8.42097i	0.876360	+	0.505967i	0.00690380	+	0.999976i	$0.497802\pi$
$278$	6.65721			0.399273
$279$		0			0
$280$	3.37591	−	0.521687i	0.201749	−	0.0311768i
$281$			8.61535i			0.513949i	0.966418	+	0.256974i	$0.0827256\pi$
$281$			8.61535i			0.513949i	−0.966418	+	0.256974i	$0.917274\pi$
$282$		0			0
$283$	−23.9192	+	13.8098i	−1.42185	+	0.820905i	−0.996457	−	0.0841040i	$-0.973197\pi$
$283$	−23.9192	+	13.8098i	−1.42185	+	0.820905i	−0.425392	+	0.905009i	$0.639864\pi$
$284$	−12.8513	+	7.41968i	−0.762582	+	0.440277i
$285$		0			0
$286$	−0.986699	−	4.64493i	−0.0583447	−	0.274661i
$287$		−	2.39736i		−	0.141512i
$288$		0			0
$289$	−7.26867	−	12.5897i	−0.427569	−	0.740570i
$290$	−9.78686	+	1.51239i	−0.574704	+	0.0888103i
$291$		0			0
$292$	2.99472	−	5.18700i	0.175253	−	0.303546i
$293$	15.1250	−	26.1973i	0.883614	−	1.53046i	0.0363205	−	0.999340i	$-0.488436\pi$
$293$	15.1250	−	26.1973i	0.883614	−	1.53046i	0.847294	−	0.531125i	$-0.178230\pi$
$294$		0			0
$295$	−3.57650	−	23.1441i	−0.208232	−	1.34750i
$296$	1.40148	+	2.42743i	0.0814593	+	0.141092i
$297$		0			0
$298$		−	3.01108i		−	0.174427i
$299$	−28.9501	−	9.41048i	−1.67422	−	0.544222i
$300$		0			0
$301$	−6.99684	+	4.03963i	−0.403291	+	0.232840i
$302$	−10.4052	+	6.00745i	−0.598753	+	0.345690i
$303$		0			0
$304$			4.82738i			0.276869i
$305$	−11.0109	+	1.70154i	−0.630484	+	0.0974300i
$306$		0			0
$307$	−14.1392			−0.806966			−0.403483	−	0.914987i	$-0.632201\pi$
$307$	−14.1392			−0.806966			−0.403483	+	0.914987i	$0.632201\pi$
$308$	−1.74242	−	1.00599i	−0.0992837	−	0.0573215i
$309$		0			0
$310$	3.39246	+	1.31690i	0.192679	+	0.0747948i
$311$	9.97427			0.565589			0.282794	−	0.959181i	$-0.408739\pi$
$311$	9.97427			0.565589			0.282794	+	0.959181i	$0.408739\pi$
$312$		0			0
$313$			3.08460i			0.174352i	0.996193	+	0.0871760i	$0.0277843\pi$
$313$			3.08460i			0.174352i	−0.996193	+	0.0871760i	$0.972216\pi$
$314$	2.61155	−	1.50778i	0.147378	−	0.0850888i
$315$		0			0
$316$	−2.43816	+	4.22302i	−0.137157	+	0.237563i
$317$	−14.2980			−0.803054			−0.401527	−	0.915847i	$-0.631520\pi$
$317$	−14.2980			−0.803054			−0.401527	+	0.915847i	$0.631520\pi$
$318$		0			0
$319$	5.05132	+	2.91638i	0.282820	+	0.163286i
$320$	−1.40066	−	1.74303i	−0.0782992	−	0.0974384i
$321$		0			0
$322$	−11.1699	+	6.44897i	−0.622476	+	0.359387i
$323$	3.78778	+	6.56062i	0.210757	+	0.365043i
$324$		0			0
$325$	−15.6810	+	8.89424i	−0.869823	+	0.493363i
$326$	−9.91624			−0.549210
$327$		0			0
$328$	−1.35904	+	0.784645i	−0.0750407	+	0.0433248i
$329$	−3.77757	+	6.54295i	−0.208264	+	0.360724i
$330$		0			0
$331$	−9.89017	−	5.71009i	−0.543613	−	0.313855i	0.202929	−	0.979193i	$-0.434954\pi$
$331$	−9.89017	−	5.71009i	−0.543613	−	0.313855i	−0.746542	+	0.665338i	$0.768287\pi$
$332$	3.19510	−	5.53408i	0.175354	−	0.303722i
$333$		0			0
$334$	−6.49472	+	11.2492i	−0.355375	+	0.615528i
$335$	−2.24351	+	5.77948i	−0.122576	+	0.315767i
$336$		0			0
$337$		−	5.53208i		−	0.301352i	−0.988583	−	0.150676i	$-0.951855\pi$
$337$		−	5.53208i		−	0.301352i	0.988583	−	0.150676i	$-0.0481450\pi$
$338$	11.8774	−	5.28458i	0.646047	−	0.287443i
$339$		0			0
$340$	−3.27122	−	1.26984i	−0.177407	−	0.0688665i
$341$	−1.07169	−	1.85622i	−0.0580353	−	0.100520i
$342$		0			0
$343$	−17.8222			−0.962307
$344$	4.58006	+	2.64430i	0.246940	+	0.142571i
$345$		0			0
$346$		−	3.87696i		−	0.208427i
$347$	2.44226	+	1.41004i	0.131107	+	0.0756949i	0.564119	−	0.825693i	$-0.309216\pi$
$347$	2.44226	+	1.41004i	0.131107	+	0.0756949i	−0.433012	+	0.901388i	$0.642549\pi$
$348$		0			0
$349$	23.0704	−	13.3197i	1.23493	−	0.712986i	0.266875	−	0.963731i	$-0.414009\pi$
$349$	23.0704	−	13.3197i	1.23493	−	0.712986i	0.968053	+	0.250745i	$0.0806757\pi$
$350$	−1.64425	+	7.45930i	−0.0878889	+	0.398717i
$351$		0			0
$352$			1.31702i			0.0701973i
$353$	−6.61308	−	11.4542i	−0.351979	−	0.609645i	0.634617	−	0.772826i	$-0.281158\pi$
$353$	−6.61308	−	11.4542i	−0.351979	−	0.609645i	−0.986596	+	0.163182i	$0.947824\pi$
$354$		0			0
$355$	−5.06751	−	32.7926i	−0.268955	−	1.74045i
$356$		−	18.4450i		−	0.977584i
$357$		0			0
$358$	−7.05325	+	12.2166i	−0.372776	+	0.645667i
$359$			12.3827i			0.653532i	0.945105	+	0.326766i	$0.105959\pi$
$359$			12.3827i			0.653532i	−0.945105	+	0.326766i	$0.894041\pi$
$360$		0			0
$361$	2.15178	+	3.72700i	0.113252	+	0.196158i
$362$	13.0736	+	22.6441i	0.687133	+	1.19015i
$363$		0			0
$364$	1.70276	−	5.23831i	0.0892489	−	0.274562i
$365$	8.38916	+	10.4398i	0.439109	+	0.546443i
$366$		0			0
$367$	6.14226	−	3.54624i	0.320623	−	0.185112i	−0.331047	−	0.943614i	$-0.607402\pi$
$367$	6.14226	−	3.54624i	0.320623	−	0.185112i	0.651670	+	0.758502i	$0.274069\pi$
$368$	7.31172	+	4.22143i	0.381150	+	0.220057i
$369$		0			0
$370$	−6.19408	+	0.957185i	−0.322015	+	0.0497617i
$371$	−18.4110	−	10.6296i	−0.955854	−	0.551862i
$372$		0			0
$373$	−32.0259	−	18.4902i	−1.65824	−	0.957384i	−0.973528	−	0.228568i	$-0.926596\pi$
$373$	−32.0259	−	18.4902i	−1.65824	−	0.957384i	−0.684709	−	0.728816i	$-0.740071\pi$
$374$	1.03339	+	1.78989i	0.0534354	+	0.0925528i
$375$		0			0
$376$	4.94552			0.255046
$377$	−4.93634	+	15.1860i	−0.254235	+	0.782118i
$378$		0			0
$379$	−29.6252	+	17.1041i	−1.52174	+	0.878580i	−0.522075	+	0.852900i	$0.674842\pi$
$379$	−29.6252	+	17.1041i	−1.52174	+	0.878580i	−0.999670	+	0.0256802i	$0.991825\pi$
$380$	−10.0628	−	3.90621i	−0.516209	−	0.200384i
$381$		0			0
$382$	−18.8543			−0.964668
$383$	13.0170	−	22.5461i	0.665137	−	1.15205i	−0.314111	−	0.949386i	$-0.601706\pi$
$383$	13.0170	−	22.5461i	0.665137	−	1.15205i	0.979248	−	0.202665i	$-0.0649603\pi$
$384$		0			0
$385$	3.50693	−	2.81809i	0.178730	−	0.143623i
$386$	8.94600	−	15.4949i	0.455340	−	0.788671i
$387$		0			0
$388$	−0.963028	−	1.66801i	−0.0488904	−	0.0846806i
$389$	6.23568			0.316162			0.158081	−	0.987426i	$-0.449469\pi$
$389$	6.23568			0.316162			0.158081	+	0.987426i	$0.449469\pi$
$390$		0			0
$391$	13.2493			0.670045
$392$	2.33310	+	4.04106i	0.117840	+	0.204104i
$393$		0			0
$394$	0.312928	−	0.542008i	0.0157651	−	0.0273060i
$395$	−6.83007	−	8.49958i	−0.343658	−	0.427660i
$396$		0			0
$397$	18.3498	−	31.7827i	0.920948	−	1.59513i	0.122997	−	0.992407i	$-0.460750\pi$
$397$	18.3498	−	31.7827i	0.920948	−	1.59513i	0.797951	−	0.602722i	$-0.205917\pi$
$398$	17.6811			0.886275
$399$		0			0
$400$	4.76677	−	1.50928i	0.238338	−	0.0754640i
$401$	−24.5044	+	14.1476i	−1.22369	+	0.706498i	−0.965703	−	0.259651i	$-0.916393\pi$
$401$	−24.5044	+	14.1476i	−1.22369	+	0.706498i	−0.257987	+	0.966148i	$0.583059\pi$
$402$		0			0
$403$	4.36116	−	3.92581i	0.217245	−	0.195559i
$404$	2.43859			0.121324
$405$		0			0
$406$	3.38286	+	5.85928i	0.167888	+	0.290791i
$407$	3.19697	+	1.84577i	0.158468	+	0.0914915i
$408$		0			0
$409$	13.2744	+	7.66400i	0.656379	+	0.378961i	0.790896	−	0.611951i	$-0.209615\pi$
$409$	13.2744	+	7.66400i	0.656379	+	0.378961i	−0.134517	+	0.990911i	$0.542948\pi$
$410$	−0.535898	−	3.46788i	−0.0264661	−	0.171266i
$411$		0			0
$412$	10.7647	+	6.21501i	0.530339	+	0.306191i
$413$	−13.8561	+	7.99982i	−0.681814	+	0.393645i
$414$		0			0
$415$	8.95050	+	11.1383i	0.439363	+	0.546758i
$416$	−3.52686	+	0.749192i	−0.172918	+	0.0367322i
$417$		0			0
$418$	3.17887	+	5.50597i	0.155484	+	0.269306i
$419$	13.4692	+	23.3293i	0.658013	+	1.13971i	0.981129	+	0.193353i	$0.0619362\pi$
$419$	13.4692	+	23.3293i	0.658013	+	1.13971i	−0.323116	+	0.946359i	$0.604730\pi$
$420$		0			0
$421$		−	38.5359i		−	1.87812i	−0.343747	−	0.939062i	$-0.611696\pi$
$421$		−	38.5359i		−	1.87812i	0.343747	−	0.939062i	$-0.388304\pi$
$422$	−8.62227	+	14.9342i	−0.419725	+	0.726986i
$423$		0			0
$424$			13.9161i			0.675824i
$425$	5.29400	−	5.79140i	0.256797	−	0.280924i
$426$		0			0
$427$	3.80596	+	6.59212i	0.184183	+	0.319015i
$428$		−	10.4766i		−	0.506407i
$429$		0			0
$430$	−9.21818	+	7.40752i	−0.444540	+	0.357222i
$431$	−2.48744	+	1.43612i	−0.119816	+	0.0691756i	−0.558710	−	0.829363i	$-0.688704\pi$
$431$	−2.48744	+	1.43612i	−0.119816	+	0.0691756i	0.438894	+	0.898539i	$0.355370\pi$
$432$		0			0
$433$	11.2344	+	6.48619i	0.539891	+	0.311706i	0.745035	−	0.667026i	$-0.232433\pi$
$433$	11.2344	+	6.48619i	0.539891	+	0.311706i	−0.205144	+	0.978732i	$0.565766\pi$
$434$		−	2.48622i		−	0.119342i
$435$		0			0
$436$	−14.8782	−	8.58994i	−0.712537	−	0.411383i
$437$	40.7568			1.94966
$438$		0			0
$439$	−1.02411	−	1.77380i	−0.0488779	−	0.0846590i	0.840551	−	0.541732i	$-0.182231\pi$
$439$	−1.02411	−	1.77380i	−0.0488779	−	0.0846590i	−0.889429	+	0.457073i	$0.848898\pi$
$440$	−2.74535	−	1.06570i	−0.130880	−	0.0508054i
$441$		0			0
$442$	−4.20530	+	3.78551i	−0.200026	+	0.180059i
$443$			25.7082i			1.22143i	0.791849	+	0.610717i	$0.209119\pi$
$443$			25.7082i			1.22143i	−0.791849	+	0.610717i	$0.790881\pi$
$444$		0			0
$445$	38.4490	+	14.9253i	1.82266	+	0.707528i
$446$	2.44858	−	4.24107i	0.115944	−	0.200820i
$447$		0			0
$448$	−0.763837	+	1.32301i	−0.0360879	+	0.0625061i
$449$	16.0756	+	9.28127i	0.758656	+	0.438010i	0.828813	−	0.559526i	$-0.189017\pi$
$449$	16.0756	+	9.28127i	0.758656	+	0.438010i	−0.0701571	+	0.997536i	$0.522350\pi$
$450$		0			0
$451$	−1.03339	+	1.78989i	−0.0486605	+	0.0842824i
$452$	−2.25151	+	1.29991i	−0.105902	+	0.0611427i
$453$		0			0
$454$	−10.1513			−0.476426
$455$	9.54153	+	7.78817i	0.447314	+	0.365115i
$456$		0			0
$457$	12.3213	+	21.3412i	0.576368	+	0.998299i	0.995891	+	0.0905546i	$0.0288640\pi$
$457$	12.3213	+	21.3412i	0.576368	+	0.998299i	−0.419523	+	0.907745i	$0.637803\pi$
$458$	13.3332	−	7.69794i	0.623020	−	0.359701i
$459$		0			0
$460$	−14.7161	+	11.8256i	−0.686144	+	0.551369i
$461$	27.5693	+	15.9171i	1.28403	+	0.741334i	0.977582	−	0.210554i	$-0.0675268\pi$
$461$	27.5693	+	15.9171i	1.28403	+	0.741334i	0.306446	+	0.951888i	$0.400860\pi$
$462$		0			0
$463$	−3.18319			−0.147936			−0.0739678	−	0.997261i	$-0.523566\pi$
$463$	−3.18319			−0.147936			−0.0739678	+	0.997261i	$0.523566\pi$
$464$	2.21438	−	3.83543i	0.102800	−	0.178055i
$465$		0			0
$466$	−8.58772	+	4.95812i	−0.397818	+	0.229680i
$467$		−	21.6747i		−	1.00298i	−0.865162	−	0.501492i	$-0.832785\pi$
$467$		−	21.6747i		−	1.00298i	0.865162	−	0.501492i	$-0.167215\pi$
$468$		0			0
$469$	4.23559			0.195581
$470$	−4.00181	+	10.3090i	−0.184590	+	0.475521i
$471$		0			0
$472$	9.07005	+	5.23660i	0.417483	+	0.241034i
$473$	6.96517			0.320259
$474$		0			0
$475$	16.2852	−	17.8152i	0.747215	−	0.817419i
$476$			2.39736i			0.109883i
$477$		0			0
$478$	−8.19404	+	4.73083i	−0.374787	+	0.216383i
$479$	25.3765	−	14.6511i	1.15948	−	0.669426i	0.208300	−	0.978065i	$-0.433207\pi$
$479$	25.3765	−	14.6511i	1.15948	−	0.669426i	0.951179	+	0.308639i	$0.0998735\pi$
$480$		0			0
$481$	−3.12420	+	9.61118i	−0.142451	+	0.438232i
$482$		−	13.1038i		−	0.596861i
$483$		0			0
$484$	−4.63273	−	8.02413i	−0.210579	−	0.364733i
$485$	4.25627	−	0.657731i	0.193267	−	0.0298660i
$486$		0			0
$487$	21.2643	−	36.8309i	0.963579	−	1.66897i	0.250194	−	0.968196i	$-0.419506\pi$
$487$	21.2643	−	36.8309i	0.963579	−	1.66897i	0.713385	−	0.700772i	$-0.247161\pi$
$488$	2.49134	−	4.31513i	0.112778	−	0.195337i
$489$		0			0
$490$	−10.3116	+	1.59347i	−0.465829	+	0.0719856i
$491$	−6.32521	−	10.9556i	−0.285453	−	0.494418i	0.687266	−	0.726406i	$-0.258811\pi$
$491$	−6.32521	−	10.9556i	−0.285453	−	0.494418i	−0.972719	+	0.231987i	$0.925477\pi$
$492$		0			0
$493$		−	6.95002i		−	0.313013i
$494$	−12.9362	+	11.6448i	−0.582026	+	0.523925i
$495$		0			0
$496$	−1.40941	+	0.813725i	−0.0632845	+	0.0365373i
$497$	−19.6325	+	11.3349i	−0.880640	+	0.508438i
$498$		0			0
$499$		−	4.54007i		−	0.203242i	−0.994823	−	0.101621i	$-0.967597\pi$
$499$		−	4.54007i		−	0.203242i	0.994823	−	0.101621i	$-0.0324028\pi$
$500$	−0.711042	+	11.1577i	−0.0317988	+	0.498988i
$501$		0			0
$502$	23.1644			1.03388
$503$	−17.2476	−	9.95791i	−0.769033	−	0.444001i	0.0634967	−	0.997982i	$-0.479775\pi$
$503$	−17.2476	−	9.95791i	−0.769033	−	0.444001i	−0.832529	+	0.553981i	$0.813108\pi$
$504$		0			0
$505$	−1.97325	+	5.08328i	−0.0878086	+	0.226203i
$506$	11.1194			0.494317
$507$		0			0
$508$		−	8.10083i		−	0.359416i
$509$	9.09532	−	5.25118i	0.403143	−	0.232755i	−0.284696	−	0.958618i	$-0.591893\pi$
$509$	9.09532	−	5.25118i	0.403143	−	0.232755i	0.687839	+	0.725863i	$0.258559\pi$
$510$		0			0
$511$	4.57496	−	7.92406i	0.202384	−	0.350540i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.32895	−	1.92197i	−0.146834	−	0.0847746i
$515$	−21.6659	+	17.4102i	−0.954713	+	0.767185i
$516$		0			0
$517$	5.64072	−	3.25667i	0.248078	−	0.143228i
$518$	2.14100	+	3.70833i	0.0940703	+	0.162934i
$519$		0			0
$520$	1.29215	−	7.95804i	0.0566646	−	0.348983i
$521$	24.5221			1.07433			0.537166	−	0.843477i	$-0.319495\pi$
$521$	24.5221			1.07433			0.537166	+	0.843477i	$0.319495\pi$
$522$		0			0
$523$	−21.6924	+	12.5241i	−0.948541	+	0.547641i	−0.892627	−	0.450795i	$-0.851141\pi$
$523$	−21.6924	+	12.5241i	−0.948541	+	0.547641i	−0.0559138	+	0.998436i	$0.517807\pi$
$524$	−1.16253	+	2.01356i	−0.0507853	+	0.0879628i
$525$		0			0
$526$	26.5060	+	15.3032i	1.15572	+	0.667253i
$527$	−1.27697	+	2.21178i	−0.0556257	+	0.0963466i
$528$		0			0
$529$	24.1409	−	41.8132i	1.04960	−	1.81797i
$530$	−29.0084	−	11.2606i	−1.26004	−	0.489129i
$531$		0			0
$532$			7.37466i			0.319732i
$533$	−5.38100	−	1.74914i	−0.233077	−	0.0757638i
$534$		0			0
$535$	21.8387	+	8.47746i	0.944171	+	0.366513i
$536$	−1.38628	−	2.40112i	−0.0598784	−	0.103712i
$537$		0			0
$538$	18.0874			0.779803
$539$	5.32214	+	3.07274i	0.229241	+	0.132352i
$540$		0			0
$541$			20.6859i			0.889356i	0.895690	+	0.444678i	$0.146682\pi$
$541$			20.6859i			0.889356i	−0.895690	+	0.444678i	$0.853318\pi$
$542$	−12.2869	−	7.09382i	−0.527765	−	0.304705i
$543$		0			0
$544$	1.35904	−	0.784645i	0.0582686	−	0.0336414i
$545$	29.9450	−	24.0631i	1.28270	−	1.03075i
$546$		0			0
$547$			40.5960i			1.73576i	0.496773	+	0.867880i	$0.334518\pi$
$547$			40.5960i			1.73576i	−0.496773	+	0.867880i	$0.665482\pi$
$548$	6.14192	+	10.6381i	0.262370	+	0.454438i
$549$		0			0
$550$	4.44296	−	4.86040i	0.189449	−	0.207248i
$551$		−	21.3793i		−	0.910790i
$552$		0			0
$553$	−3.72472	+	6.45140i	−0.158391	+	0.274342i
$554$		−	16.8419i		−	0.715545i
$555$		0			0
$556$	−3.32861	−	5.76531i	−0.141164	−	0.244504i
$557$	20.6032	+	35.6858i	0.872985	+	1.51205i	0.858894	+	0.512153i	$0.171152\pi$
$557$	20.6032	+	35.6858i	0.872985	+	1.51205i	0.0140907	+	0.999901i	$0.495515\pi$
$558$		0			0
$559$	3.96217	+	18.6521i	0.167582	+	0.788900i
$560$	−2.13975	−	2.66278i	−0.0904210	−	0.112523i
$561$		0			0
$562$	7.46112	−	4.30768i	0.314728	−	0.181708i
$563$	−13.0933	−	7.55940i	−0.551815	−	0.318591i	0.198038	−	0.980194i	$-0.436543\pi$
$563$	−13.0933	−	7.55940i	−0.551815	−	0.318591i	−0.749854	+	0.661603i	$0.769876\pi$
$564$		0			0
$565$	−0.887817	−	5.74519i	−0.0373507	−	0.241702i
$566$	23.9192	+	13.8098i	1.00540	+	0.580468i
$567$		0			0
$568$	12.8513	+	7.41968i	0.539227	+	0.311323i
$569$	13.2995	+	23.0353i	0.557542	+	0.965692i	0.997701	+	0.0677716i	$0.0215889\pi$
$569$	13.2995	+	23.0353i	0.557542	+	0.965692i	−0.440159	+	0.897920i	$0.645078\pi$
$570$		0			0
$571$	31.8452			1.33268			0.666340	−	0.745648i	$-0.267860\pi$
$571$	31.8452			1.33268			0.666340	+	0.745648i	$0.267860\pi$
$572$	−3.52928	+	3.17697i	−0.147567	+	0.132836i
$573$		0			0
$574$	−2.07618	+	1.19868i	−0.0866580	+	0.0500320i
$575$	−12.7426	−	40.2451i	−0.531404	−	1.67834i
$576$		0			0
$577$	1.20258			0.0500639			0.0250319	−	0.999687i	$-0.492031\pi$
$577$	1.20258			0.0500639			0.0250319	+	0.999687i	$0.492031\pi$
$578$	−7.26867	+	12.5897i	−0.302337	+	0.523662i
$579$		0			0
$580$	6.20319	+	7.71948i	0.257574	+	0.320534i
$581$	4.88108	−	8.45427i	0.202501	−	0.350742i
$582$		0			0
$583$	9.16386	+	15.8723i	0.379528	+	0.657362i
$584$	−5.98944			−0.247845
$585$		0			0
$586$	−30.2501			−1.24962
$587$	−9.53243	−	16.5107i	−0.393446	−	0.681468i	0.599456	−	0.800408i	$-0.295384\pi$
$587$	−9.53243	−	16.5107i	−0.393446	−	0.681468i	−0.992901	+	0.118940i	$0.962050\pi$
$588$		0			0
$589$	−3.92816	+	6.80377i	−0.161857	+	0.280344i
$590$	−18.2551	+	14.6694i	−0.751550	+	0.603929i
$591$		0			0
$592$	1.40148	−	2.42743i	0.0576004	−	0.0997668i
$593$	−11.8496			−0.486606			−0.243303	−	0.969950i	$-0.578231\pi$
$593$	−11.8496			−0.486606			−0.243303	+	0.969950i	$0.578231\pi$
$594$		0			0
$595$	−4.99736	−	1.93990i	−0.204872	−	0.0795280i
$596$	−2.60768	+	1.50554i	−0.106815	+	0.0616694i
$597$		0			0
$598$	6.32532	+	29.7767i	0.258661	+	1.21766i
$599$	−13.1277			−0.536382			−0.268191	−	0.963366i	$-0.586426\pi$
$599$	−13.1277			−0.536382			−0.268191	+	0.963366i	$0.586426\pi$
$600$		0			0
$601$	17.8125	+	30.8522i	0.726589	+	1.25849i	0.958317	+	0.285708i	$0.0922288\pi$
$601$	17.8125	+	30.8522i	0.726589	+	1.25849i	−0.231728	+	0.972781i	$0.574438\pi$
$602$	6.99684	+	4.03963i	0.285170	+	0.164643i
$603$		0			0
$604$	10.4052	+	6.00745i	0.423382	+	0.244440i
$605$	20.4752	−	3.16407i	0.832434	−	0.128638i
$606$		0			0
$607$	4.20075	+	2.42530i	0.170503	+	0.0984400i	0.582823	−	0.812599i	$-0.301948\pi$
$607$	4.20075	+	2.42530i	0.170503	+	0.0984400i	−0.412320	+	0.911039i	$0.635281\pi$
$608$	4.18063	−	2.41369i	0.169547	−	0.0978880i
$609$		0			0
$610$	6.97904	+	8.68497i	0.282573	+	0.351644i
$611$	11.9298	+	13.2528i	0.482629	+	0.536149i
$612$		0			0
$613$	−11.7172	−	20.2948i	−0.473253	−	0.819698i	0.526279	−	0.850312i	$-0.323587\pi$
$613$	−11.7172	−	20.2948i	−0.473253	−	0.819698i	−0.999531	+	0.0306146i	$0.990254\pi$
$614$	7.06959	+	12.2449i	0.285306	+	0.494164i
$615$		0			0
$616$			2.01198i			0.0810648i
$617$	−7.01830	+	12.1560i	−0.282546	+	0.489384i	−0.972011	−	0.234935i	$-0.924512\pi$
$617$	−7.01830	+	12.1560i	−0.282546	+	0.489384i	0.689465	+	0.724319i	$0.257846\pi$
$618$		0			0
$619$			16.1470i			0.649002i	0.945885	+	0.324501i	$0.105196\pi$
$619$			16.1470i			0.649002i	−0.945885	+	0.324501i	$0.894804\pi$
$620$	−0.555760	−	3.59640i	−0.0223199	−	0.144435i
$621$		0			0
$622$	−4.98713	−	8.63797i	−0.199966	−	0.346351i
$623$		−	28.1780i		−	1.12893i
$624$		0			0
$625$	−22.6831	−	10.5108i	−0.907325	−	0.420431i
$626$	2.67134	−	1.54230i	0.106768	−	0.0616428i
$627$		0			0
$628$	−2.61155	−	1.50778i	−0.104212	−	0.0601669i
$629$		−	4.39865i		−	0.175386i
$630$		0			0
$631$	16.3611	+	9.44608i	0.651325	+	0.376043i	0.788964	−	0.614440i	$-0.210618\pi$
$631$	16.3611	+	9.44608i	0.651325	+	0.376043i	−0.137639	+	0.990483i	$0.543951\pi$
$632$	4.87632			0.193970
$633$		0			0
$634$	7.14899	+	12.3824i	0.283922	+	0.491768i
$635$	16.8863	+	6.55502i	0.670114	+	0.260128i
$636$		0			0
$637$	−5.20100	+	16.0002i	−0.206071	+	0.633950i
$638$		−	5.83277i		−	0.230921i
$639$		0			0
$640$	−0.809179	+	2.08452i	−0.0319856	+	0.0823979i
$641$	−3.57648	+	6.19465i	−0.141262	+	0.244674i	−0.927972	−	0.372649i	$-0.878449\pi$
$641$	−3.57648	+	6.19465i	−0.141262	+	0.244674i	0.786710	+	0.617323i	$0.211783\pi$
$642$		0			0
$643$	−19.9623	+	34.5756i	−0.787235	+	1.36353i	0.140420	+	0.990092i	$0.455155\pi$
$643$	−19.9623	+	34.5756i	−0.787235	+	1.36353i	−0.927655	+	0.373438i	$0.878179\pi$
$644$	11.1699	+	6.44897i	0.440157	+	0.254125i
$645$		0			0
$646$	3.78778	−	6.56062i	0.149028	−	0.258124i
$647$	12.0656	−	6.96608i	0.474348	−	0.273865i	−0.243710	−	0.969848i	$-0.578365\pi$
$647$	12.0656	−	6.96608i	0.474348	−	0.273865i	0.718058	+	0.695983i	$0.245031\pi$
$648$		0			0
$649$	13.7934			0.541438
$650$	15.5431	+	9.13299i	0.609651	+	0.358225i
$651$		0			0
$652$	4.95812	+	8.58772i	0.194175	+	0.336321i
$653$	−25.7670	+	14.8766i	−1.00834	+	0.582165i	−0.910705	−	0.413058i	$-0.864461\pi$
$653$	−25.7670	+	14.8766i	−1.00834	+	0.582165i	−0.0976340	+	0.995222i	$0.531127\pi$
$654$		0			0
$655$	−3.25662	−	4.05265i	−0.127246	−	0.158350i
$656$	1.35904	+	0.784645i	0.0530618	+	0.0306352i
$657$		0			0
$658$	7.55515			0.294530
$659$	14.6318	−	25.3431i	0.569975	−	0.987226i	−0.426593	−	0.904444i	$-0.640286\pi$
$659$	14.6318	−	25.3431i	0.569975	−	0.987226i	0.996568	−	0.0827819i	$-0.0263805\pi$
$660$		0			0
$661$	−30.0903	+	17.3726i	−1.17038	+	0.675717i	−0.953769	−	0.300541i	$-0.902833\pi$
$661$	−30.0903	+	17.3726i	−1.17038	+	0.675717i	−0.216608	+	0.976259i	$0.569499\pi$
$662$			11.4202i			0.443858i
$663$		0			0
$664$	−6.39020			−0.247988
$665$	−15.3726	−	5.96742i	−0.596125	−	0.231407i
$666$		0			0
$667$	−32.3819	−	18.6957i	−1.25383	−	0.723901i
$668$	12.9894			0.502576
$669$		0			0
$670$	6.12693	−	0.946808i	0.236704	−	0.0365784i
$671$		−	6.56228i		−	0.253334i
$672$		0			0
$673$	28.1953	−	16.2786i	1.08685	−	0.627492i	0.154113	−	0.988053i	$-0.450748\pi$
$673$	28.1953	−	16.2786i	1.08685	−	0.627492i	0.932736	+	0.360561i	$0.117415\pi$
$674$	−4.79092	+	2.76604i	−0.184539	+	0.106544i
$675$		0			0
$676$	−10.5153	−	7.64386i	−0.404434	−	0.293995i
$677$			32.2002i			1.23756i	0.785566	+	0.618778i	$0.212372\pi$
$677$			32.2002i			1.23756i	−0.785566	+	0.618778i	$0.787628\pi$
$678$		0			0
$679$	−1.47119	−	2.54818i	−0.0564593	−	0.0977903i
$680$	0.535898	+	3.46788i	0.0205508	+	0.132987i
$681$		0			0
$682$	−1.07169	+	1.85622i	−0.0410372	+	0.0710784i
$683$	3.19280	−	5.53009i	0.122169	−	0.211603i	−0.798454	−	0.602056i	$-0.794348\pi$
$683$	3.19280	−	5.53009i	0.122169	−	0.211603i	0.920623	+	0.390453i	$0.127682\pi$
$684$		0			0
$685$	−27.1453	+	4.19482i	−1.03717	+	0.160276i
$686$	8.91109	+	15.4345i	0.340227	+	0.589290i
$687$		0			0
$688$		−	5.28860i		−	0.201626i
$689$	−37.2916	+	33.5690i	−1.42070	+	1.27888i
$690$		0			0
$691$	13.6788	−	7.89748i	0.520368	−	0.300434i	−0.216717	−	0.976234i	$-0.569535\pi$
$691$	13.6788	−	7.89748i	0.520368	−	0.300434i	0.737085	+	0.675800i	$0.236202\pi$
$692$	−3.35755	+	1.93848i	−0.127635	+	0.0736900i
$693$		0			0
$694$		−	2.82008i		−	0.107049i
$695$	14.7114	−	2.27338i	0.558034	−	0.0862342i
$696$		0			0
$697$	2.46267			0.0932803
$698$	−23.0704	−	13.3197i	−0.873226	−	0.504157i
$699$		0			0
$700$	7.28207	−	2.30569i	0.275236	−	0.0871469i
$701$	43.7481			1.65234			0.826171	−	0.563420i	$-0.190515\pi$
$701$	43.7481			1.65234			0.826171	+	0.563420i	$0.190515\pi$
$702$		0			0
$703$		−	13.5309i		−	0.510329i
$704$	1.14057	−	0.658509i	0.0429869	−	0.0248185i
$705$		0			0
$706$	−6.61308	+	11.4542i	−0.248886	+	0.431084i
$707$	3.72537			0.140107
$708$		0			0
$709$	−30.0167	−	17.3302i	−1.12730	−	0.650848i	−0.184046	−	0.982918i	$-0.558920\pi$
$709$	−30.0167	−	17.3302i	−1.12730	−	0.650848i	−0.943255	+	0.332070i	$0.892253\pi$
$710$	−25.8654	+	20.7849i	−0.970713	+	0.780042i
$711$		0			0
$712$	−15.9738	+	9.22251i	−0.598645	+	0.345628i
$713$	6.87016	+	11.8995i	0.257290	+	0.445639i
$714$		0			0
$715$	−3.76665	−	9.92760i	−0.140865	−	0.371271i
$716$	14.1065			0.527185
$717$		0			0
$718$	10.7237	−	6.19133i	0.400205	−	0.231058i
$719$	21.9251	−	37.9755i	0.817670	−	1.41625i	−0.0897253	−	0.995967i	$-0.528599\pi$
$719$	21.9251	−	37.9755i	0.817670	−	1.41625i	0.907395	−	0.420279i	$-0.138068\pi$
$720$		0			0
$721$	16.4450	+	9.49451i	0.612443	+	0.353594i
$722$	2.15178	−	3.72700i	0.0800811	−	0.138704i
$723$		0			0
$724$	13.0736	−	22.6441i	0.485876	−	0.841563i
$725$	−21.1109	+	6.68425i	−0.784040	+	0.248247i
$726$		0			0
$727$		−	17.2599i		−	0.640136i	−0.947395	−	0.320068i	$-0.896294\pi$
$727$		−	17.2599i		−	0.640136i	0.947395	−	0.320068i	$-0.103706\pi$
$728$	−5.38789	+	1.14452i	−0.199688	+	0.0424188i
$729$		0			0
$730$	4.84653	−	12.4851i	0.179378	−	0.462095i
$731$	−4.14967	−	7.18744i	−0.153481	−	0.265837i
$732$		0			0
$733$	0.304799			0.0112580			0.00562900	−	0.999984i	$-0.498208\pi$
$733$	0.304799			0.0112580			0.00562900	+	0.999984i	$0.498208\pi$
$734$	−6.14226	−	3.54624i	−0.226715	−	0.130894i
$735$		0			0
$736$		−	8.44285i		−	0.311208i
$737$	−3.16231	−	1.82576i	−0.116485	−	0.0672528i
$738$		0			0
$739$	3.14941	−	1.81831i	0.115853	−	0.0668877i	−0.440954	−	0.897530i	$-0.645360\pi$
$739$	3.14941	−	1.81831i	0.115853	−	0.0668877i	0.556807	+	0.830642i	$0.312026\pi$
$740$	3.92599	+	4.88564i	0.144322	+	0.179600i
$741$		0			0
$742$			21.2592i			0.780451i
$743$	15.1150	+	26.1800i	0.554517	+	0.960451i	0.997941	+	0.0641394i	$0.0204302\pi$
$743$	15.1150	+	26.1800i	0.554517	+	0.960451i	−0.443424	+	0.896312i	$0.646236\pi$
$744$		0			0
$745$	−1.02826	−	6.65401i	−0.0376725	−	0.243784i
$746$			36.9803i			1.35395i
$747$		0			0
$748$	1.03339	−	1.78989i	0.0377845	−	0.0654447i
$749$		−	16.0049i		−	0.584805i
$750$		0			0
$751$	−0.00159080	−	0.00275535i	−5.80493e−5	−	0.000100544i	0.865996	−	0.500050i	$-0.166685\pi$
$751$	−0.00159080	−	0.00275535i	−5.80493e−5	−	0.000100544i	−0.866054	+	0.499950i	$0.833352\pi$
$752$	−2.47276	−	4.28295i	−0.0901723	−	0.156183i
$753$		0			0
$754$	15.6196	−	3.31800i	0.568833	−	0.120834i
$755$	−20.9423	+	16.8288i	−0.762170	+	0.612462i
$756$		0			0
$757$	−36.4328	+	21.0345i	−1.32417	+	0.764512i	−0.984392	−	0.175992i	$-0.943687\pi$
$757$	−36.4328	+	21.0345i	−1.32417	+	0.764512i	−0.339782	+	0.940504i	$0.610353\pi$
$758$	29.6252	+	17.1041i	1.07604	+	0.621250i
$759$		0			0
$760$	1.64851	+	10.6677i	0.0597976	+	0.386959i
$761$	−21.1489	−	12.2103i	−0.766646	−	0.442623i	0.0650310	−	0.997883i	$-0.479285\pi$
$761$	−21.1489	−	12.2103i	−0.766646	−	0.442623i	−0.831677	+	0.555260i	$0.812619\pi$
$762$		0			0
$763$	−22.7291	−	13.1226i	−0.822847	−	0.475071i
$764$	9.42713	+	16.3283i	0.341062	+	0.590736i
$765$		0			0
$766$	−26.0340			−0.940646
$767$	7.84643	+	36.9374i	0.283318	+	1.33373i
$768$		0			0
$769$	−28.1198	+	16.2350i	−1.01403	+	0.585449i	−0.912368	−	0.409370i	$-0.865748\pi$
$769$	−28.1198	+	16.2350i	−1.01403	+	0.585449i	−0.101659	+	0.994819i	$0.532415\pi$
$770$	−4.19401	−	1.62805i	−0.151141	−	0.0586708i
$771$		0			0
$772$	−17.8920			−0.643947
$773$	−4.13819	+	7.16756i	−0.148840	+	0.257799i	−0.930799	−	0.365531i	$-0.880887\pi$
$773$	−4.13819	+	7.16756i	−0.148840	+	0.257799i	0.781959	+	0.623330i	$0.214221\pi$
$774$		0			0
$775$	7.94649	+	1.75164i	0.285446	+	0.0629208i
$776$	−0.963028	+	1.66801i	−0.0345707	+	0.0598782i
$777$		0			0
$778$	−3.11784	−	5.40026i	−0.111780	−	0.193609i
$779$	7.57555			0.271422
$780$		0			0
$781$	19.5437			0.699328
$782$	−6.62464	−	11.4742i	−0.236897	−	0.410317i
$783$		0			0
$784$	2.33310	−	4.04106i	0.0833252	−	0.144323i
$785$	5.25620	−	4.22376i	0.187602	−	0.150753i
$786$		0			0
$787$	1.61500	−	2.79726i	0.0575685	−	0.0997115i	−0.835805	−	0.549027i	$-0.814999\pi$
$787$	1.61500	−	2.79726i	0.0575685	−	0.0997115i	0.893373	+	0.449315i	$0.148332\pi$
$788$	−0.625857			−0.0222952
$789$		0			0
$790$	−3.94582	+	10.1648i	−0.140386	+	0.361647i
$791$	−3.43958	+	1.98584i	−0.122297	+	0.0706085i
$792$		0			0
$793$	17.5732	−	3.73299i	0.624043	−	0.132562i
$794$	−36.6995			−1.30242
$795$		0			0
$796$	−8.84057	−	15.3123i	−0.313346	−	0.542731i
$797$	35.1612	+	20.3003i	1.24547	+	0.719075i	0.970203	−	0.242292i	$-0.0778990\pi$
$797$	35.1612	+	20.3003i	1.24547	+	0.719075i	0.275271	+	0.961367i	$0.411232\pi$
$798$		0			0
$799$	−6.72118	−	3.88048i	−0.237778	−	0.137281i
$800$	−3.69046	−	3.37350i	−0.130477	−	0.119271i
$801$		0			0
$802$	24.5044	+	14.1476i	0.865279	+	0.499569i
$803$	−6.83138	+	3.94410i	−0.241074	+	0.139184i
$804$		0			0
$805$	−22.4815	+	18.0656i	−0.792368	+	0.636729i
$806$	−5.58043	−	1.81397i	−0.196562	−	0.0638944i
$807$		0			0
$808$	−1.21929	−	2.11188i	−0.0428946	−	0.0742956i
$809$	−0.000840236	−	0.00145533i	−2.95411e−5	−	5.11667e-5i	0.866011	−	0.500026i	$-0.166676\pi$
$809$	−0.000840236	−	0.00145533i	−2.95411e−5	−	5.11667e-5i	−0.866040	+	0.499974i	$0.833343\pi$
$810$		0			0
$811$		−	34.9476i		−	1.22718i	−0.789626	−	0.613588i	$-0.789726\pi$
$811$		−	34.9476i		−	1.22718i	0.789626	−	0.613588i	$-0.210274\pi$
$812$	3.38286	−	5.85928i	0.118715	−	0.205621i
$813$		0			0
$814$		−	3.69154i		−	0.129389i
$815$	−21.9133	+	3.38631i	−0.767589	+	0.118617i
$816$		0			0
$817$	−12.7650	−	22.1097i	−0.446592	−	0.773519i
$818$		−	15.3280i		−	0.535931i
$819$		0			0
$820$	−2.73532	+	2.19804i	−0.0955215	+	0.0767589i
$821$	−22.0044	+	12.7042i	−0.767957	+	0.443380i	−0.832145	−	0.554557i	$-0.812888\pi$
$821$	−22.0044	+	12.7042i	−0.767957	+	0.443380i	0.0641882	+	0.997938i	$0.479554\pi$
$822$		0			0
$823$	−18.9040	−	10.9142i	−0.658952	−	0.380446i	0.132926	−	0.991126i	$-0.457563\pi$
$823$	−18.9040	−	10.9142i	−0.658952	−	0.380446i	−0.791878	+	0.610680i	$0.790896\pi$
$824$		−	12.4300i		−	0.433020i
$825$		0			0
$826$	13.8561	+	7.99982i	0.482115	+	0.278349i
$827$	18.9366			0.658492			0.329246	−	0.944244i	$-0.393206\pi$
$827$	18.9366			0.658492			0.329246	+	0.944244i	$0.393206\pi$
$828$		0			0
$829$	−0.304309	−	0.527078i	−0.0105691	−	0.0183062i	0.860692	−	0.509125i	$-0.170031\pi$
$829$	−0.304309	−	0.527078i	−0.0105691	−	0.0183062i	−0.871262	+	0.490819i	$0.836698\pi$
$830$	5.17082	−	13.3205i	0.179482	−	0.462362i
$831$		0			0
$832$	2.41225	+	2.67975i	0.0836296	+	0.0929036i
$833$		−	7.32263i		−	0.253714i
$834$		0			0
$835$	−10.5108	+	27.0768i	−0.363741	+	0.937030i
$836$	3.17887	−	5.50597i	0.109944	−	0.190428i
$837$		0			0
$838$	13.4692	−	23.3293i	0.465286	−	0.805898i
$839$	23.3215	+	13.4647i	0.805148	+	0.464853i	0.845268	−	0.534342i	$-0.179441\pi$
$839$	23.3215	+	13.4647i	0.805148	+	0.464853i	−0.0401198	+	0.999195i	$0.512774\pi$
$840$		0			0
$841$	4.69300	−	8.12852i	0.161828	−	0.280294i
$842$	−33.3731	+	19.2679i	−1.15011	+	0.664017i
$843$		0			0
$844$	17.2445			0.593581
$845$	24.4425	−	15.7341i	0.840849	−	0.541270i
$846$		0			0
$847$	−7.07731	−	12.2583i	−0.243179	−	0.421199i
$848$	12.0517	−	6.95804i	0.413856	−	0.238940i
$849$		0			0
$850$	−7.66250	−	1.68904i	−0.262822	−	0.0579336i
$851$	−20.4944	−	11.8325i	−0.702541	−	0.405612i
$852$		0			0
$853$	41.3790			1.41679			0.708394	−	0.705817i	$-0.249420\pi$
$853$	41.3790			1.41679			0.708394	+	0.705817i	$0.249420\pi$
$854$	3.80596	−	6.59212i	0.130237	−	0.225578i
$855$		0			0
$856$	−9.07302	+	5.23831i	−0.310109	+	0.179042i
$857$		−	30.6051i		−	1.04545i	−0.852501	−	0.522726i	$-0.824915\pi$
$857$		−	30.6051i		−	1.04545i	0.852501	−	0.522726i	$-0.175085\pi$
$858$		0			0
$859$	30.9385			1.05561			0.527803	−	0.849367i	$-0.323016\pi$
$859$	30.9385			1.05561			0.527803	+	0.849367i	$0.323016\pi$
$860$	11.0242	+	4.27942i	0.375922	+	0.145927i
$861$		0			0
$862$	2.48744	+	1.43612i	0.0847225	+	0.0489145i
$863$	−15.1133			−0.514464			−0.257232	−	0.966350i	$-0.582810\pi$
$863$	−15.1133			−0.514464			−0.257232	+	0.966350i	$0.582810\pi$
$864$		0			0
$865$	−1.32395	−	8.56746i	−0.0450156	−	0.291302i
$866$		−	12.9724i		−	0.440819i
$867$		0			0
$868$	−2.15313	+	1.24311i	−0.0730819	+	0.0421938i
$869$	5.56179	−	3.21110i	0.188671	−	0.108929i
$870$		0			0
$871$	3.09033	−	9.50698i	0.104712	−	0.322132i
$872$			17.1799i			0.581784i
$873$		0			0
$874$	−20.3784	−	35.2964i	−0.689310	−	1.19392i
$875$	−1.08624	+	17.0453i	−0.0367216	+	0.576238i
$876$		0			0
$877$	5.54757	−	9.60868i	0.187328	−	0.324462i	−0.757030	−	0.653380i	$-0.773351\pi$
$877$	5.54757	−	9.60868i	0.187328	−	0.324462i	0.944359	+	0.328918i	$0.106684\pi$
$878$	−1.02411	+	1.77380i	−0.0345619	+	0.0598629i
$879$		0			0
$880$	0.449750	+	2.91040i	0.0151611	+	0.0981094i
$881$	−22.3598	−	38.7283i	−0.753321	−	1.30479i	−0.946205	−	0.323568i	$-0.895117\pi$
$881$	−22.3598	−	38.7283i	−0.753321	−	1.30479i	0.192884	−	0.981222i	$-0.438216\pi$
$882$		0			0
$883$			10.9779i			0.369435i	0.982792	+	0.184718i	$0.0591371\pi$
$883$			10.9779i			0.369435i	−0.982792	+	0.184718i	$0.940863\pi$
$884$	5.38100	+	1.74914i	0.180983	+	0.0588301i
$885$		0			0
$886$	22.2640	−	12.8541i	0.747973	−	0.431842i
$887$	33.2555	−	19.2001i	1.11661	−	0.644675i	0.176076	−	0.984377i	$-0.443659\pi$
$887$	33.2555	−	19.2001i	1.11661	−	0.644675i	0.940533	+	0.339702i	$0.110326\pi$
$888$		0			0
$889$		−	12.3754i		−	0.415059i
$890$	−6.29881	−	40.7605i	−0.211136	−	1.36629i
$891$		0			0
$892$	−4.89716			−0.163969
$893$	−20.6754	−	11.9369i	−0.691876	−	0.399455i
$894$		0			0
$895$	−11.4147	+	29.4053i	−0.381551	+	0.982911i
$896$	1.52767			0.0510360
$897$		0			0
$898$		−	18.5625i		−	0.619440i
$899$	6.24197	−	3.60380i	0.208181	−	0.120193i
$900$		0			0
$901$	10.9192	−	18.9126i	0.363770	−	0.630069i
$902$	2.06678			0.0688163
$903$		0			0
$904$	2.25151	+	1.29991i	0.0748842	+	0.0432344i
$905$	36.6233	+	45.5754i	1.21740	+	1.51498i
$906$		0			0
$907$	−34.3953	+	19.8581i	−1.14208	+	0.659378i	−0.946944	−	0.321399i	$-0.895847\pi$
$907$	−34.3953	+	19.8581i	−1.14208	+	0.659378i	−0.195133	+	0.980777i	$0.562514\pi$
$908$	5.07567	+	8.79132i	0.168442	+	0.291750i
$909$		0			0
$910$	1.97399	−	12.1573i	0.0654370	−	0.403010i
$911$	−17.9575			−0.594959			−0.297479	−	0.954728i	$-0.596146\pi$
$911$	−17.9575			−0.594959			−0.297479	+	0.954728i	$0.596146\pi$
$912$		0			0
$913$	−7.28848	+	4.20801i	−0.241213	+	0.139265i
$914$	12.3213	−	21.3412i	0.407554	−	0.705904i
$915$		0			0
$916$	−13.3332	−	7.69794i	−0.440542	−	0.254347i
$917$	−1.77597	+	3.07607i	−0.0586476	+	0.101581i
$918$		0			0
$919$	10.0149	−	17.3463i	0.330361	−	0.572203i	−0.652221	−	0.758029i	$-0.726163\pi$
$919$	10.0149	−	17.3463i	0.330361	−	0.572203i	0.982583	+	0.185826i	$0.0594961\pi$
$920$	17.5993	+	6.83178i	0.580232	+	0.225237i
$921$		0			0
$922$		−	31.8342i		−	1.04840i
$923$	11.1175	+	52.3363i	0.365938	+	1.72267i
$924$		0			0
$925$	−13.3610	+	4.23045i	−0.439308	+	0.139096i
$926$	1.59160	+	2.75673i	0.0523031	+	0.0905916i
$927$		0			0
$928$	−4.42877			−0.145381
$929$	−35.1451	−	20.2910i	−1.15307	−	0.665727i	−0.203439	−	0.979088i	$-0.565212\pi$
$929$	−35.1451	−	20.2910i	−1.15307	−	0.665727i	−0.949634	+	0.313361i	$0.898545\pi$
$930$		0			0
$931$		−	22.5255i		−	0.738245i
$932$	8.58772	+	4.95812i	0.281300	+	0.162409i
$933$		0			0
$934$	−18.7708	+	10.8373i	−0.614200	+	0.354609i
$935$	2.89486	+	3.60246i	0.0946719	+	0.117813i
$936$		0			0
$937$			47.1112i			1.53905i	0.638614	+	0.769527i	$0.279508\pi$
$937$			47.1112i			1.53905i	−0.638614	+	0.769527i	$0.720492\pi$
$938$	−2.11779	−	3.66812i	−0.0691484	−	0.119769i
$939$		0			0
$940$	10.9288	−	1.68885i	0.356458	−	0.0550842i
$941$			4.35101i			0.141839i	0.997482	+	0.0709195i	$0.0225933\pi$
$941$			4.35101i			0.141839i	−0.997482	+	0.0709195i	$0.977407\pi$
$942$		0			0
$943$	6.62464	−	11.4742i	0.215728	−	0.373652i
$944$		−	10.4732i		−	0.340873i
$945$		0			0
$946$	−3.48259	−	6.03202i	−0.113229	−	0.196118i
$947$	−17.4580	−	30.2381i	−0.567307	−	0.982605i	−0.996831	−	0.0795494i	$-0.974652\pi$
$947$	−17.4580	−	30.2381i	−0.567307	−	0.982605i	0.429524	−	0.903056i	$-0.358681\pi$
$948$		0			0
$949$	−14.4480	−	16.0502i	−0.469002	−	0.521011i
$950$	−23.5710	−	5.19575i	−0.764745	−	0.168572i
$951$		0			0
$952$	2.07618	−	1.19868i	0.0672893	−	0.0388495i
$953$	−8.39700	−	4.84801i	−0.272005	−	0.157042i	0.357793	−	0.933801i	$-0.383529\pi$
$953$	−8.39700	−	4.84801i	−0.272005	−	0.157042i	−0.629799	+	0.776758i	$0.716863\pi$
$954$		0			0
$955$	−41.6649	+	6.43856i	−1.34824	+	0.208347i
$956$	8.19404	+	4.73083i	0.265014	+	0.153006i
$957$		0			0
$958$	−25.3765	−	14.6511i	−0.819876	−	0.473356i
$959$	9.38286	+	16.2516i	0.302988	+	0.524791i
$960$		0			0
$961$	28.3514			0.914561
$962$	9.88562	−	2.09995i	0.318725	−	0.0677052i
$963$		0			0
$964$	−11.3482	+	6.55189i	−0.365501	+	0.211022i
$965$	14.4778	−	37.2963i	0.466058	−	1.20061i
$966$		0			0
$967$	36.1715			1.16320			0.581599	−	0.813476i	$-0.302427\pi$
$967$	36.1715			1.16320			0.581599	+	0.813476i	$0.302427\pi$
$968$	−4.63273	+	8.02413i	−0.148902	+	0.257905i
$969$		0			0
$970$	−2.69775	−	3.35718i	−0.0866195	−	0.107792i
$971$	−0.194688	+	0.337209i	−0.00624783	+	0.0108216i	−0.869132	−	0.494579i	$-0.835322\pi$
$971$	−0.194688	+	0.337209i	−0.00624783	+	0.0108216i	0.862885	+	0.505401i	$0.168655\pi$
$972$		0			0
$973$	−5.08503	−	8.80753i	−0.163019	−	0.282356i
$974$	−42.5287			−1.36271
$975$		0			0
$976$	−4.98268			−0.159492
$977$	2.70086	+	4.67802i	0.0864080	+	0.149663i	0.905990	−	0.423298i	$-0.139128\pi$
$977$	2.70086	+	4.67802i	0.0864080	+	0.149663i	−0.819582	+	0.572961i	$0.805794\pi$
$978$		0			0
$979$	−12.1462	+	21.0378i	−0.388194	+	0.672372i
$980$	6.53577	+	8.13334i	0.208777	+	0.259810i
$981$		0			0
$982$	−6.32521	+	10.9556i	−0.201845	+	0.349607i
$983$	−43.6819			−1.39324			−0.696618	−	0.717442i	$-0.745313\pi$
$983$	−43.6819			−1.39324			−0.696618	+	0.717442i	$0.745313\pi$
$984$		0			0
$985$	0.506430	−	1.30461i	0.0161362	−	0.0415684i
$986$	−6.01889	+	3.47501i	−0.191681	+	0.110667i
$987$		0			0
$988$	16.5528	+	5.38064i	0.526615	+	0.171181i
$989$	−44.6508			−1.41981
$990$		0			0
$991$	27.9427	+	48.3981i	0.887628	+	1.53742i	0.842671	+	0.538428i	$0.180982\pi$
$991$	27.9427	+	48.3981i	0.887628	+	1.53742i	0.0449569	+	0.998989i	$0.485685\pi$
$992$	1.40941	+	0.813725i	0.0447489	+	0.0258358i
$993$		0			0
$994$	19.6325	+	11.3349i	0.622706	+	0.359520i
$995$	39.0725	−	6.03795i	1.23868	−	0.191416i
$996$		0			0
$997$	30.9866	+	17.8901i	0.981357	+	0.566587i	0.902680	−	0.430314i	$-0.141597\pi$
$997$	30.9866	+	17.8901i	0.981357	+	0.566587i	0.0786773	+	0.996900i	$0.474930\pi$
$998$	−3.93182	+	2.27004i	−0.124460	+	0.0718567i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.c.829.2		12
3.2	odd	2		390.2.x.b.49.5	yes	12
5.4	even	2		1170.2.bj.d.829.5		12
13.4	even	6		1170.2.bj.d.199.5		12
15.2	even	4		1950.2.bc.i.751.1		12
15.8	even	4		1950.2.bc.j.751.6		12
15.14	odd	2		390.2.x.a.49.2	✓	12
39.17	odd	6		390.2.x.a.199.2	yes	12
65.4	even	6	inner	1170.2.bj.c.199.2		12
195.17	even	12		1950.2.bc.i.901.1		12
195.134	odd	6		390.2.x.b.199.5	yes	12
195.173	even	12		1950.2.bc.j.901.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.2	✓	12	15.14	odd	2
390.2.x.a.199.2	yes	12	39.17	odd	6
390.2.x.b.49.5	yes	12	3.2	odd	2
390.2.x.b.199.5	yes	12	195.134	odd	6
1170.2.bj.c.199.2		12	65.4	even	6	inner
1170.2.bj.c.829.2		12	1.1	even	1	trivial
1170.2.bj.d.199.5		12	13.4	even	6
1170.2.bj.d.829.5		12	5.4	even	2
1950.2.bc.i.751.1		12	15.2	even	4
1950.2.bc.i.901.1		12	195.17	even	12
1950.2.bc.j.751.6		12	15.8	even	4
1950.2.bc.j.901.6		12	195.173	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(-0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(-0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(-0.809179 + 2.08452i) q^{10} +(1.14057 - 0.658509i) q^{11} +(2.41225 + 2.67975i) q^{13} +1.52767 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.35904 - 0.784645i) q^{17} +(-4.18063 - 2.41369i) q^{19} +(2.20984 - 0.341491i) q^{20} +(-1.14057 - 0.658509i) q^{22} +(-7.31172 + 4.22143i) q^{23} +(-1.07631 + 4.88278i) q^{25} +(1.11461 - 3.42894i) q^{26} +(-0.763837 - 1.32301i) q^{28} +(2.21438 + 3.83543i) q^{29} -1.62745i q^{31} +(-0.500000 + 0.866025i) q^{32} +1.56929i q^{34} +(3.37591 - 0.521687i) q^{35} +(1.40148 + 2.42743i) q^{37} +4.82738i q^{38} +(-1.40066 - 1.74303i) q^{40} +(-1.35904 + 0.784645i) q^{41} +(4.58006 + 2.64430i) q^{43} +1.31702i q^{44} +(7.31172 + 4.22143i) q^{46} +4.94552 q^{47} +(2.33310 + 4.04106i) q^{49} +(4.76677 - 1.50928i) q^{50} +(-3.52686 + 0.749192i) q^{52} +13.9161i q^{53} +(-2.74535 - 1.06570i) q^{55} +(-0.763837 + 1.32301i) q^{56} +(2.21438 - 3.83543i) q^{58} +(9.07005 + 5.23660i) q^{59} +(2.49134 - 4.31513i) q^{61} +(-1.40941 + 0.813725i) q^{62} +1.00000 q^{64} +(1.29215 - 7.95804i) q^{65} +(-1.38628 - 2.40112i) q^{67} +(1.35904 - 0.784645i) q^{68} +(-2.13975 - 2.66278i) q^{70} +(12.8513 + 7.41968i) q^{71} -5.98944 q^{73} +(1.40148 - 2.42743i) q^{74} +(4.18063 - 2.41369i) q^{76} +2.01198i q^{77} +4.87632 q^{79} +(-0.809179 + 2.08452i) q^{80} +(1.35904 + 0.784645i) q^{82} -6.39020 q^{83} +(0.535898 + 3.46788i) q^{85} -5.28860i q^{86} +(1.14057 - 0.658509i) q^{88} +(-15.9738 + 9.22251i) q^{89} +(-5.38789 + 1.14452i) q^{91} -8.44285i q^{92} +(-2.47276 - 4.28295i) q^{94} +(1.64851 + 10.6677i) q^{95} +(-0.963028 + 1.66801i) q^{97} +(2.33310 - 4.04106i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

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