LMFDB - Embedded newform 585.2.j.h.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 50x^6 - 42x^5 + 124x^4 - 12x^3 + 96x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.1
Root			$1.31604 - 2.27945i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.h.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31604 - 2.27945i) q^{2} +(-2.46394 + 4.26767i) q^{4} +1.00000 q^{5} +(-0.544875 + 0.943751i) q^{7} +7.70645 q^{8} +O(q^{10})$	\(q+(-1.31604 - 2.27945i) q^{2} +(-2.46394 + 4.26767i) q^{4} +1.00000 q^{5} +(-0.544875 + 0.943751i) q^{7} +7.70645 q^{8} +(-1.31604 - 2.27945i) q^{10} +(-2.36092 - 4.08923i) q^{11} +(-3.42647 + 1.12219i) q^{13} +2.86832 q^{14} +(-5.21415 - 9.03117i) q^{16} +(-2.61184 + 4.52384i) q^{17} +(-1.46394 + 2.53562i) q^{19} +(-2.46394 + 4.26767i) q^{20} +(-6.21415 + 10.7632i) q^{22} +(3.85323 + 6.67399i) q^{23} +1.00000 q^{25} +(7.06737 + 6.33362i) q^{26} +(-2.68508 - 4.65070i) q^{28} +(-0.655591 - 1.13552i) q^{29} -2.32091 q^{31} +(-6.01764 + 10.4229i) q^{32} +13.7492 q^{34} +(-0.544875 + 0.943751i) q^{35} +(5.21415 + 9.03117i) q^{37} +7.70645 q^{38} +7.70645 q^{40} +(-2.49373 - 4.31926i) q^{41} +(-2.98419 + 5.16877i) q^{43} +23.2687 q^{44} +(10.1420 - 17.5665i) q^{46} -8.51804 q^{47} +(2.90622 + 5.03372i) q^{49} +(-1.31604 - 2.27945i) q^{50} +(3.65346 - 17.3881i) q^{52} -9.67627 q^{53} +(-2.36092 - 4.08923i) q^{55} +(-4.19906 + 7.27298i) q^{56} +(-1.72557 + 2.98878i) q^{58} +(1.58348 - 2.74266i) q^{59} +(-3.16045 + 5.47406i) q^{61} +(3.05441 + 5.29040i) q^{62} +10.8213 q^{64} +(-3.42647 + 1.12219i) q^{65} +(0.787679 + 1.36430i) q^{67} +(-12.8709 - 22.2930i) q^{68} +2.86832 q^{70} +(3.00113 - 5.19810i) q^{71} +12.3098 q^{73} +(13.7241 - 23.7708i) q^{74} +(-7.21415 - 12.4953i) q^{76} +5.14562 q^{77} -3.04333 q^{79} +(-5.21415 - 9.03117i) q^{80} +(-6.56371 + 11.3687i) q^{82} -1.40782 q^{83} +(-2.61184 + 4.52384i) q^{85} +15.7093 q^{86} +(-18.1943 - 31.5135i) q^{88} +(4.33742 + 7.51262i) q^{89} +(0.807924 - 3.84519i) q^{91} -37.9765 q^{92} +(11.2101 + 19.4165i) q^{94} +(-1.46394 + 2.53562i) q^{95} +(5.51622 - 9.55437i) q^{97} +(7.64943 - 13.2492i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8	$ 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8 - 2 * q^10 - 8 * q^11 + q^13 - 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 - 14 * q^22 + 6 * q^23 + 10 * q^25 - 10 * q^26 + 2 * q^28 - 16 * q^29 + 18 * q^31 - 14 * q^32 - q^35 + 4 * q^37 + 12 * q^38 + 12 * q^40 - 6 * q^41 - 15 * q^43 + 28 * q^44 + 16 * q^46 + 20 * q^47 - 10 * q^49 - 2 * q^50 - 22 * q^52 - 40 * q^53 - 8 * q^55 + 2 * q^56 + 4 * q^58 - 12 * q^59 - 11 * q^61 + 22 * q^62 + 8 * q^64 + q^65 - 5 * q^67 - 50 * q^68 - 8 * q^70 - 10 * q^71 + 2 * q^73 + 26 * q^74 - 24 * q^76 + 84 * q^77 - 34 * q^79 - 4 * q^80 - 16 * q^82 + 32 * q^83 + 88 * q^86 - 20 * q^88 - 4 * q^89 - q^91 - 68 * q^92 + 16 * q^94 + 4 * q^95 + 11 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.31604	−	2.27945i	−0.930584	−	1.61182i	−0.782326	−	0.622869i	$-0.785967\pi$
$2$	−1.31604	−	2.27945i	−0.930584	−	1.61182i	−0.148258	−	0.988949i	$-0.547366\pi$
$3$		0			0
$3$		0			0
$4$	−2.46394	+	4.26767i	−1.23197	+	2.13384i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.544875	+	0.943751i	−0.205943	+	0.356704i	−0.950433	−	0.310930i	$-0.899360\pi$
$7$	−0.544875	+	0.943751i	−0.205943	+	0.356704i	0.744489	+	0.667634i	$0.232693\pi$
$8$	7.70645			2.72464
$9$		0			0
$10$	−1.31604	−	2.27945i	−0.416170	−	0.720827i
$11$	−2.36092	−	4.08923i	−0.711844	−	1.23295i	−0.964164	−	0.265306i	$-0.914527\pi$
$11$	−2.36092	−	4.08923i	−0.711844	−	1.23295i	0.252320	−	0.967644i	$-0.418806\pi$
$12$		0			0
$13$	−3.42647	+	1.12219i	−0.950331	+	0.311241i
$13$	−3.42647	+	1.12219i	−0.950331	+	0.311241i
$14$	2.86832			0.766590
$15$		0			0
$16$	−5.21415	−	9.03117i	−1.30354	−	2.25779i
$17$	−2.61184	+	4.52384i	−0.633465	+	1.09719i	0.353373	+	0.935482i	$0.385035\pi$
$17$	−2.61184	+	4.52384i	−0.633465	+	1.09719i	−0.986838	+	0.161711i	$0.948299\pi$
$18$		0			0
$19$	−1.46394	+	2.53562i	−0.335852	+	0.581712i	−0.983648	−	0.180101i	$-0.942357\pi$
$19$	−1.46394	+	2.53562i	−0.335852	+	0.581712i	0.647796	+	0.761813i	$0.275691\pi$
$20$	−2.46394	+	4.26767i	−0.550954	+	0.954281i
$21$		0			0
$22$	−6.21415	+	10.7632i	−1.32486	+	2.29473i
$23$	3.85323	+	6.67399i	0.803453	+	1.39162i	0.917330	+	0.398127i	$0.130340\pi$
$23$	3.85323	+	6.67399i	0.803453	+	1.39162i	−0.113877	+	0.993495i	$0.536327\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	7.06737	+	6.33362i	1.38603	+	1.24213i
$27$		0			0
$28$	−2.68508	−	4.65070i	−0.507433	−	0.878900i
$29$	−0.655591	−	1.13552i	−0.121740	−	0.210860i	0.798714	−	0.601711i	$-0.205514\pi$
$29$	−0.655591	−	1.13552i	−0.121740	−	0.210860i	−0.920454	+	0.390851i	$0.872181\pi$
$30$		0			0
$31$	−2.32091			−0.416847			−0.208423	−	0.978039i	$-0.566833\pi$
$31$	−2.32091			−0.416847			−0.208423	+	0.978039i	$0.566833\pi$
$32$	−6.01764	+	10.4229i	−1.06378	+	1.84252i
$33$		0			0
$34$	13.7492			2.35797
$35$	−0.544875	+	0.943751i	−0.0921007	+	0.159523i
$36$		0			0
$37$	5.21415	+	9.03117i	0.857200	+	1.48471i	0.874589	+	0.484866i	$0.161132\pi$
$37$	5.21415	+	9.03117i	0.857200	+	1.48471i	−0.0173882	+	0.999849i	$0.505535\pi$
$38$	7.70645			1.25015
$39$		0			0
$40$	7.70645			1.21850
$41$	−2.49373	−	4.31926i	−0.389455	−	0.674555i	0.602921	−	0.797801i	$-0.294003\pi$
$41$	−2.49373	−	4.31926i	−0.389455	−	0.674555i	−0.992376	+	0.123245i	$0.960670\pi$
$42$		0			0
$43$	−2.98419	+	5.16877i	−0.455084	+	0.788229i	−0.998693	−	0.0511094i	$-0.983724\pi$
$43$	−2.98419	+	5.16877i	−0.455084	+	0.788229i	0.543609	+	0.839339i	$0.317058\pi$
$44$	23.2687			3.50789
$45$		0			0
$46$	10.1420	−	17.5665i	1.49536	−	2.59004i
$47$	−8.51804			−1.24248			−0.621242	−	0.783619i	$-0.713372\pi$
$47$	−8.51804			−1.24248			−0.621242	+	0.783619i	$0.713372\pi$
$48$		0			0
$49$	2.90622	+	5.03372i	0.415175	+	0.719104i
$50$	−1.31604	−	2.27945i	−0.186117	−	0.322364i
$51$		0			0
$52$	3.65346	−	17.3881i	0.506644	−	2.41129i
$53$	−9.67627			−1.32914			−0.664569	−	0.747227i	$-0.731385\pi$
$53$	−9.67627			−1.32914			−0.664569	+	0.747227i	$0.731385\pi$
$54$		0			0
$55$	−2.36092	−	4.08923i	−0.318346	−	0.551392i
$56$	−4.19906	+	7.27298i	−0.561122	+	0.971892i
$57$		0			0
$58$	−1.72557	+	2.98878i	−0.226579	+	0.392446i
$59$	1.58348	−	2.74266i	0.206151	−	0.357064i	−0.744348	−	0.667792i	$-0.767239\pi$
$59$	1.58348	−	2.74266i	0.206151	−	0.357064i	0.950499	+	0.310728i	$0.100573\pi$
$60$		0			0
$61$	−3.16045	+	5.47406i	−0.404655	+	0.700882i	−0.994281	−	0.106794i	$-0.965942\pi$
$61$	−3.16045	+	5.47406i	−0.404655	+	0.700882i	0.589627	+	0.807676i	$0.299275\pi$
$62$	3.05441	+	5.29040i	0.387911	+	0.671881i
$63$		0			0
$64$	10.8213			1.35266
$65$	−3.42647	+	1.12219i	−0.425001	+	0.139191i
$66$		0			0
$67$	0.787679	+	1.36430i	0.0962303	+	0.166676i	0.910121	−	0.414342i	$-0.135988\pi$
$67$	0.787679	+	1.36430i	0.0962303	+	0.166676i	−0.813891	+	0.581017i	$0.802655\pi$
$68$	−12.8709	−	22.2930i	−1.56082	−	2.70342i
$69$		0			0
$70$	2.86832			0.342830
$71$	3.00113	−	5.19810i	0.356168	−	0.616901i	−0.631149	−	0.775662i	$-0.717416\pi$
$71$	3.00113	−	5.19810i	0.356168	−	0.616901i	0.987317	+	0.158760i	$0.0507497\pi$
$72$		0			0
$73$	12.3098			1.44075			0.720374	−	0.693586i	$-0.243970\pi$
$73$	12.3098			1.44075			0.720374	+	0.693586i	$0.243970\pi$
$74$	13.7241	−	23.7708i	1.59539	−	2.76330i
$75$		0			0
$76$	−7.21415	−	12.4953i	−0.827519	−	1.43331i
$77$	5.14562			0.586398
$78$		0			0
$79$	−3.04333			−0.342401			−0.171201	−	0.985236i	$-0.554765\pi$
$79$	−3.04333			−0.342401			−0.171201	+	0.985236i	$0.554765\pi$
$80$	−5.21415	−	9.03117i	−0.582959	−	1.00972i
$81$		0			0
$82$	−6.56371	+	11.3687i	−0.724840	+	1.25546i
$83$	−1.40782			−0.154528			−0.0772640	−	0.997011i	$-0.524618\pi$
$83$	−1.40782			−0.154528			−0.0772640	+	0.997011i	$0.524618\pi$
$84$		0			0
$85$	−2.61184	+	4.52384i	−0.283294	+	0.490680i
$86$	15.7093			1.69398
$87$		0			0
$88$	−18.1943	−	31.5135i	−1.93952	−	3.35935i
$89$	4.33742	+	7.51262i	0.459765	+	0.796337i	0.998948	−	0.0458520i	$-0.0146003\pi$
$89$	4.33742	+	7.51262i	0.459765	+	0.796337i	−0.539183	+	0.842189i	$0.681267\pi$
$90$		0			0
$91$	0.807924	−	3.84519i	0.0846935	−	0.403085i
$92$	−37.9765			−3.95933
$93$		0			0
$94$	11.2101	+	19.4165i	1.15624	+	2.00266i
$95$	−1.46394	+	2.53562i	−0.150197	+	0.260150i
$96$		0			0
$97$	5.51622	−	9.55437i	0.560087	−	0.970099i	−0.437401	−	0.899266i	$-0.644101\pi$
$97$	5.51622	−	9.55437i	0.560087	−	0.970099i	0.997488	−	0.0708327i	$-0.0225657\pi$
$98$	7.64943	−	13.2492i	0.772709	−	1.33837i
$99$		0			0
$100$	−2.46394	+	4.26767i	−0.246394	+	0.426767i
$101$	4.60746	+	7.98035i	0.458459	+	0.794075i	0.998880	−	0.0473204i	$-0.0150682\pi$
$101$	4.60746	+	7.98035i	0.458459	+	0.794075i	−0.540421	+	0.841395i	$0.681735\pi$
$102$		0			0
$103$	14.8586			1.46406			0.732031	−	0.681271i	$-0.238572\pi$
$103$	14.8586			1.46406			0.732031	+	0.681271i	$0.238572\pi$
$104$	−26.4059	+	8.64814i	−2.58931	+	0.848020i
$105$		0			0
$106$	12.7344	+	22.0566i	1.23687	+	2.14233i
$107$	−3.44743	−	5.97113i	−0.333276	−	0.577251i	0.649876	−	0.760040i	$-0.274821\pi$
$107$	−3.44743	−	5.97113i	−0.333276	−	0.577251i	−0.983152	+	0.182789i	$0.941487\pi$
$108$		0			0
$109$	−14.5790			−1.39642			−0.698208	−	0.715895i	$-0.746019\pi$
$109$	−14.5790			−1.39642			−0.698208	+	0.715895i	$0.746019\pi$
$110$	−6.21415	+	10.7632i	−0.592496	+	1.02623i
$111$		0			0
$112$	11.3642			1.07382
$113$	−6.64689	+	11.5127i	−0.625286	+	1.08303i	0.363199	+	0.931712i	$0.381685\pi$
$113$	−6.64689	+	11.5127i	−0.625286	+	1.08303i	−0.988485	+	0.151316i	$0.951649\pi$
$114$		0			0
$115$	3.85323	+	6.67399i	0.359315	+	0.622352i
$116$	6.46136			0.599922
$117$		0			0
$118$	−8.33570			−0.767364
$119$	−2.84626	−	4.92986i	−0.260916	−	0.451920i
$120$		0			0
$121$	−5.64788	+	9.78241i	−0.513443	+	0.889310i
$122$	16.6372			1.50626
$123$		0			0
$124$	5.71858	−	9.90487i	0.513544	−	0.889484i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.72740	−	13.3842i	−0.685696	−	1.18766i	−0.973218	−	0.229886i	$-0.926165\pi$
$127$	−7.72740	−	13.3842i	−0.685696	−	1.18766i	0.287522	−	0.957774i	$-0.407169\pi$
$128$	−2.20605	−	3.82099i	−0.194989	−	0.337731i
$129$		0			0
$130$	7.06737	+	6.33362i	0.619850	+	0.555495i
$131$	−8.48870			−0.741661			−0.370831	−	0.928701i	$-0.620927\pi$
$131$	−8.48870			−0.741661			−0.370831	+	0.928701i	$0.620927\pi$
$132$		0			0
$133$	−1.59533	−	2.76320i	−0.138333	−	0.239600i
$134$	2.07324	−	3.59096i	0.179101	−	0.310211i
$135$		0			0
$136$	−20.1280	+	34.8628i	−1.72597	+	2.98946i
$137$	2.86093	−	4.95527i	0.244426	−	0.423357i	−0.717544	−	0.696513i	$-0.754734\pi$
$137$	2.86093	−	4.95527i	0.244426	−	0.423357i	0.961970	+	0.273155i	$0.0880673\pi$
$138$		0			0
$139$	9.19692	−	15.9295i	0.780072	−	1.35112i	−0.151827	−	0.988407i	$-0.548516\pi$
$139$	9.19692	−	15.9295i	0.780072	−	1.35112i	0.931899	−	0.362718i	$-0.118151\pi$
$140$	−2.68508	−	4.65070i	−0.226931	−	0.393056i
$141$		0			0
$142$	−15.7985			−1.32578
$143$	12.6785	+	11.3622i	1.06023	+	0.950156i
$144$		0			0
$145$	−0.655591	−	1.13552i	−0.0544439	−	0.0942996i
$146$	−16.2002	−	28.0595i	−1.34074	−	2.32222i
$147$		0			0
$148$	−51.3894			−4.22419
$149$	−11.3302	+	19.6244i	−0.928202	+	1.60769i	−0.141874	+	0.989885i	$0.545313\pi$
$149$	−11.3302	+	19.6244i	−0.928202	+	1.60769i	−0.786328	+	0.617809i	$0.788021\pi$
$150$		0			0
$151$	−2.26871			−0.184625			−0.0923125	−	0.995730i	$-0.529426\pi$
$151$	−2.26871			−0.184625			−0.0923125	+	0.995730i	$0.529426\pi$
$152$	−11.2818	+	19.5407i	−0.915076	+	1.58496i
$153$		0			0
$154$	−6.77187	−	11.7292i	−0.545693	−	0.945167i
$155$	−2.32091			−0.186420
$156$		0			0
$157$	−13.8934			−1.10882			−0.554409	−	0.832245i	$-0.687056\pi$
$157$	−13.8934			−1.10882			−0.554409	+	0.832245i	$0.687056\pi$
$158$	4.00515	+	6.93713i	0.318633	+	0.551888i
$159$		0			0
$160$	−6.01764	+	10.4229i	−0.475736	+	0.823999i
$161$	−8.39811			−0.661864
$162$		0			0
$163$	−12.3109	+	21.3231i	−0.964264	+	1.67015i	−0.252684	+	0.967549i	$0.581313\pi$
$163$	−12.3109	+	21.3231i	−0.964264	+	1.67015i	−0.711580	+	0.702605i	$0.752020\pi$
$164$	24.5776			1.91919
$165$		0			0
$166$	1.85275	+	3.20906i	0.143801	+	0.249071i
$167$	−1.89994	−	3.29079i	−0.147022	−	0.254649i	0.783104	−	0.621891i	$-0.213635\pi$
$167$	−1.89994	−	3.29079i	−0.147022	−	0.254649i	−0.930125	+	0.367242i	$0.880302\pi$
$168$		0			0
$169$	10.4814	−	7.69033i	0.806258	−	0.591564i
$170$	13.7492			1.05452
$171$		0			0
$172$	−14.7057	−	25.4711i	−1.12130	−	1.94215i
$173$	−9.04014	+	15.6580i	−0.687309	+	1.19045i	0.285396	+	0.958410i	$0.407875\pi$
$173$	−9.04014	+	15.6580i	−0.687309	+	1.19045i	−0.972705	+	0.232044i	$0.925459\pi$
$174$		0			0
$175$	−0.544875	+	0.943751i	−0.0411887	+	0.0713409i
$176$	−24.6204	+	42.6437i	−1.85583	+	3.21439i
$177$		0			0
$178$	11.4165	−	19.7739i	0.855700	−	1.48212i
$179$	−12.8224	−	22.2091i	−0.958394	−	1.65999i	−0.726403	−	0.687269i	$-0.758809\pi$
$179$	−12.8224	−	22.2091i	−0.958394	−	1.65999i	−0.231991	−	0.972718i	$-0.574524\pi$
$180$		0			0
$181$	−19.0957			−1.41937			−0.709686	−	0.704518i	$-0.751163\pi$
$181$	−19.0957			−1.41937			−0.709686	+	0.704518i	$0.751163\pi$
$182$	−9.82820	+	3.21881i	−0.728515	+	0.238594i
$183$		0			0
$184$	29.6947	+	51.4328i	2.18912	+	3.79167i
$185$	5.21415	+	9.03117i	0.383352	+	0.663985i
$186$		0			0
$187$	24.6654			1.80371
$188$	20.9880	−	36.3522i	1.53071	−	2.65126i
$189$		0			0
$190$	7.70645			0.559085
$191$	12.0769	−	20.9178i	0.873853	−	1.51356i	0.0158737	−	0.999874i	$-0.494947\pi$
$191$	12.0769	−	20.9178i	0.873853	−	1.51356i	0.857979	−	0.513684i	$-0.171720\pi$
$192$		0			0
$193$	−6.39781	−	11.0813i	−0.460524	−	0.797652i	0.538463	−	0.842649i	$-0.319005\pi$
$193$	−6.39781	−	11.0813i	−0.460524	−	0.797652i	−0.998987	+	0.0449976i	$0.985672\pi$
$194$	−29.0383			−2.08483
$195$		0			0
$196$	−28.6431			−2.04593
$197$	−0.326273	−	0.565122i	−0.0232460	−	0.0402632i	0.854168	−	0.519997i	$-0.174067\pi$
$197$	−0.326273	−	0.565122i	−0.0232460	−	0.0402632i	−0.877414	+	0.479733i	$0.840733\pi$
$198$		0			0
$199$	3.19389	−	5.53198i	0.226409	−	0.392152i	−0.730332	−	0.683092i	$-0.760635\pi$
$199$	3.19389	−	5.53198i	0.226409	−	0.392152i	0.956741	+	0.290940i	$0.0939681\pi$
$200$	7.70645			0.544929
$201$		0			0
$202$	12.1272	−	21.0050i	0.853269	−	1.47791i
$203$	1.42886			0.100286
$204$		0			0
$205$	−2.49373	−	4.31926i	−0.174169	−	0.301670i
$206$	−19.5546	−	33.8695i	−1.36243	−	2.35980i
$207$		0			0
$208$	28.0008	+	25.0937i	1.94151	+	1.73994i
$209$	13.8250			0.956296
$210$		0			0
$211$	8.74879	+	15.1534i	0.602292	+	1.04320i	0.992473	+	0.122462i	$0.0390789\pi$
$211$	8.74879	+	15.1534i	0.602292	+	1.04320i	−0.390182	+	0.920738i	$0.627588\pi$
$212$	23.8418	−	41.2952i	1.63746	−	2.83617i
$213$		0			0
$214$	−9.07395	+	15.7165i	−0.620282	+	1.07436i
$215$	−2.98419	+	5.16877i	−0.203520	+	0.352507i
$216$		0			0
$217$	1.26460	−	2.19036i	0.0858469	−	0.148691i
$218$	19.1866	+	33.2322i	1.29948	+	2.25077i
$219$		0			0
$220$	23.2687			1.56877
$221$	3.87276	−	18.4318i	0.260510	−	1.23986i
$222$		0			0
$223$	1.32675	+	2.29800i	0.0888458	+	0.153885i	0.907024	−	0.421080i	$-0.138349\pi$
$223$	1.32675	+	2.29800i	0.0888458	+	0.153885i	−0.818178	+	0.574965i	$0.805016\pi$
$224$	−6.55772	−	11.3583i	−0.438156	−	0.758909i
$225$		0			0
$226$	34.9904			2.32753
$227$	2.55482	−	4.42508i	0.169569	−	0.293703i	−0.768699	−	0.639611i	$-0.779096\pi$
$227$	2.55482	−	4.42508i	0.169569	−	0.293703i	0.938269	+	0.345908i	$0.112429\pi$
$228$		0			0
$229$	17.2929			1.14275			0.571375	−	0.820689i	$-0.306410\pi$
$229$	17.2929			1.14275			0.571375	+	0.820689i	$0.306410\pi$
$230$	10.1420	−	17.5665i	0.668746	−	1.15830i
$231$		0			0
$232$	−5.05228	−	8.75081i	−0.331699	−	0.574519i
$233$	2.40701			0.157688			0.0788441	−	0.996887i	$-0.474877\pi$
$233$	2.40701			0.157688			0.0788441	+	0.996887i	$0.474877\pi$
$234$		0			0
$235$	−8.51804			−0.555656
$236$	7.80320	+	13.5155i	0.507945	+	0.879786i
$237$		0			0
$238$	−7.49160	+	12.9758i	−0.485608	+	0.841098i
$239$	8.83530			0.571508			0.285754	−	0.958303i	$-0.407756\pi$
$239$	8.83530			0.571508			0.285754	+	0.958303i	$0.407756\pi$
$240$		0			0
$241$	4.27027	−	7.39633i	0.275072	−	0.476439i	−0.695081	−	0.718931i	$-0.744632\pi$
$241$	4.27027	−	7.39633i	0.275072	−	0.476439i	0.970153	+	0.242492i	$0.0779648\pi$
$242$	29.7314			1.91121
$243$		0			0
$244$	−15.5744	−	26.9756i	−0.997046	−	1.72693i
$245$	2.90622	+	5.03372i	0.185672	+	0.321593i
$246$		0			0
$247$	2.17069	−	10.3311i	0.138118	−	0.657350i
$248$	−17.8860			−1.13576
$249$		0			0
$250$	−1.31604	−	2.27945i	−0.0832339	−	0.144165i
$251$	−1.27257	+	2.20415i	−0.0803237	+	0.139125i	−0.903389	−	0.428822i	$-0.858929\pi$
$251$	−1.27257	+	2.20415i	−0.0803237	+	0.139125i	0.823065	+	0.567947i	$0.192262\pi$
$252$		0			0
$253$	18.1943	−	31.5135i	1.14387	−	1.98124i
$254$	−20.3392	+	35.2285i	−1.27619	+	2.21043i
$255$		0			0
$256$	5.01480	−	8.68589i	0.313425	−	0.542868i
$257$	−6.02563	−	10.4367i	−0.375868	−	0.651023i	0.614588	−	0.788848i	$-0.289322\pi$
$257$	−6.02563	−	10.4367i	−0.375868	−	0.651023i	−0.990457	+	0.137825i	$0.955989\pi$
$258$		0			0
$259$	−11.3642			−0.706139
$260$	3.65346	−	17.3881i	0.226578	−	1.07836i
$261$		0			0
$262$	11.1715	+	19.3496i	0.690178	+	1.19542i
$263$	5.23646	+	9.06982i	0.322894	+	0.559269i	0.981084	−	0.193583i	$-0.0620109\pi$
$263$	5.23646	+	9.06982i	0.322894	+	0.559269i	−0.658190	+	0.752852i	$0.728678\pi$
$264$		0			0
$265$	−9.67627			−0.594409
$266$	−4.19906	+	7.27298i	−0.257461	+	0.445935i
$267$		0			0
$268$	−7.76318			−0.474212
$269$	−4.46163	+	7.72777i	−0.272030	+	0.471170i	−0.969382	−	0.245559i	$-0.921028\pi$
$269$	−4.46163	+	7.72777i	−0.272030	+	0.471170i	0.697351	+	0.716729i	$0.254362\pi$
$270$		0			0
$271$	−3.38740	−	5.86714i	−0.205770	−	0.356403i	0.744608	−	0.667502i	$-0.232636\pi$
$271$	−3.38740	−	5.86714i	−0.205770	−	0.356403i	−0.950378	+	0.311098i	$0.899303\pi$
$272$	54.4741			3.30298
$273$		0			0
$274$	−15.0604			−0.909834
$275$	−2.36092	−	4.08923i	−0.142369	−	0.246590i
$276$		0			0
$277$	2.81829	−	4.88142i	0.169335	−	0.293296i	−0.768852	−	0.639427i	$-0.779171\pi$
$277$	2.81829	−	4.88142i	0.169335	−	0.293296i	0.938186	+	0.346131i	$0.112505\pi$
$278$	−48.4142			−2.90369
$279$		0			0
$280$	−4.19906	+	7.27298i	−0.250942	+	0.434644i
$281$	−12.5297			−0.747456			−0.373728	−	0.927538i	$-0.621921\pi$
$281$	−12.5297			−0.747456			−0.373728	+	0.927538i	$0.621921\pi$
$282$		0			0
$283$	−12.6721	−	21.9487i	−0.753279	−	1.30472i	−0.946226	−	0.323508i	$-0.895138\pi$
$283$	−12.6721	−	21.9487i	−0.753279	−	1.30472i	0.192947	−	0.981209i	$-0.438196\pi$
$284$	14.7892	+	25.6157i	0.877578	+	1.52001i
$285$		0			0
$286$	9.21415	−	43.8533i	0.544844	−	2.59310i
$287$	5.43508			0.320823
$288$		0			0
$289$	−5.14344	−	8.90871i	−0.302556	−	0.524042i
$290$	−1.72557	+	2.98878i	−0.101329	+	0.175507i
$291$		0			0
$292$	−30.3305	+	52.5340i	−1.77496	+	3.07432i
$293$	−8.92273	+	15.4546i	−0.521272	+	0.902869i	0.478422	+	0.878130i	$0.341209\pi$
$293$	−8.92273	+	15.4546i	−0.521272	+	0.902869i	−0.999694	+	0.0247390i	$0.992125\pi$
$294$		0			0
$295$	1.58348	−	2.74266i	0.0921936	−	0.159684i
$296$	40.1826	+	69.5983i	2.33557	+	4.04532i
$297$		0			0
$298$	59.6439			3.45508
$299$	−20.6925	−	18.5441i	−1.19668	−	1.07243i
$300$		0			0
$301$	−3.25202	−	5.63266i	−0.187443	−	0.324661i
$302$	2.98572	+	5.17142i	0.171809	+	0.297582i
$303$		0			0
$304$	30.5329			1.75118
$305$	−3.16045	+	5.47406i	−0.180967	+	0.313444i
$306$		0			0
$307$	10.0377			0.572880			0.286440	−	0.958098i	$-0.407528\pi$
$307$	10.0377			0.572880			0.286440	+	0.958098i	$0.407528\pi$
$308$	−12.6785	+	21.9599i	−0.722426	+	1.25128i
$309$		0			0
$310$	3.05441	+	5.29040i	0.173479	+	0.300475i
$311$	8.76317			0.496914			0.248457	−	0.968643i	$-0.420077\pi$
$311$	8.76317			0.496914			0.248457	+	0.968643i	$0.420077\pi$
$312$		0			0
$313$	4.37893			0.247512			0.123756	−	0.992313i	$-0.460506\pi$
$313$	4.37893			0.247512			0.123756	+	0.992313i	$0.460506\pi$
$314$	18.2844	+	31.6695i	1.03185	+	1.78721i
$315$		0			0
$316$	7.49859	−	12.9879i	0.421829	−	0.730629i
$317$	11.7036			0.657338			0.328669	−	0.944445i	$-0.393400\pi$
$317$	11.7036			0.657338			0.328669	+	0.944445i	$0.393400\pi$
$318$		0			0
$319$	−3.09559	+	5.36173i	−0.173320	+	0.300199i
$320$	10.8213			0.604930
$321$		0			0
$322$	11.0523	+	19.1431i	0.615920	+	1.06680i
$323$	−7.64718	−	13.2453i	−0.425500	−	0.736988i
$324$		0			0
$325$	−3.42647	+	1.12219i	−0.190066	+	0.0622482i
$326$	64.8067			3.58931
$327$		0			0
$328$	−19.2178	−	33.2862i	−1.06113	−	1.83792i
$329$	4.64127	−	8.03891i	0.255881	−	0.443200i
$330$		0			0
$331$	6.36162	−	11.0186i	0.349666	−	0.605640i	−0.636524	−	0.771257i	$-0.719628\pi$
$331$	6.36162	−	11.0186i	0.349666	−	0.605640i	0.986190	+	0.165617i	$0.0529617\pi$
$332$	3.46878	−	6.00811i	0.190374	−	0.329738i
$333$		0			0
$334$	−5.00081	+	8.66166i	−0.273632	+	0.473945i
$335$	0.787679	+	1.36430i	0.0430355	+	0.0745397i
$336$		0			0
$337$	−4.03730			−0.219926			−0.109963	−	0.993936i	$-0.535073\pi$
$337$	−4.03730			−0.219926			−0.109963	+	0.993936i	$0.535073\pi$
$338$	−31.3237	−	13.7710i	−1.70378	−	0.749042i
$339$		0			0
$340$	−12.8709	−	22.2930i	−0.698021	−	1.20901i
$341$	5.47947	+	9.49072i	0.296730	+	0.513951i
$342$		0			0
$343$	−13.9624			−0.753897
$344$	−22.9975	+	39.8329i	−1.23994	+	2.14764i
$345$		0			0
$346$	47.5889			2.55839
$347$	−0.172172	+	0.298211i	−0.00924268	+	0.0160088i	−0.870610	−	0.491974i	$-0.836275\pi$
$347$	−0.172172	+	0.298211i	−0.00924268	+	0.0160088i	0.861367	+	0.507983i	$0.169609\pi$
$348$		0			0
$349$	17.3201	+	29.9993i	0.927125	+	1.60583i	0.788108	+	0.615537i	$0.211061\pi$
$349$	17.3201	+	29.9993i	0.927125	+	1.60583i	0.139017	+	0.990290i	$0.455606\pi$
$350$	2.86832			0.153318
$351$		0			0
$352$	56.8286			3.02898
$353$	8.92012	+	15.4501i	0.474770	+	0.822326i	0.999583	−	0.0288917i	$-0.00919781\pi$
$353$	8.92012	+	15.4501i	0.474770	+	0.822326i	−0.524812	+	0.851218i	$0.675864\pi$
$354$		0			0
$355$	3.00113	−	5.19810i	0.159283	−	0.275887i
$356$	−42.7486			−2.26567
$357$		0			0
$358$	−33.7498	+	58.4563i	−1.78373	+	3.08951i
$359$	−7.22285			−0.381207			−0.190604	−	0.981667i	$-0.561045\pi$
$359$	−7.22285			−0.381207			−0.190604	+	0.981667i	$0.561045\pi$
$360$		0			0
$361$	5.21374	+	9.03046i	0.274407	+	0.475288i
$362$	25.1308	+	43.5278i	1.32084	+	2.28777i
$363$		0			0
$364$	14.4193	+	12.9223i	0.755779	+	0.677312i
$365$	12.3098			0.644322
$366$		0			0
$367$	14.8752	+	25.7647i	0.776481	+	1.34490i	0.933958	+	0.357382i	$0.116331\pi$
$367$	14.8752	+	25.7647i	0.776481	+	1.34490i	−0.157477	+	0.987523i	$0.550336\pi$
$368$	40.1826	−	69.5983i	2.09466	−	3.62806i
$369$		0			0
$370$	13.7241	−	23.7708i	0.713482	−	1.23579i
$371$	5.27236	−	9.13200i	0.273727	−	0.474110i
$372$		0			0
$373$	−1.92089	+	3.32707i	−0.0994597	+	0.172269i	−0.911461	−	0.411386i	$-0.865045\pi$
$373$	−1.92089	+	3.32707i	−0.0994597	+	0.172269i	0.812001	+	0.583655i	$0.198378\pi$
$374$	−32.4607	−	56.2237i	−1.67851	−	2.90726i
$375$		0			0
$376$	−65.6439			−3.38533
$377$	3.52063	+	3.15511i	0.181322	+	0.162497i
$378$		0			0
$379$	−15.5513	−	26.9356i	−0.798816	−	1.38359i	−0.920388	−	0.391006i	$-0.872127\pi$
$379$	−15.5513	−	26.9356i	−0.798816	−	1.38359i	0.121572	−	0.992583i	$-0.461206\pi$
$380$	−7.21415	−	12.4953i	−0.370078	−	0.640994i
$381$		0			0
$382$	−63.5749			−3.25277
$383$	−6.48045	+	11.2245i	−0.331136	+	0.573544i	−0.982735	−	0.185020i	$-0.940765\pi$
$383$	−6.48045	+	11.2245i	−0.331136	+	0.573544i	0.651599	+	0.758563i	$0.274098\pi$
$384$		0			0
$385$	5.14562			0.262245
$386$	−16.8396	+	29.1670i	−0.857113	+	1.48456i
$387$		0			0
$388$	27.1833	+	47.0828i	1.38002	+	2.39027i
$389$	14.1302			0.716432			0.358216	−	0.933639i	$-0.383385\pi$
$389$	14.1302			0.716432			0.358216	+	0.933639i	$0.383385\pi$
$390$		0			0
$391$	−40.2561			−2.03584
$392$	22.3967	+	38.7922i	1.13120	+	1.95930i
$393$		0			0
$394$	−0.858780	+	1.48745i	−0.0432647	+	0.0749366i
$395$	−3.04333			−0.153126
$396$		0			0
$397$	14.1550	−	24.5172i	0.710419	−	1.23048i	−0.254280	−	0.967131i	$-0.581839\pi$
$397$	14.1550	−	24.5172i	0.710419	−	1.23048i	0.964700	−	0.263352i	$-0.0848281\pi$
$398$	−16.8132			−0.842770
$399$		0			0
$400$	−5.21415	−	9.03117i	−0.260707	−	0.451558i
$401$	−2.21775	−	3.84126i	−0.110749	−	0.191824i	0.805323	−	0.592836i	$-0.201992\pi$
$401$	−2.21775	−	3.84126i	−0.110749	−	0.191824i	−0.916073	+	0.401012i	$0.868658\pi$
$402$		0			0
$403$	7.95251	−	2.60451i	0.396143	−	0.129740i
$404$	−45.4101			−2.25923
$405$		0			0
$406$	−1.88044	−	3.25702i	−0.0933249	−	0.161643i
$407$	24.6204	−	42.6437i	1.22039	−	2.11377i
$408$		0			0
$409$	4.48420	−	7.76686i	0.221729	−	0.384046i	−0.733604	−	0.679577i	$-0.762163\pi$
$409$	4.48420	−	7.76686i	0.221729	−	0.384046i	0.955333	+	0.295531i	$0.0954965\pi$
$410$	−6.56371	+	11.3687i	−0.324159	+	0.561459i
$411$		0			0
$412$	−36.6108	+	63.4117i	−1.80368	+	3.12407i
$413$	1.72560	+	2.98882i	0.0849110	+	0.147070i
$414$		0			0
$415$	−1.40782			−0.0691071
$416$	8.92277	−	42.4665i	0.437475	−	2.08209i
$417$		0			0
$418$	−18.1943	−	31.5135i	−0.889913	−	1.54137i
$419$	17.1960	+	29.7844i	0.840081	+	1.45506i	0.889826	+	0.456301i	$0.150826\pi$
$419$	17.1960	+	29.7844i	0.840081	+	1.45506i	−0.0497447	+	0.998762i	$0.515841\pi$
$420$		0			0
$421$	20.1940			0.984198			0.492099	−	0.870539i	$-0.336230\pi$
$421$	20.1940			0.984198			0.492099	+	0.870539i	$0.336230\pi$
$422$	23.0276	−	39.8850i	1.12097	−	1.94157i
$423$		0			0
$424$	−74.5698			−3.62143
$425$	−2.61184	+	4.52384i	−0.126693	+	0.219439i
$426$		0			0
$427$	−3.44410	−	5.96536i	−0.166672	−	0.288684i
$428$	33.9771			1.64235
$429$		0			0
$430$	15.7093			0.757569
$431$	−10.3846	−	17.9866i	−0.500208	−	0.866385i	−1.00000		0.000240043i	$-0.999924\pi$
$431$	−10.3846	−	17.9866i	−0.500208	−	0.866385i	0.499792	−	0.866145i	$-0.333410\pi$
$432$		0			0
$433$	−18.3462	+	31.7765i	−0.881661	+	1.52708i	−0.0321670	+	0.999483i	$0.510241\pi$
$433$	−18.3462	+	31.7765i	−0.881661	+	1.52708i	−0.849494	+	0.527599i	$0.823092\pi$
$434$	−6.65710			−0.319551
$435$		0			0
$436$	35.9218	−	62.2185i	1.72034	−	2.97972i
$437$	−22.5636			−1.07936
$438$		0			0
$439$	10.1493	+	17.5791i	0.484400	+	0.839005i	0.999839	−	0.0179207i	$-0.00570465\pi$
$439$	10.1493	+	17.5791i	0.484400	+	0.839005i	−0.515440	+	0.856926i	$0.672371\pi$
$440$	−18.1943	−	31.5135i	−0.867380	−	1.50235i
$441$		0			0
$442$	−47.1112	+	15.4293i	−2.24085	+	0.733896i
$443$	−10.0068			−0.475439			−0.237720	−	0.971334i	$-0.576400\pi$
$443$	−10.0068			−0.475439			−0.237720	+	0.971334i	$0.576400\pi$
$444$		0			0
$445$	4.33742	+	7.51262i	0.205613	+	0.356133i
$446$	3.49212	−	6.04854i	0.165357	−	0.286406i
$447$		0			0
$448$	−5.89626	+	10.2126i	−0.278572	+	0.482501i
$449$	5.28181	−	9.14837i	0.249264	−	0.431738i	−0.714058	−	0.700087i	$-0.753145\pi$
$449$	5.28181	−	9.14837i	0.249264	−	0.431738i	0.963322	+	0.268349i	$0.0864779\pi$
$450$		0			0
$451$	−11.7750	+	20.3949i	−0.554462	+	0.960356i
$452$	−32.7551	−	56.7335i	−1.54067	−	2.66852i
$453$		0			0
$454$	−13.4490			−0.631194
$455$	0.807924	−	3.84519i	0.0378761	−	0.180265i
$456$		0			0
$457$	2.40645	+	4.16810i	0.112569	+	0.194975i	0.916805	−	0.399334i	$-0.130759\pi$
$457$	2.40645	+	4.16810i	0.112569	+	0.194975i	−0.804236	+	0.594310i	$0.797425\pi$
$458$	−22.7583	−	39.4185i	−1.06342	−	1.84190i
$459$		0			0
$460$	−37.9765			−1.77067
$461$	9.78195	−	16.9428i	0.455591	−	0.789106i	−0.543131	−	0.839648i	$-0.682761\pi$
$461$	9.78195	−	16.9428i	0.455591	−	0.789106i	0.998722	+	0.0505415i	$0.0160947\pi$
$462$		0			0
$463$	1.03118			0.0479230			0.0239615	−	0.999713i	$-0.492372\pi$
$463$	1.03118			0.0479230			0.0239615	+	0.999713i	$0.492372\pi$
$464$	−6.83670	+	11.8415i	−0.317386	+	0.549728i
$465$		0			0
$466$	−3.16772	−	5.48666i	−0.146742	−	0.254165i
$467$	12.4884			0.577896			0.288948	−	0.957345i	$-0.406694\pi$
$467$	12.4884			0.577896			0.288948	+	0.957345i	$0.406694\pi$
$468$		0			0
$469$	−1.71675			−0.0792720
$470$	11.2101	+	19.4165i	0.517084	+	0.895616i
$471$		0			0
$472$	12.2030	−	21.1362i	0.561689	−	0.972873i
$473$	28.1817			1.29580
$474$		0			0
$475$	−1.46394	+	2.53562i	−0.0671703	+	0.116342i
$476$	28.0521			1.28576
$477$		0			0
$478$	−11.6276	−	20.1397i	−0.531836	−	0.921167i
$479$	−3.32202	−	5.75390i	−0.151787	−	0.262902i	0.780098	−	0.625658i	$-0.215169\pi$
$479$	−3.32202	−	5.75390i	−0.151787	−	0.262902i	−0.931884	+	0.362755i	$0.881836\pi$
$480$		0			0
$481$	−28.0008	−	25.0937i	−1.27673	−	1.14417i
$482$	−22.4795			−1.02391
$483$		0			0
$484$	−27.8321	−	48.2066i	−1.26510	−	2.19121i
$485$	5.51622	−	9.55437i	0.250479	−	0.433842i
$486$		0			0
$487$	−0.413437	+	0.716093i	−0.0187346	+	0.0324493i	−0.875241	−	0.483688i	$-0.839297\pi$
$487$	−0.413437	+	0.716093i	−0.0187346	+	0.0324493i	0.856506	+	0.516137i	$0.172630\pi$
$488$	−24.3559	+	42.1856i	−1.10254	+	1.90965i
$489$		0			0
$490$	7.64943	−	13.2492i	0.345566	−	0.598538i
$491$	−6.40991	−	11.1023i	−0.289275	−	0.501039i	0.684362	−	0.729143i	$-0.260081\pi$
$491$	−6.40991	−	11.1023i	−0.289275	−	0.501039i	−0.973637	+	0.228103i	$0.926748\pi$
$492$		0			0
$493$	6.84920			0.308473
$494$	−26.4059	+	8.64814i	−1.18806	+	0.389098i
$495$		0			0
$496$	12.1015	+	20.9605i	0.543375	+	0.941154i
$497$	3.27048	+	5.66463i	0.146701	+	0.254094i
$498$		0			0
$499$	19.8651			0.889283			0.444642	−	0.895709i	$-0.353331\pi$
$499$	19.8651			0.889283			0.444642	+	0.895709i	$0.353331\pi$
$500$	−2.46394	+	4.26767i	−0.110191	+	0.190856i
$501$		0			0
$502$	6.69901			0.298992
$503$	−9.35451	+	16.2025i	−0.417097	+	0.722433i	−0.995646	−	0.0932144i	$-0.970286\pi$
$503$	−9.35451	+	16.2025i	−0.417097	+	0.722433i	0.578549	+	0.815648i	$0.303619\pi$
$504$		0			0
$505$	4.60746	+	7.98035i	0.205029	+	0.355121i
$506$	−95.7781			−4.25785
$507$		0			0
$508$	76.1595			3.37903
$509$	5.01811	+	8.69163i	0.222424	+	0.385250i	0.955543	−	0.294850i	$-0.0952697\pi$
$509$	5.01811	+	8.69163i	0.222424	+	0.385250i	−0.733119	+	0.680100i	$0.761936\pi$
$510$		0			0
$511$	−6.70728	+	11.6174i	−0.296713	+	0.513921i
$512$	−35.2230			−1.55665
$513$		0			0
$514$	−15.8600	+	27.4703i	−0.699554	+	1.21166i
$515$	14.8586			0.654749
$516$		0			0
$517$	20.1104	+	34.8323i	0.884455	+	1.53192i
$518$	14.9558	+	25.9043i	0.657122	+	1.13817i
$519$		0			0
$520$	−26.4059	+	8.64814i	−1.15798	+	0.379246i
$521$	−2.06270			−0.0903687			−0.0451844	−	0.998979i	$-0.514388\pi$
$521$	−2.06270			−0.0903687			−0.0451844	+	0.998979i	$0.514388\pi$
$522$		0			0
$523$	16.0184	+	27.7448i	0.700438	+	1.21319i	0.968313	+	0.249740i	$0.0803453\pi$
$523$	16.0184	+	27.7448i	0.700438	+	1.21319i	−0.267875	+	0.963454i	$0.586321\pi$
$524$	20.9157	−	36.2270i	0.913706	−	1.58258i
$525$		0			0
$526$	13.7828	−	23.8726i	0.600960	−	1.04089i
$527$	6.06184	−	10.4994i	0.264058	−	0.457362i
$528$		0			0
$529$	−18.1947	+	31.5142i	−0.791075	+	1.37018i
$530$	12.7344	+	22.0566i	0.553147	+	0.958079i
$531$		0			0
$532$	15.7232			0.681689
$533$	13.3917	+	12.0014i	0.580060	+	0.519837i
$534$		0			0
$535$	−3.44743	−	5.97113i	−0.149046	−	0.258154i
$536$	6.07021	+	10.5139i	0.262193	+	0.454132i
$537$		0			0
$538$	23.4868			1.01259
$539$	13.7227	−	23.7684i	0.591079	−	1.02378i
$540$		0			0
$541$	−11.1795			−0.480644			−0.240322	−	0.970693i	$-0.577253\pi$
$541$	−11.1795			−0.480644			−0.240322	+	0.970693i	$0.577253\pi$
$542$	−8.91592	+	15.4428i	−0.382972	+	0.663326i
$543$		0			0
$544$	−31.4342	−	54.4457i	−1.34773	−	2.33434i
$545$	−14.5790			−0.624496
$546$		0			0
$547$	−0.0903080			−0.00386129			−0.00193064	−	0.999998i	$-0.500615\pi$
$547$	−0.0903080			−0.00386129			−0.00193064	+	0.999998i	$0.500615\pi$
$548$	14.0983	+	24.4190i	0.602251	+	1.04313i
$549$		0			0
$550$	−6.21415	+	10.7632i	−0.264972	+	0.458945i
$551$	3.83899			0.163547
$552$		0			0
$553$	1.65823	−	2.87215i	0.0705153	−	0.122136i
$554$	−14.8360			−0.630320
$555$		0			0
$556$	45.3214	+	78.4989i	1.92205	+	3.32909i
$557$	14.0621	+	24.3562i	0.595829	+	1.03201i	0.993429	+	0.114447i	$0.0365098\pi$
$557$	14.0621	+	24.3562i	0.595829	+	1.03201i	−0.397600	+	0.917559i	$0.630157\pi$
$558$		0			0
$559$	4.42486	−	21.0594i	0.187152	−	0.890720i
$560$	11.3642			0.480227
$561$		0			0
$562$	16.4896	+	28.5608i	0.695571	+	1.20476i
$563$	11.8278	−	20.4864i	0.498484	−	0.863399i	−0.501515	−	0.865149i	$-0.667224\pi$
$563$	11.8278	−	20.4864i	0.498484	−	0.863399i	0.999998	+	0.00175021i	$0.000557108\pi$
$564$		0			0
$565$	−6.64689	+	11.5127i	−0.279637	+	0.484345i
$566$	−33.3541	+	57.7710i	−1.40198	+	2.42830i
$567$		0			0
$568$	23.1280	−	40.0590i	0.970431	−	1.68084i
$569$	4.88343	+	8.45835i	0.204724	+	0.354593i	0.950045	−	0.312114i	$-0.101037\pi$
$569$	4.88343	+	8.45835i	0.204724	+	0.354593i	−0.745321	+	0.666706i	$0.767704\pi$
$570$		0			0
$571$	−20.9688			−0.877518			−0.438759	−	0.898605i	$-0.644582\pi$
$571$	−20.9688			−0.877518			−0.438759	+	0.898605i	$0.644582\pi$
$572$	−79.7294	+	26.1120i	−3.33365	+	1.09180i
$573$		0			0
$574$	−7.15280	−	12.3890i	−0.298552	−	0.517108i
$575$	3.85323	+	6.67399i	0.160691	+	0.278324i
$576$		0			0
$577$	−7.22602			−0.300823			−0.150412	−	0.988623i	$-0.548060\pi$
$577$	−7.22602			−0.300823			−0.150412	+	0.988623i	$0.548060\pi$
$578$	−13.5380	+	23.4485i	−0.563106	+	0.975329i
$579$		0			0
$580$	6.46136			0.268293
$581$	0.767085	−	1.32863i	0.0318240	−	0.0551209i
$582$		0			0
$583$	22.8449	+	39.5685i	0.946139	+	1.63876i
$584$	94.8646			3.92552
$585$		0			0
$586$	46.9708			1.94035
$587$	−12.0952	−	20.9495i	−0.499221	−	0.864677i	0.500778	−	0.865576i	$-0.333047\pi$
$587$	−12.0952	−	20.9495i	−0.499221	−	0.864677i	−1.00000		0.000898897i	$0.999714\pi$
$588$		0			0
$589$	3.39767	−	5.88494i	0.139999	−	0.242485i
$590$	−8.33570			−0.343176
$591$		0			0
$592$	54.3746	−	94.1796i	2.23478	−	3.87076i
$593$	10.5786			0.434410			0.217205	−	0.976126i	$-0.430306\pi$
$593$	10.5786			0.434410			0.217205	+	0.976126i	$0.430306\pi$
$594$		0			0
$595$	−2.84626	−	4.92986i	−0.116685	−	0.202105i
$596$	−55.8337	−	96.7068i	−2.28704	−	3.96127i
$597$		0			0
$598$	−15.0383	+	71.5724i	−0.614962	+	2.92681i
$599$	25.8978			1.05816			0.529078	−	0.848573i	$-0.322538\pi$
$599$	25.8978			1.05816			0.529078	+	0.848573i	$0.322538\pi$
$600$		0			0
$601$	7.65231	+	13.2542i	0.312144	+	0.540650i	0.978826	−	0.204692i	$-0.0656194\pi$
$601$	7.65231	+	13.2542i	0.312144	+	0.540650i	−0.666682	+	0.745342i	$0.732286\pi$
$602$	−8.55960	+	14.8257i	−0.348863	+	0.604249i
$603$		0			0
$604$	5.58997	−	9.68211i	0.227453	−	0.393960i
$605$	−5.64788	+	9.78241i	−0.229619	+	0.397712i
$606$		0			0
$607$	19.4724	−	33.7272i	0.790360	−	1.36894i	−0.135384	−	0.990793i	$-0.543227\pi$
$607$	19.4724	−	33.7272i	0.790360	−	1.36894i	0.925744	−	0.378151i	$-0.123440\pi$
$608$	−17.6190	−	30.5169i	−0.714543	−	1.23762i
$609$		0			0
$610$	16.6372			0.673620
$611$	29.1868	−	9.55890i	1.18077	−	0.386712i
$612$		0			0
$613$	−20.2800	−	35.1259i	−0.819100	−	1.41872i	−0.906346	−	0.422536i	$-0.861140\pi$
$613$	−20.2800	−	35.1259i	−0.819100	−	1.41872i	0.0872463	−	0.996187i	$-0.472193\pi$
$614$	−13.2100	−	22.8804i	−0.533113	−	0.923378i
$615$		0			0
$616$	39.6545			1.59773
$617$	−15.8304	+	27.4190i	−0.637307	+	1.10385i	0.348715	+	0.937229i	$0.386618\pi$
$617$	−15.8304	+	27.4190i	−0.637307	+	1.10385i	−0.986021	+	0.166619i	$0.946715\pi$
$618$		0			0
$619$	18.4523			0.741661			0.370831	−	0.928700i	$-0.379073\pi$
$619$	18.4523			0.741661			0.370831	+	0.928700i	$0.379073\pi$
$620$	5.71858	−	9.90487i	0.229664	−	0.397789i
$621$		0			0
$622$	−11.5327	−	19.9752i	−0.462420	−	0.800934i
$623$	−9.45340			−0.378742
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.76287	−	9.98158i	−0.230331	−	0.398944i
$627$		0			0
$628$	34.2327	−	59.2927i	1.36603	−	2.36604i
$629$	−54.4741			−2.17203
$630$		0			0
$631$	−16.7536	+	29.0181i	−0.666952	+	1.15519i	0.311801	+	0.950148i	$0.399068\pi$
$631$	−16.7536	+	29.0181i	−0.666952	+	1.15519i	−0.978752	+	0.205046i	$0.934265\pi$
$632$	−23.4533			−0.932921
$633$		0			0
$634$	−15.4024	−	26.6778i	−0.611708	−	1.05951i
$635$	−7.72740	−	13.3842i	−0.306652	−	0.531138i
$636$		0			0
$637$	−15.6069	−	13.9865i	−0.618368	−	0.554167i
$638$	16.2958			0.645155
$639$		0			0
$640$	−2.20605	−	3.82099i	−0.0872017	−	0.151038i
$641$	−7.97169	+	13.8074i	−0.314863	+	0.545359i	−0.979408	−	0.201889i	$-0.935292\pi$
$641$	−7.97169	+	13.8074i	−0.314863	+	0.545359i	0.664545	+	0.747248i	$0.268625\pi$
$642$		0			0
$643$	7.36007	−	12.7480i	0.290253	−	0.502733i	−0.683617	−	0.729841i	$-0.739594\pi$
$643$	7.36007	−	12.7480i	0.290253	−	0.502733i	0.973869	+	0.227109i	$0.0729272\pi$
$644$	20.6925	−	35.8404i	0.815397	−	1.41231i
$645$		0			0
$646$	−20.1280	+	34.8628i	−0.791927	+	1.37166i
$647$	18.5419	+	32.1155i	0.728957	+	1.26259i	0.957324	+	0.289016i	$0.0933281\pi$
$647$	18.5419	+	32.1155i	0.728957	+	1.26259i	−0.228367	+	0.973575i	$0.573339\pi$
$648$		0			0
$649$	−14.9538			−0.586990
$650$	7.06737	+	6.33362i	0.277205	+	0.248425i
$651$		0			0
$652$	−60.6667	−	105.078i	−2.37589	−	4.11517i
$653$	10.2853	+	17.8146i	0.402494	+	0.697140i	0.994026	−	0.109141i	$-0.0348101\pi$
$653$	10.2853	+	17.8146i	0.402494	+	0.697140i	−0.591532	+	0.806281i	$0.701477\pi$
$654$		0			0
$655$	−8.48870			−0.331681
$656$	−26.0053	+	45.0425i	−1.01534	+	1.75862i
$657$		0			0
$658$	−24.4325			−0.952476
$659$	−14.8316	+	25.6891i	−0.577758	+	1.00071i	0.417978	+	0.908457i	$0.362739\pi$
$659$	−14.8316	+	25.6891i	−0.577758	+	1.00071i	−0.995736	+	0.0922489i	$0.970594\pi$
$660$		0			0
$661$	8.05269	+	13.9477i	0.313213	+	0.542501i	0.979056	−	0.203591i	$-0.0652612\pi$
$661$	8.05269	+	13.9477i	0.313213	+	0.542501i	−0.665843	+	0.746092i	$0.731928\pi$
$662$	−33.4887			−1.30157
$663$		0			0
$664$	−10.8493			−0.421034
$665$	−1.59533	−	2.76320i	−0.0618643	−	0.107152i
$666$		0			0
$667$	5.05228	−	8.75081i	0.195625	−	0.338833i
$668$	18.7254			0.724507
$669$		0			0
$670$	2.07324	−	3.59096i	0.0800963	−	0.138731i
$671$	29.8463			1.15220
$672$		0			0
$673$	−3.53317	−	6.11963i	−0.136194	−	0.235894i	0.789859	−	0.613288i	$-0.210154\pi$
$673$	−3.53317	−	6.11963i	−0.136194	−	0.235894i	−0.926053	+	0.377394i	$0.876820\pi$
$674$	5.31326	+	9.20284i	0.204659	+	0.354480i
$675$		0			0
$676$	6.99434	+	63.6796i	0.269013	+	2.44921i
$677$	−23.6740			−0.909866			−0.454933	−	0.890526i	$-0.650337\pi$
$677$	−23.6740			−0.909866			−0.454933	+	0.890526i	$0.650337\pi$
$678$		0			0
$679$	6.01130	+	10.4119i	0.230693	+	0.399571i
$680$	−20.1280	+	34.8628i	−0.771875	+	1.33693i
$681$		0			0
$682$	14.4224	−	24.9804i	0.552264	−	0.956549i
$683$	10.0997	−	17.4932i	0.386454	−	0.669359i	−0.605515	−	0.795834i	$-0.707033\pi$
$683$	10.0997	−	17.4932i	0.386454	−	0.669359i	0.991970	+	0.126475i	$0.0403663\pi$
$684$		0			0
$685$	2.86093	−	4.95527i	0.109310	−	0.189331i
$686$	18.3751	+	31.8266i	0.701564	+	1.21514i
$687$		0			0
$688$	62.2400			2.37288
$689$	33.1554	−	10.8587i	1.26312	−	0.413682i
$690$		0			0
$691$	15.5689	+	26.9661i	0.592269	+	1.02584i	0.993926	+	0.110050i	$0.0351010\pi$
$691$	15.5689	+	26.9661i	0.592269	+	1.02584i	−0.401657	+	0.915790i	$0.631566\pi$
$692$	−44.5488	−	77.1607i	−1.69349	−	2.93321i
$693$		0			0
$694$	0.906344			0.0344044
$695$	9.19692	−	15.9295i	0.348859	−	0.604241i
$696$		0			0
$697$	26.0529			0.986824
$698$	45.5881	−	78.9609i	1.72553	−	2.98871i
$699$		0			0
$700$	−2.68508	−	4.65070i	−0.101487	−	0.175780i
$701$	24.0928			0.909974			0.454987	−	0.890498i	$-0.349644\pi$
$701$	24.0928			0.909974			0.454987	+	0.890498i	$0.349644\pi$
$702$		0			0
$703$	−30.5329			−1.15157
$704$	−25.5482	−	44.2509i	−0.962886	−	1.66777i
$705$		0			0
$706$	23.4785	−	40.6660i	0.883627	−	1.53049i
$707$	−10.0420			−0.377667
$708$		0			0
$709$	−2.39040	+	4.14030i	−0.0897734	+	0.155492i	−0.907415	−	0.420235i	$-0.861948\pi$
$709$	−2.39040	+	4.14030i	−0.0897734	+	0.155492i	0.817642	+	0.575727i	$0.195281\pi$
$710$	−15.7985			−0.592906
$711$		0			0
$712$	33.4261	+	57.8957i	1.25270	+	2.16973i
$713$	−8.94298	−	15.4897i	−0.334917	−	0.580094i
$714$		0			0
$715$	12.6785	+	11.3622i	0.474150	+	0.424923i
$716$	126.375			4.72286
$717$		0			0
$718$	9.50558	+	16.4642i	0.354745	+	0.614437i
$719$	6.75421	−	11.6986i	0.251889	−	0.436285i	−0.712157	−	0.702021i	$-0.752281\pi$
$719$	6.75421	−	11.6986i	0.251889	−	0.436285i	0.964046	+	0.265735i	$0.0856147\pi$
$720$		0			0
$721$	−8.09609	+	14.0228i	−0.301514	+	0.522238i
$722$	13.7230	−	23.7690i	0.510718	−	0.884590i
$723$		0			0
$724$	47.0507	−	81.4942i	1.74863	−	3.02871i
$725$	−0.655591	−	1.13552i	−0.0243480	−	0.0421720i
$726$		0			0
$727$	−6.06108			−0.224793			−0.112397	−	0.993663i	$-0.535853\pi$
$727$	−6.06108			−0.224793			−0.112397	+	0.993663i	$0.535853\pi$
$728$	6.22623	−	29.6328i	0.230759	−	1.09826i
$729$		0			0
$730$	−16.2002	−	28.0595i	−0.599596	−	1.03853i
$731$	−15.5885	−	27.0000i	−0.576560	−	0.998631i
$732$		0			0
$733$	5.63897			0.208280			0.104140	−	0.994563i	$-0.466791\pi$
$733$	5.63897			0.208280			0.104140	+	0.994563i	$0.466791\pi$
$734$	39.1529	−	67.8149i	1.44516	−	2.50309i
$735$		0			0
$736$	−92.7493			−3.41878
$737$	3.71929	−	6.44200i	0.137002	−	0.237294i
$738$		0			0
$739$	1.56358	+	2.70820i	0.0575173	+	0.0996229i	0.893350	−	0.449361i	$-0.148348\pi$
$739$	1.56358	+	2.70820i	0.0575173	+	0.0996229i	−0.835833	+	0.548984i	$0.815015\pi$
$740$	−51.3894			−1.88911
$741$		0			0
$742$	−27.7546			−1.01890
$743$	−24.3946	−	42.2528i	−0.894953	−	1.55010i	−0.833863	−	0.551971i	$-0.813876\pi$
$743$	−24.3946	−	42.2528i	−0.894953	−	1.55010i	−0.0610897	−	0.998132i	$-0.519458\pi$
$744$		0			0
$745$	−11.3302	+	19.6244i	−0.415105	+	0.718982i
$746$	10.1119			0.370222
$747$		0			0
$748$	−60.7741	+	105.264i	−2.22212	+	3.84883i
$749$	7.51368			0.274544
$750$		0			0
$751$	22.3404	+	38.6947i	0.815212	+	1.41199i	0.909176	+	0.416413i	$0.136713\pi$
$751$	22.3404	+	38.6947i	0.815212	+	1.41199i	−0.0939637	+	0.995576i	$0.529954\pi$
$752$	44.4143	+	76.9279i	1.61962	+	2.80527i
$753$		0			0
$754$	2.55863	−	12.1774i	0.0931797	−	0.443474i
$755$	−2.26871			−0.0825668
$756$		0			0
$757$	4.54891	+	7.87894i	0.165333	+	0.286365i	0.936773	−	0.349936i	$-0.113797\pi$
$757$	4.54891	+	7.87894i	0.165333	+	0.286365i	−0.771441	+	0.636301i	$0.780463\pi$
$758$	−40.9323	+	70.8969i	−1.48673	+	2.57509i
$759$		0			0
$760$	−11.2818	+	19.5407i	−0.409234	+	0.708815i
$761$	−15.2874	+	26.4785i	−0.554167	+	0.959846i	0.443801	+	0.896126i	$0.353630\pi$
$761$	−15.2874	+	26.4785i	−0.554167	+	0.959846i	−0.997968	+	0.0637201i	$0.979704\pi$
$762$		0			0
$763$	7.94374	−	13.7590i	0.287583	−	0.498108i
$764$	59.5135	+	103.080i	2.15312	+	3.72932i
$765$		0			0
$766$	34.1142			1.23260
$767$	−2.34793	+	11.1746i	−0.0847789	+	0.403492i
$768$		0			0
$769$	13.6230	+	23.5957i	0.491257	+	0.850882i	0.999949	−	0.0100665i	$-0.00320432\pi$
$769$	13.6230	+	23.5957i	0.491257	+	0.850882i	−0.508693	+	0.860948i	$0.669871\pi$
$770$	−6.77187	−	11.7292i	−0.244041	−	0.422692i
$771$		0			0
$772$	63.0554			2.26941
$773$	3.66765	−	6.35256i	0.131916	−	0.228486i	−0.792499	−	0.609873i	$-0.791220\pi$
$773$	3.66765	−	6.35256i	0.131916	−	0.228486i	0.924415	+	0.381388i	$0.124554\pi$
$774$		0			0
$775$	−2.32091			−0.0833694
$776$	42.5105	−	73.6303i	1.52604	−	2.64317i
$777$		0			0
$778$	−18.5960	−	32.2092i	−0.666700	−	1.15476i
$779$	14.6027			0.523196
$780$		0			0
$781$	−28.3417			−1.01414
$782$	52.9788	+	91.7620i	1.89452	+	3.28140i
$783$		0			0
$784$	30.3069	−	52.4932i	1.08239	−	1.87476i
$785$	−13.8934			−0.495878
$786$		0			0
$787$	−25.6877	+	44.4925i	−0.915669	+	1.58599i	−0.109750	+	0.993959i	$0.535005\pi$
$787$	−25.6877	+	44.4925i	−0.915669	+	1.58599i	−0.805919	+	0.592026i	$0.798328\pi$
$788$	3.21567			0.114554
$789$		0			0
$790$	4.00515	+	6.93713i	0.142497	+	0.246812i
$791$	−7.24345	−	12.5460i	−0.257547	−	0.446085i
$792$		0			0
$793$	4.68622	−	22.3033i	0.166413	−	0.792015i
$794$	−74.5144			−2.64442
$795$		0			0
$796$	15.7391	+	27.2610i	0.557859	+	0.966240i
$797$	−17.6659	+	30.5982i	−0.625758	+	1.08385i	0.362635	+	0.931931i	$0.381877\pi$
$797$	−17.6659	+	30.5982i	−0.625758	+	1.08385i	−0.988394	+	0.151914i	$0.951456\pi$
$798$		0			0
$799$	22.2478	−	38.5343i	0.787070	−	1.36325i
$800$	−6.01764	+	10.4229i	−0.212756	+	0.368503i
$801$		0			0
$802$	−5.83732	+	10.1105i	−0.206123	+	0.357016i
$803$	−29.0623	−	50.3375i	−1.02559	−	1.77637i
$804$		0			0
$805$	−8.39811			−0.295995
$806$	−16.4027	−	14.6997i	−0.577761	−	0.517776i
$807$		0			0
$808$	35.5072	+	61.5002i	1.24914	+	2.16357i
$809$	−15.5217	−	26.8844i	−0.545715	−	0.945206i	−0.998562	−	0.0536179i	$-0.982925\pi$
$809$	−15.5217	−	26.8844i	−0.545715	−	0.945206i	0.452846	−	0.891589i	$-0.350409\pi$
$810$		0			0
$811$	−9.39427			−0.329878			−0.164939	−	0.986304i	$-0.552743\pi$
$811$	−9.39427			−0.329878			−0.164939	+	0.986304i	$0.552743\pi$
$812$	−3.52063	+	6.09791i	−0.123550	+	0.213995i
$813$		0			0
$814$	−129.606			−4.54268
$815$	−12.3109	+	21.3231i	−0.431232	+	0.746916i
$816$		0			0
$817$	−8.73737	−	15.1336i	−0.305682	−	0.529456i
$818$	−23.6056			−0.825350
$819$		0			0
$820$	24.5776			0.858287
$821$	−3.09317	−	5.35753i	−0.107952	−	0.186979i	0.806988	−	0.590568i	$-0.201096\pi$
$821$	−3.09317	−	5.35753i	−0.107952	−	0.186979i	−0.914941	+	0.403588i	$0.867763\pi$
$822$		0			0
$823$	−11.3355	+	19.6337i	−0.395131	+	0.684388i	−0.993118	−	0.117119i	$-0.962634\pi$
$823$	−11.3355	+	19.6337i	−0.395131	+	0.684388i	0.597987	+	0.801506i	$0.295968\pi$
$824$	114.507			3.98905
$825$		0			0
$826$	4.54192	−	7.86683i	0.158034	−	0.273722i
$827$	−11.1599			−0.388066			−0.194033	−	0.980995i	$-0.562157\pi$
$827$	−11.1599			−0.388066			−0.194033	+	0.980995i	$0.562157\pi$
$828$		0			0
$829$	9.89830	+	17.1444i	0.343782	+	0.595448i	0.985132	−	0.171801i	$-0.0549585\pi$
$829$	9.89830	+	17.1444i	0.343782	+	0.595448i	−0.641350	+	0.767249i	$0.721625\pi$
$830$	1.85275	+	3.20906i	0.0643099	+	0.111388i
$831$		0			0
$832$	−37.0789	+	12.1436i	−1.28548	+	0.421004i
$833$	−30.3624			−1.05199
$834$		0			0
$835$	−1.89994	−	3.29079i	−0.0657502	−	0.113883i
$836$	−34.0640	+	59.0006i	−1.17813	+	2.04058i
$837$		0			0
$838$	45.2615	−	78.3951i	1.56353	−	2.70812i
$839$	0.641334	−	1.11082i	0.0221413	−	0.0383499i	−0.854742	−	0.519052i	$-0.826285\pi$
$839$	0.641334	−	1.11082i	0.0221413	−	0.0383499i	0.876884	+	0.480702i	$0.159618\pi$
$840$		0			0
$841$	13.6404	−	23.6259i	0.470359	−	0.814685i
$842$	−26.5762	−	46.0314i	−0.915878	−	1.58635i
$843$		0			0
$844$	−86.2261			−2.96803
$845$	10.4814	−	7.69033i	0.360570	−	0.264555i
$846$		0			0
$847$	−6.15478	−	10.6604i	−0.211481	−	0.366295i
$848$	50.4535	+	87.3880i	1.73258	+	3.00092i
$849$		0			0
$850$	13.7492			0.471594
$851$	−40.1826	+	69.5983i	−1.37744	+	2.38580i
$852$		0			0
$853$	−12.0390			−0.412208			−0.206104	−	0.978530i	$-0.566078\pi$
$853$	−12.0390			−0.412208			−0.206104	+	0.978530i	$0.566078\pi$
$854$	−9.06519	+	15.7014i	−0.310204	+	0.537290i
$855$		0			0
$856$	−26.5675	−	46.0162i	−0.908058	−	1.57280i
$857$	28.1181			0.960497			0.480248	−	0.877133i	$-0.340547\pi$
$857$	28.1181			0.960497			0.480248	+	0.877133i	$0.340547\pi$
$858$		0			0
$859$	−50.0048			−1.70614			−0.853071	−	0.521795i	$-0.825263\pi$
$859$	−50.0048			−1.70614			−0.853071	+	0.521795i	$0.825263\pi$
$860$	−14.7057	−	25.4711i	−0.501462	−	0.868557i
$861$		0			0
$862$	−27.3331	+	47.3424i	−0.930970	+	1.61249i
$863$	41.7180			1.42010			0.710048	−	0.704153i	$-0.248673\pi$
$863$	41.7180			1.42010			0.710048	+	0.704153i	$0.248673\pi$
$864$		0			0
$865$	−9.04014	+	15.6580i	−0.307374	+	0.532387i
$866$	96.5775			3.28184
$867$		0			0
$868$	6.23182	+	10.7938i	0.211522	+	0.366367i
$869$	7.18505	+	12.4449i	0.243736	+	0.422164i
$870$		0			0
$871$	−4.22997	−	3.79080i	−0.143327	−	0.128446i
$872$	−112.352			−3.80473
$873$		0			0
$874$	29.6947	+	51.4328i	1.00444	+	1.73974i
$875$	−0.544875	+	0.943751i	−0.0184201	+	0.0319046i
$876$		0			0
$877$	21.1023	−	36.5502i	0.712573	−	1.23421i	−0.251315	−	0.967905i	$-0.580863\pi$
$877$	21.1023	−	36.5502i	0.712573	−	1.23421i	0.963888	−	0.266307i	$-0.0858036\pi$
$878$	26.7139	−	46.2698i	0.901549	−	1.56153i
$879$		0			0
$880$	−24.6204	+	42.6437i	−0.829952	+	1.43752i
$881$	24.7312	+	42.8356i	0.833214	+	1.44317i	0.895476	+	0.445109i	$0.146835\pi$
$881$	24.7312	+	42.8356i	0.833214	+	1.44317i	−0.0622621	+	0.998060i	$0.519831\pi$
$882$		0			0
$883$	−7.24684			−0.243876			−0.121938	−	0.992538i	$-0.538911\pi$
$883$	−7.24684			−0.243876			−0.121938	+	0.992538i	$0.538911\pi$
$884$	69.1187	+	61.9426i	2.32471	+	2.08335i
$885$		0			0
$886$	13.1694	+	22.8101i	0.442436	+	0.766322i
$887$	13.2308	+	22.9164i	0.444246	+	0.769457i	0.997999	−	0.0632238i	$-0.0201382\pi$
$887$	13.2308	+	22.9164i	0.444246	+	0.769457i	−0.553753	+	0.832681i	$0.686805\pi$
$888$		0			0
$889$	16.8419			0.564858
$890$	11.4165	−	19.7739i	0.382681	−	0.662822i
$891$		0			0
$892$	−13.0762			−0.437822
$893$	12.4699	−	21.5986i	0.417290	−	0.722768i
$894$		0			0
$895$	−12.8224	−	22.2091i	−0.428607	−	0.742369i
$896$	4.80808			0.160627
$897$		0			0
$898$	−27.8044			−0.927844
$899$	1.52157	+	2.63543i	0.0507470	+	0.0878964i
$900$		0			0
$901$	25.2729	−	43.7739i	0.841962	−	1.45832i
$902$	61.9855			2.06389
$903$		0			0
$904$	−51.2239	+	88.7224i	−1.70368	+	2.95086i
$905$	−19.0957			−0.634762
$906$		0			0
$907$	5.41637	+	9.38143i	0.179848	+	0.311505i	0.941828	−	0.336095i	$-0.109106\pi$
$907$	5.41637	+	9.38143i	0.179848	+	0.311505i	−0.761981	+	0.647600i	$0.775773\pi$
$908$	12.5899	+	21.8063i	0.417809	+	0.723667i
$909$		0			0
$910$	−9.82820	+	3.21881i	−0.325802	+	0.106703i
$911$	1.47923			0.0490092			0.0245046	−	0.999700i	$-0.492199\pi$
$911$	1.47923			0.0490092			0.0245046	+	0.999700i	$0.492199\pi$
$912$		0			0
$913$	3.32374	+	5.75689i	0.110000	+	0.190525i
$914$	6.33399	−	10.9708i	0.209510	−	0.362882i
$915$		0			0
$916$	−42.6088	+	73.8006i	−1.40783	+	2.43844i
$917$	4.62528	−	8.01122i	0.152740	−	0.264554i
$918$		0			0
$919$	12.4060	−	21.4878i	0.409236	−	0.708818i	−0.585568	−	0.810623i	$-0.699129\pi$
$919$	12.4060	−	21.4878i	0.409236	−	0.708818i	0.994804	+	0.101805i	$0.0324619\pi$
$920$	29.6947	+	51.4328i	0.979006	+	1.69569i
$921$		0			0
$922$	−51.4939			−1.69586
$923$	−4.44998	+	21.1790i	−0.146473	+	0.697115i
$924$		0			0
$925$	5.21415	+	9.03117i	0.171440	+	0.296943i
$926$	−1.35708	−	2.35053i	−0.0445964	−	0.0772432i
$927$		0			0
$928$	15.7804			0.518018
$929$	0.301828	−	0.522782i	0.00990266	−	0.0171519i	−0.861032	−	0.508551i	$-0.830181\pi$
$929$	0.301828	−	0.522782i	0.00990266	−	0.0171519i	0.870934	+	0.491400i	$0.163515\pi$
$930$		0			0
$931$	−17.0182			−0.557748
$932$	−5.93072	+	10.2723i	−0.194267	+	0.336481i
$933$		0			0
$934$	−16.4353	−	28.4668i	−0.537781	−	0.931464i
$935$	24.6654			0.806645
$936$		0			0
$937$	−1.64793			−0.0538355			−0.0269178	−	0.999638i	$-0.508569\pi$
$937$	−1.64793			−0.0538355			−0.0269178	+	0.999638i	$0.508569\pi$
$938$	2.25931	+	3.91325i	0.0737692	+	0.127772i
$939$		0			0
$940$	20.9880	−	36.3522i	0.684552	−	1.18568i
$941$	47.2291			1.53962			0.769812	−	0.638271i	$-0.220350\pi$
$941$	47.2291			1.53962			0.769812	+	0.638271i	$0.220350\pi$
$942$		0			0
$943$	19.2178	−	33.2862i	0.625818	−	1.08395i
$944$	−33.0259			−1.07490
$945$		0			0
$946$	−37.0884	−	64.2389i	−1.20585	−	2.08859i
$947$	−16.0704	−	27.8347i	−0.522217	−	0.904506i	−0.999666	−	0.0258464i	$-0.991772\pi$
$947$	−16.0704	−	27.8347i	−0.522217	−	0.904506i	0.477449	−	0.878659i	$-0.341561\pi$
$948$		0			0
$949$	−42.1790	+	13.8139i	−1.36919	+	0.448420i
$950$	7.70645			0.250030
$951$		0			0
$952$	−21.9345	−	37.9917i	−0.710903	−	1.23132i
$953$	−7.32952	+	12.6951i	−0.237427	+	0.411235i	−0.959975	−	0.280085i	$-0.909637\pi$
$953$	−7.32952	+	12.6951i	−0.237427	+	0.411235i	0.722549	+	0.691320i	$0.242971\pi$
$954$		0			0
$955$	12.0769	−	20.9178i	0.390799	−	0.676884i
$956$	−21.7697	+	37.7062i	−0.704082	+	1.21951i
$957$		0			0
$958$	−8.74384	+	15.1448i	−0.282501	+	0.489305i
$959$	3.11770	+	5.40001i	0.100676	+	0.174375i
$960$		0			0
$961$	−25.6134			−0.826239
$962$	−20.3497	+	96.8511i	−0.656099	+	3.12260i
$963$		0			0
$964$	21.0434	+	36.4483i	0.677763	+	1.17392i
$965$	−6.39781	−	11.0813i	−0.205953	−	0.356721i
$966$		0			0
$967$	8.77101			0.282057			0.141028	−	0.990006i	$-0.454959\pi$
$967$	8.77101			0.282057			0.141028	+	0.990006i	$0.454959\pi$
$968$	−43.5251	+	75.3877i	−1.39895	+	2.42305i
$969$		0			0
$970$	−29.0383			−0.932365
$971$	−2.64741	+	4.58544i	−0.0849593	+	0.147154i	−0.905374	−	0.424615i	$-0.860409\pi$
$971$	−2.64741	+	4.58544i	−0.0849593	+	0.147154i	0.820415	+	0.571769i	$0.193743\pi$
$972$		0			0
$973$	10.0223	+	17.3592i	0.321302	+	0.556511i
$974$	2.17640			0.0697365
$975$		0			0
$976$	65.9163			2.10993
$977$	−11.6167	−	20.1207i	−0.371651	−	0.643719i	0.618168	−	0.786046i	$-0.287875\pi$
$977$	−11.6167	−	20.1207i	−0.371651	−	0.643719i	−0.989820	+	0.142327i	$0.954542\pi$
$978$		0			0
$979$	20.4806	−	35.4734i	0.654562	−	1.13373i
$980$	−28.6431			−0.914969
$981$		0			0
$982$	−16.8714	+	29.2222i	−0.538389	+	0.932518i
$983$	41.7741			1.33239			0.666194	−	0.745779i	$-0.267922\pi$
$983$	41.7741			1.33239			0.666194	+	0.745779i	$0.267922\pi$
$984$		0			0
$985$	−0.326273	−	0.565122i	−0.0103959	−	0.0180063i
$986$	−9.01385	−	15.6124i	−0.287060	−	0.497202i
$987$		0			0
$988$	38.7412	+	34.7190i	1.23252	+	1.10456i
$989$	−45.9950			−1.46256
$990$		0			0
$991$	−13.8143	−	23.9270i	−0.438825	−	0.760067i	0.558774	−	0.829320i	$-0.311272\pi$
$991$	−13.8143	−	23.9270i	−0.438825	−	0.760067i	−0.997599	+	0.0692527i	$0.977939\pi$
$992$	13.9664	−	24.1905i	0.443433	−	0.768048i
$993$		0			0
$994$	8.60819	−	14.9098i	0.273035	−	0.472911i
$995$	3.19389	−	5.53198i	0.101253	−	0.175376i
$996$		0			0
$997$	4.57449	−	7.92325i	0.144876	−	0.250932i	−0.784451	−	0.620191i	$-0.787055\pi$
$997$	4.57449	−	7.92325i	0.144876	−	0.250932i	0.929326	+	0.369259i	$0.120388\pi$
$998$	−26.1433	−	45.2816i	−0.827552	−	1.43336i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.h.406.1	✓	10
3.2	odd	2		585.2.j.i.406.5	yes	10
13.3	even	3		7605.2.a.co.1.5		5
13.9	even	3	inner	585.2.j.h.451.1	yes	10
13.10	even	6		7605.2.a.cl.1.1		5
39.23	odd	6		7605.2.a.cn.1.5		5
39.29	odd	6		7605.2.a.cm.1.1		5
39.35	odd	6		585.2.j.i.451.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.j.h.406.1	✓	10	1.1	even	1	trivial
585.2.j.h.451.1	yes	10	13.9	even	3	inner
585.2.j.i.406.5	yes	10	3.2	odd	2
585.2.j.i.451.5	yes	10	39.35	odd	6
7605.2.a.cl.1.1		5	13.10	even	6
7605.2.a.cm.1.1		5	39.29	odd	6
7605.2.a.cn.1.5		5	39.23	odd	6
7605.2.a.co.1.5		5	13.3	even	3

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31604 - 2.27945i) q^{2} +(-2.46394 + 4.26767i) q^{4} +1.00000 q^{5} +(-0.544875 + 0.943751i) q^{7} +7.70645 q^{8} +O(q^{10})\)	\(q+(-1.31604 - 2.27945i) q^{2} +(-2.46394 + 4.26767i) q^{4} +1.00000 q^{5} +(-0.544875 + 0.943751i) q^{7} +7.70645 q^{8} +(-1.31604 - 2.27945i) q^{10} +(-2.36092 - 4.08923i) q^{11} +(-3.42647 + 1.12219i) q^{13} +2.86832 q^{14} +(-5.21415 - 9.03117i) q^{16} +(-2.61184 + 4.52384i) q^{17} +(-1.46394 + 2.53562i) q^{19} +(-2.46394 + 4.26767i) q^{20} +(-6.21415 + 10.7632i) q^{22} +(3.85323 + 6.67399i) q^{23} +1.00000 q^{25} +(7.06737 + 6.33362i) q^{26} +(-2.68508 - 4.65070i) q^{28} +(-0.655591 - 1.13552i) q^{29} -2.32091 q^{31} +(-6.01764 + 10.4229i) q^{32} +13.7492 q^{34} +(-0.544875 + 0.943751i) q^{35} +(5.21415 + 9.03117i) q^{37} +7.70645 q^{38} +7.70645 q^{40} +(-2.49373 - 4.31926i) q^{41} +(-2.98419 + 5.16877i) q^{43} +23.2687 q^{44} +(10.1420 - 17.5665i) q^{46} -8.51804 q^{47} +(2.90622 + 5.03372i) q^{49} +(-1.31604 - 2.27945i) q^{50} +(3.65346 - 17.3881i) q^{52} -9.67627 q^{53} +(-2.36092 - 4.08923i) q^{55} +(-4.19906 + 7.27298i) q^{56} +(-1.72557 + 2.98878i) q^{58} +(1.58348 - 2.74266i) q^{59} +(-3.16045 + 5.47406i) q^{61} +(3.05441 + 5.29040i) q^{62} +10.8213 q^{64} +(-3.42647 + 1.12219i) q^{65} +(0.787679 + 1.36430i) q^{67} +(-12.8709 - 22.2930i) q^{68} +2.86832 q^{70} +(3.00113 - 5.19810i) q^{71} +12.3098 q^{73} +(13.7241 - 23.7708i) q^{74} +(-7.21415 - 12.4953i) q^{76} +5.14562 q^{77} -3.04333 q^{79} +(-5.21415 - 9.03117i) q^{80} +(-6.56371 + 11.3687i) q^{82} -1.40782 q^{83} +(-2.61184 + 4.52384i) q^{85} +15.7093 q^{86} +(-18.1943 - 31.5135i) q^{88} +(4.33742 + 7.51262i) q^{89} +(0.807924 - 3.84519i) q^{91} -37.9765 q^{92} +(11.2101 + 19.4165i) q^{94} +(-1.46394 + 2.53562i) q^{95} +(5.51622 - 9.55437i) q^{97} +(7.64943 - 13.2492i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8	\( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8 - 2 * q^10 - 8 * q^11 + q^13 - 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 - 14 * q^22 + 6 * q^23 + 10 * q^25 - 10 * q^26 + 2 * q^28 - 16 * q^29 + 18 * q^31 - 14 * q^32 - q^35 + 4 * q^37 + 12 * q^38 + 12 * q^40 - 6 * q^41 - 15 * q^43 + 28 * q^44 + 16 * q^46 + 20 * q^47 - 10 * q^49 - 2 * q^50 - 22 * q^52 - 40 * q^53 - 8 * q^55 + 2 * q^56 + 4 * q^58 - 12 * q^59 - 11 * q^61 + 22 * q^62 + 8 * q^64 + q^65 - 5 * q^67 - 50 * q^68 - 8 * q^70 - 10 * q^71 + 2 * q^73 + 26 * q^74 - 24 * q^76 + 84 * q^77 - 34 * q^79 - 4 * q^80 - 16 * q^82 + 32 * q^83 + 88 * q^86 - 20 * q^88 - 4 * q^89 - q^91 - 68 * q^92 + 16 * q^94 + 4 * q^95 + 11 * q^97 - 30 * q^98

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