LMFDB - Embedded newform 225.2.h.e.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.1130304400000000000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + 5x^{12} - 10x^{10} + 205x^{8} - 700x^{6} + 1250x^{4} - 1250x^{2} + 625 $ x^16 - 5x^14 + 5x^12 - 10x^10 + 205x^8 - 700x^6 + 1250x^4 - 1250*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.2
Root			$0.994142 - 0.627414i$ of defining polynomial
Character	$\chi$	$=$	225.136
Dual form			225.2.h.e.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.757918 + 0.550660i) q^{2} +(-0.346820 + 1.06740i) q^{4} +(1.42964 - 1.71934i) q^{5} +2.74037 q^{7} +(-0.903913 - 2.78196i) q^{8} +O(q^{10})$	\(q+(-0.757918 + 0.550660i) q^{2} +(-0.346820 + 1.06740i) q^{4} +(1.42964 - 1.71934i) q^{5} +2.74037 q^{7} +(-0.903913 - 2.78196i) q^{8} +(-0.136773 + 2.09036i) q^{10} +(-0.236224 + 0.171627i) q^{11} +(2.87714 + 2.09036i) q^{13} +(-2.07697 + 1.50901i) q^{14} +(0.401030 + 0.291365i) q^{16} +(1.35198 + 4.16097i) q^{17} +(0.789953 + 2.43123i) q^{19} +(1.33941 + 2.12230i) q^{20} +(0.0845304 - 0.260158i) q^{22} +(4.15146 - 3.01621i) q^{23} +(-0.912286 - 4.91607i) q^{25} -3.33172 q^{26} +(-0.950415 + 2.92508i) q^{28} +(-2.90477 + 8.93997i) q^{29} +(-2.76373 - 8.50589i) q^{31} +5.38585 q^{32} +(-3.31597 - 2.40920i) q^{34} +(3.91773 - 4.71163i) q^{35} +(0.594670 + 0.432053i) q^{37} +(-1.93750 - 1.40767i) q^{38} +(-6.07541 - 2.42305i) q^{40} +(-9.13695 - 6.63838i) q^{41} +0.249982 q^{43} +(-0.101267 - 0.311669i) q^{44} +(-1.48556 + 4.57209i) q^{46} +(-0.891336 + 2.74325i) q^{47} +0.509614 q^{49} +(3.39852 + 3.22362i) q^{50} +(-3.22911 + 2.34609i) q^{52} +(1.50729 - 4.63896i) q^{53} +(-0.0426286 + 0.651513i) q^{55} +(-2.47705 - 7.62358i) q^{56} +(-2.72130 - 8.37531i) q^{58} +(-4.12708 - 2.99850i) q^{59} +(1.61108 - 1.17052i) q^{61} +(6.77853 + 4.92489i) q^{62} +(-4.88410 + 3.54850i) q^{64} +(7.70732 - 1.95833i) q^{65} +(-4.23771 - 13.0423i) q^{67} -4.91033 q^{68} +(-0.374808 + 5.72837i) q^{70} +(-3.83432 + 11.8008i) q^{71} +(-3.68133 + 2.67464i) q^{73} -0.688626 q^{74} -2.86907 q^{76} +(-0.647340 + 0.470320i) q^{77} +(2.33206 - 7.17733i) q^{79} +(1.07428 - 0.272962i) q^{80} +10.5806 q^{82} +(-3.44931 - 10.6159i) q^{83} +(9.08699 + 3.62415i) q^{85} +(-0.189466 + 0.137655i) q^{86} +(0.690983 + 0.502029i) q^{88} +(-6.46715 + 4.69866i) q^{89} +(7.88442 + 5.72837i) q^{91} +(1.77970 + 5.47736i) q^{92} +(-0.835038 - 2.56998i) q^{94} +(5.30946 + 2.11756i) q^{95} +(-5.10143 + 15.7006i) q^{97} +(-0.386246 + 0.280624i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.757918	+	0.550660i	−0.535929	+	0.389375i	−0.822571	−	0.568662i	$-0.807461\pi$
$2$	−0.757918	+	0.550660i	−0.535929	+	0.389375i	0.286642	+	0.958038i	$0.407461\pi$
$3$		0			0
$3$		0			0
$4$	−0.346820	+	1.06740i	−0.173410	+	0.533701i
$5$	1.42964	−	1.71934i	0.639352	−	0.768914i
$5$	1.42964	−	1.71934i	0.639352	−	0.768914i
$6$		0			0
$7$	2.74037			1.03576			0.517881	−	0.855453i	$-0.326721\pi$
$7$	2.74037			1.03576			0.517881	+	0.855453i	$0.326721\pi$
$8$	−0.903913	−	2.78196i	−0.319581	−	0.983570i
$9$		0			0
$10$	−0.136773	+	2.09036i	−0.0432514	+	0.661031i
$11$	−0.236224	+	0.171627i	−0.0712241	+	0.0517473i	−0.622828	−	0.782359i	$-0.714016\pi$
$11$	−0.236224	+	0.171627i	−0.0712241	+	0.0517473i	0.551603	+	0.834106i	$0.314016\pi$
$12$		0			0
$13$	2.87714	+	2.09036i	0.797975	+	0.579763i	0.910319	−	0.413906i	$-0.135836\pi$
$13$	2.87714	+	2.09036i	0.797975	+	0.579763i	−0.112344	+	0.993669i	$0.535836\pi$
$14$	−2.07697	+	1.50901i	−0.555095	+	0.403300i
$15$		0			0
$16$	0.401030	+	0.291365i	0.100258	+	0.0728414i
$17$	1.35198	+	4.16097i	0.327904	+	1.00918i	0.970113	+	0.242655i	$0.0780182\pi$
$17$	1.35198	+	4.16097i	0.327904	+	1.00918i	−0.642209	+	0.766530i	$0.721982\pi$
$18$		0			0
$19$	0.789953	+	2.43123i	0.181228	+	0.557761i	0.999863	−	0.0165523i	$-0.00526901\pi$
$19$	0.789953	+	2.43123i	0.181228	+	0.557761i	−0.818635	+	0.574314i	$0.805269\pi$
$20$	1.33941	+	2.12230i	0.299500	+	0.474561i
$21$		0			0
$22$	0.0845304	−	0.260158i	0.0180219	−	0.0554658i
$23$	4.15146	−	3.01621i	0.865639	−	0.628924i	−0.0637740	−	0.997964i	$-0.520314\pi$
$23$	4.15146	−	3.01621i	0.865639	−	0.628924i	0.929413	+	0.369041i	$0.120314\pi$
$24$		0			0
$25$	−0.912286	−	4.91607i	−0.182457	−	0.983214i
$26$	−3.33172			−0.653404
$27$		0			0
$28$	−0.950415	+	2.92508i	−0.179611	+	0.552787i
$29$	−2.90477	+	8.93997i	−0.539403	+	1.66011i	0.194536	+	0.980895i	$0.437680\pi$
$29$	−2.90477	+	8.93997i	−0.539403	+	1.66011i	−0.733939	+	0.679216i	$0.762320\pi$
$30$		0			0
$31$	−2.76373	−	8.50589i	−0.496381	−	1.52770i	−0.814794	−	0.579751i	$-0.803150\pi$
$31$	−2.76373	−	8.50589i	−0.496381	−	1.52770i	0.318413	−	0.947952i	$-0.396850\pi$
$32$	5.38585			0.952093
$33$		0			0
$34$	−3.31597	−	2.40920i	−0.568685	−	0.413174i
$35$	3.91773	−	4.71163i	0.662217	−	0.796411i
$36$		0			0
$37$	0.594670	+	0.432053i	0.0977632	+	0.0710291i	0.635593	−	0.772024i	$-0.280756\pi$
$37$	0.594670	+	0.432053i	0.0977632	+	0.0710291i	−0.537830	+	0.843053i	$0.680756\pi$
$38$	−1.93750	−	1.40767i	−0.314304	−	0.228355i
$39$		0			0
$40$	−6.07541	−	2.42305i	−0.960606	−	0.383117i
$41$	−9.13695	−	6.63838i	−1.42695	−	1.03674i	−0.990574	−	0.136978i	$-0.956261\pi$
$41$	−9.13695	−	6.63838i	−1.42695	−	1.03674i	−0.436378	−	0.899763i	$-0.643739\pi$
$42$		0			0
$43$	0.249982			0.0381218			0.0190609	−	0.999818i	$-0.493932\pi$
$43$	0.249982			0.0381218			0.0190609	+	0.999818i	$0.493932\pi$
$44$	−0.101267	−	0.311669i	−0.0152666	−	0.0469859i
$45$		0			0
$46$	−1.48556	+	4.57209i	−0.219034	+	0.674117i
$47$	−0.891336	+	2.74325i	−0.130015	+	0.400144i	−0.994781	−	0.102030i	$-0.967466\pi$
$47$	−0.891336	+	2.74325i	−0.130015	+	0.400144i	0.864767	+	0.502174i	$0.167466\pi$
$48$		0			0
$49$	0.509614			0.0728020
$50$	3.39852	+	3.22362i	0.480623	+	0.455889i
$51$		0			0
$52$	−3.22911	+	2.34609i	−0.447797	+	0.325344i
$53$	1.50729	−	4.63896i	0.207042	−	0.637210i	−0.792581	−	0.609766i	$-0.791263\pi$
$53$	1.50729	−	4.63896i	0.207042	−	0.637210i	0.999623	−	0.0274434i	$-0.00873662\pi$
$54$		0			0
$55$	−0.0426286	+	0.651513i	−0.00574804	+	0.0878500i
$56$	−2.47705	−	7.62358i	−0.331010	−	1.01874i
$57$		0			0
$58$	−2.72130	−	8.37531i	−0.357325	−	1.09973i
$59$	−4.12708	−	2.99850i	−0.537300	−	0.390372i	0.285781	−	0.958295i	$-0.407747\pi$
$59$	−4.12708	−	2.99850i	−0.537300	−	0.390372i	−0.823081	+	0.567923i	$0.807747\pi$
$60$		0			0
$61$	1.61108	−	1.17052i	0.206277	−	0.149869i	−0.479850	−	0.877350i	$-0.659309\pi$
$61$	1.61108	−	1.17052i	0.206277	−	0.149869i	0.686128	+	0.727481i	$0.259309\pi$
$62$	6.77853	+	4.92489i	0.860875	+	0.625462i
$63$		0			0
$64$	−4.88410	+	3.54850i	−0.610512	+	0.443563i
$65$	7.70732	−	1.95833i	0.955975	−	0.242901i
$66$		0			0
$67$	−4.23771	−	13.0423i	−0.517719	−	1.59337i	−0.778280	−	0.627917i	$-0.783908\pi$
$67$	−4.23771	−	13.0423i	−0.517719	−	1.59337i	0.260562	−	0.965457i	$-0.416092\pi$
$68$	−4.91033			−0.595465
$69$		0			0
$70$	−0.374808	+	5.72837i	−0.0447982	+	0.684671i
$71$	−3.83432	+	11.8008i	−0.455050	+	1.40050i	0.416027	+	0.909352i	$0.363422\pi$
$71$	−3.83432	+	11.8008i	−0.455050	+	1.40050i	−0.871077	+	0.491147i	$0.836578\pi$
$72$		0			0
$73$	−3.68133	+	2.67464i	−0.430867	+	0.313043i	−0.781996	−	0.623284i	$-0.785798\pi$
$73$	−3.68133	+	2.67464i	−0.430867	+	0.313043i	0.351128	+	0.936327i	$0.385798\pi$
$74$	−0.688626			−0.0800511
$75$		0			0
$76$	−2.86907			−0.329105
$77$	−0.647340	+	0.470320i	−0.0737712	+	0.0535979i
$78$		0			0
$79$	2.33206	−	7.17733i	0.262377	−	0.807513i	−0.729909	−	0.683544i	$-0.760438\pi$
$79$	2.33206	−	7.17733i	0.262377	−	0.807513i	0.992286	−	0.123969i	$-0.0395622\pi$
$80$	1.07428	−	0.272962i	0.120109	−	0.0305181i
$81$		0			0
$82$	10.5806			1.16843
$83$	−3.44931	−	10.6159i	−0.378611	−	1.16524i	−0.941010	−	0.338378i	$-0.890122\pi$
$83$	−3.44931	−	10.6159i	−0.378611	−	1.16524i	0.562400	−	0.826866i	$-0.309878\pi$
$84$		0			0
$85$	9.08699	+	3.62415i	0.985622	+	0.393095i
$86$	−0.189466	+	0.137655i	−0.0204306	+	0.0148437i
$87$		0			0
$88$	0.690983	+	0.502029i	0.0736590	+	0.0535164i
$89$	−6.46715	+	4.69866i	−0.685516	+	0.498057i	−0.875183	−	0.483792i	$-0.839259\pi$
$89$	−6.46715	+	4.69866i	−0.685516	+	0.498057i	0.189667	+	0.981849i	$0.439259\pi$
$90$		0			0
$91$	7.88442	+	5.72837i	0.826512	+	0.600496i
$92$	1.77970	+	5.47736i	0.185547	+	0.571054i
$93$		0			0
$94$	−0.835038	−	2.56998i	−0.0861276	−	0.265073i
$95$	5.30946	+	2.11756i	0.544739	+	0.217258i
$96$		0			0
$97$	−5.10143	+	15.7006i	−0.517971	+	1.59415i	0.259838	+	0.965652i	$0.416331\pi$
$97$	−5.10143	+	15.7006i	−0.517971	+	1.59415i	−0.777810	+	0.628500i	$0.783669\pi$
$98$	−0.386246	+	0.280624i	−0.0390167	+	0.0283473i
$99$		0			0
$100$	5.56382	+	0.731215i	0.556382	+	0.0731215i
$101$	9.81876			0.977003			0.488501	−	0.872563i	$-0.337544\pi$
$101$	9.81876			0.977003			0.488501	+	0.872563i	$0.337544\pi$
$102$		0			0
$103$	1.52235	−	4.68531i	0.150001	−	0.461657i	−0.847619	−	0.530606i	$-0.821964\pi$
$103$	1.52235	−	4.68531i	0.150001	−	0.461657i	0.997620	+	0.0689487i	$0.0219645\pi$
$104$	3.21462	−	9.89359i	0.315220	−	0.970146i
$105$		0			0
$106$	1.41209	+	4.34595i	0.137154	+	0.422116i
$107$	−4.22786			−0.408722			−0.204361	−	0.978896i	$-0.565512\pi$
$107$	−4.22786			−0.408722			−0.204361	+	0.978896i	$0.565512\pi$
$108$		0			0
$109$	8.51690	+	6.18789i	0.815771	+	0.592692i	0.915498	−	0.402323i	$-0.131797\pi$
$109$	8.51690	+	6.18789i	0.815771	+	0.592692i	−0.0997272	+	0.995015i	$0.531797\pi$
$110$	−0.326453	−	0.517267i	−0.0311261	−	0.0493195i
$111$		0			0
$112$	1.09897	+	0.798448i	0.103843	+	0.0754463i
$113$	9.46187	+	6.87445i	0.890098	+	0.646694i	0.935903	−	0.352257i	$-0.114586\pi$
$113$	9.46187	+	6.87445i	0.890098	+	0.646694i	−0.0458059	+	0.998950i	$0.514586\pi$
$114$		0			0
$115$	0.749167	−	11.4499i	0.0698602	−	1.06771i
$116$	−8.53512	−	6.20112i	−0.792466	−	0.575760i
$117$		0			0
$118$	4.77915			0.439956
$119$	3.70493	+	11.4026i	0.339630	+	1.04527i
$120$		0			0
$121$	−3.37284	+	10.3805i	−0.306622	+	0.943685i
$122$	−0.576509	+	1.77431i	−0.0521946	+	0.160639i
$123$		0			0
$124$	10.0377			0.901414
$125$	−9.75665	−	5.45965i	−0.872661	−	0.488326i
$126$		0			0
$127$	−12.7074	+	9.23243i	−1.12760	+	0.819246i	−0.985343	−	0.170585i	$-0.945434\pi$
$127$	−12.7074	+	9.23243i	−1.12760	+	0.819246i	−0.142252	+	0.989830i	$0.545434\pi$
$128$	−1.58091	+	4.86555i	−0.139734	+	0.430058i
$129$		0			0
$130$	−4.76314	+	5.72837i	−0.417755	+	0.502411i
$131$	2.73458	+	8.41616i	0.238921	+	0.735323i	0.996577	+	0.0826693i	$0.0263445\pi$
$131$	2.73458	+	8.41616i	0.238921	+	0.735323i	−0.757656	+	0.652654i	$0.773655\pi$
$132$		0			0
$133$	2.16476	+	6.66245i	0.187709	+	0.577708i
$134$	10.3937	+	7.55148i	0.897881	+	0.652349i
$135$		0			0
$136$	10.3536	−	7.52231i	0.887812	−	0.645033i
$137$	−6.98635	−	5.07588i	−0.596884	−	0.433662i	0.247887	−	0.968789i	$-0.420264\pi$
$137$	−6.98635	−	5.07588i	−0.596884	−	0.433662i	−0.844772	+	0.535127i	$0.820264\pi$
$138$		0			0
$139$	6.48605	−	4.71239i	0.550140	−	0.399700i	−0.277697	−	0.960669i	$-0.589571\pi$
$139$	6.48605	−	4.71239i	0.550140	−	0.399700i	0.827837	+	0.560969i	$0.189571\pi$
$140$	3.67046	+	5.81588i	0.310211	+	0.491532i
$141$		0			0
$142$	−3.59214	−	11.0555i	−0.301445	−	0.927754i
$143$	−1.03841			−0.0868363
$144$		0			0
$145$	11.2181	+	17.7752i	0.931614	+	1.47615i
$146$	1.31733	−	4.05432i	0.109023	−	0.335538i
$147$		0			0
$148$	−0.667418	+	0.484908i	−0.0548615	+	0.0398592i
$149$	−12.8790			−1.05509			−0.527545	−	0.849527i	$-0.676887\pi$
$149$	−12.8790			−1.05509			−0.527545	+	0.849527i	$0.676887\pi$
$150$		0			0
$151$	−23.3541			−1.90053			−0.950263	−	0.311447i	$-0.899186\pi$
$151$	−23.3541			−1.90053			−0.950263	+	0.311447i	$0.899186\pi$
$152$	6.04951	−	4.39523i	0.490680	−	0.356500i
$153$		0			0
$154$	0.231644	−	0.712928i	0.0186664	−	0.0574494i
$155$	−18.5757	−	7.40852i	−1.49203	−	0.595066i
$156$		0			0
$157$	9.02953			0.720635			0.360317	−	0.932830i	$-0.382668\pi$
$157$	9.02953			0.720635			0.360317	+	0.932830i	$0.382668\pi$
$158$	2.18476	+	6.72400i	0.173810	+	0.534933i
$159$		0			0
$160$	7.69981	−	9.26013i	0.608723	−	0.732078i
$161$	11.3765	−	8.26553i	0.896596	−	0.651415i
$162$		0			0
$163$	−7.46699	−	5.42508i	−0.584859	−	0.424925i	0.255613	−	0.966779i	$-0.417723\pi$
$163$	−7.46699	−	5.42508i	−0.584859	−	0.424925i	−0.840473	+	0.541854i	$0.817723\pi$
$164$	10.2547	−	7.45048i	0.800758	−	0.581785i
$165$		0			0
$166$	8.46003	+	6.14657i	0.656626	+	0.477066i
$167$	−6.27950	−	19.3263i	−0.485923	−	1.49552i	−0.830640	−	0.556810i	$-0.812025\pi$
$167$	−6.27950	−	19.3263i	−0.485923	−	1.49552i	0.344718	−	0.938706i	$-0.387975\pi$
$168$		0			0
$169$	−0.108909	−	0.335187i	−0.00837761	−	0.0257836i
$170$	−8.88287	+	2.25703i	−0.681285	+	0.173106i
$171$		0			0
$172$	−0.0866986	+	0.266831i	−0.00661071	+	0.0203457i
$173$	12.8798	−	9.35771i	0.979232	−	0.711454i	0.0216952	−	0.999765i	$-0.493094\pi$
$173$	12.8798	−	9.35771i	0.979232	−	0.711454i	0.957537	+	0.288311i	$0.0930937\pi$
$174$		0			0
$175$	−2.50000	−	13.4718i	−0.188982	−	1.01838i
$176$	−0.144739			−0.0109101
$177$		0			0
$178$	2.31421	−	7.12240i	0.173457	−	0.533846i
$179$	1.55433	−	4.78373i	0.116176	−	0.357553i	−0.876014	−	0.482285i	$-0.839807\pi$
$179$	1.55433	−	4.78373i	0.116176	−	0.357553i	0.992190	+	0.124732i	$0.0398070\pi$
$180$		0			0
$181$	−0.877466	−	2.70056i	−0.0652215	−	0.200731i	0.913135	−	0.407657i	$-0.133654\pi$
$181$	−0.877466	−	2.70056i	−0.0652215	−	0.200731i	−0.978357	+	0.206926i	$0.933654\pi$
$182$	−9.13013			−0.676770
$183$		0			0
$184$	−12.1435	−	8.82279i	−0.895233	−	0.650425i
$185$	1.59301	−	0.404764i	0.117120	−	0.0297589i
$186$		0			0
$187$	−1.03350	−	0.750884i	−0.0755773	−	0.0549101i
$188$	−2.61902	−	1.90283i	−0.191012	−	0.138778i
$189$		0			0
$190$	−5.19019	+	1.31876i	−0.376536	+	0.0956732i
$191$	16.8121	+	12.2147i	1.21648	+	0.883824i	0.995803	−	0.0915227i	$-0.0291734\pi$
$191$	16.8121	+	12.2147i	1.21648	+	0.883824i	0.220677	+	0.975347i	$0.429173\pi$
$192$		0			0
$193$	−8.46086			−0.609026			−0.304513	−	0.952508i	$-0.598494\pi$
$193$	−8.46086			−0.609026			−0.304513	+	0.952508i	$0.598494\pi$
$194$	−4.77921	−	14.7089i	−0.343127	−	1.05604i
$195$		0			0
$196$	−0.176744	+	0.543963i	−0.0126246	+	0.0388545i
$197$	1.94825	−	5.99611i	0.138807	−	0.427205i	−0.857356	−	0.514725i	$-0.827894\pi$
$197$	1.94825	−	5.99611i	0.138807	−	0.427205i	0.996163	+	0.0875199i	$0.0278941\pi$
$198$		0			0
$199$	−19.4190			−1.37658			−0.688290	−	0.725436i	$-0.741638\pi$
$199$	−19.4190			−1.37658			−0.688290	+	0.725436i	$0.741638\pi$
$200$	−12.8517	+	6.98164i	−0.908750	+	0.493676i
$201$		0			0
$202$	−7.44182	+	5.40680i	−0.523604	+	0.380421i
$203$	−7.96015	+	24.4988i	−0.558693	+	1.71948i
$204$		0			0
$205$	−24.4762	+	6.21909i	−1.70949	+	0.434360i
$206$	1.42619	+	4.38938i	0.0993677	+	0.305822i
$207$		0			0
$208$	0.544760	+	1.67660i	0.0377723	+	0.116251i
$209$	−0.603868	−	0.438736i	−0.0417704	−	0.0303480i
$210$		0			0
$211$	13.9700	−	10.1498i	0.961732	−	0.698739i	0.00817983	−	0.999967i	$-0.497396\pi$
$211$	13.9700	−	10.1498i	0.961732	−	0.698739i	0.953552	+	0.301227i	$0.0973962\pi$
$212$	4.42888	+	3.21777i	0.304176	+	0.220997i
$213$		0			0
$214$	3.20437	−	2.32811i	0.219046	−	0.159146i
$215$	0.357382	−	0.429804i	0.0243733	−	0.0293124i
$216$		0			0
$217$	−7.57364	−	23.3093i	−0.514132	−	1.58234i
$218$	−9.86253			−0.667975
$219$		0			0
$220$	−0.680642	−	0.271460i	−0.0458889	−	0.0183018i
$221$	−4.80811	+	14.7978i	−0.323429	+	0.995411i
$222$		0			0
$223$	−1.15239	+	0.837259i	−0.0771697	+	0.0560670i	−0.625701	−	0.780063i	$-0.715187\pi$
$223$	−1.15239	+	0.837259i	−0.0771697	+	0.0560670i	0.548532	+	0.836130i	$0.315187\pi$
$224$	14.7592			0.986142
$225$		0			0
$226$	−10.9568			−0.728836
$227$	−7.49824	+	5.44779i	−0.497676	+	0.361583i	−0.808129	−	0.589006i	$-0.799519\pi$
$227$	−7.49824	+	5.44779i	−0.497676	+	0.361583i	0.310453	+	0.950589i	$0.399519\pi$
$228$		0			0
$229$	−5.19875	+	16.0001i	−0.343543	+	1.05732i	0.618816	+	0.785536i	$0.287613\pi$
$229$	−5.19875	+	16.0001i	−0.343543	+	1.05732i	−0.962359	+	0.271781i	$0.912387\pi$
$230$	5.73718	+	9.09060i	0.378298	+	0.599417i
$231$		0			0
$232$	27.4963			1.80522
$233$	3.05125	+	9.39077i	0.199894	+	0.615210i	0.999885	+	0.0151975i	$0.00483770\pi$
$233$	3.05125	+	9.39077i	0.199894	+	0.615210i	−0.799991	+	0.600012i	$0.795162\pi$
$234$		0			0
$235$	3.44230	+	5.45436i	0.224551	+	0.355803i
$236$	4.63196	−	3.36532i	0.301515	−	0.219064i
$237$		0			0
$238$	−9.08699	−	6.60208i	−0.589022	−	0.427949i
$239$	16.9800	−	12.3367i	1.09835	−	0.797994i	0.117556	−	0.993066i	$-0.462494\pi$
$239$	16.9800	−	12.3367i	1.09835	−	0.797994i	0.980789	+	0.195072i	$0.0624940\pi$
$240$		0			0
$241$	−0.484709	−	0.352162i	−0.0312229	−	0.0226848i	0.572064	−	0.820209i	$-0.306143\pi$
$241$	−0.484709	−	0.352162i	−0.0312229	−	0.0226848i	−0.603287	+	0.797524i	$0.706143\pi$
$242$	−3.15981	−	9.72489i	−0.203120	−	0.625139i
$243$		0			0
$244$	0.690658	+	2.12563i	0.0442148	+	0.136079i
$245$	0.728562	−	0.876202i	0.0465461	−	0.0559785i
$246$		0			0
$247$	−2.80934	+	8.64627i	−0.178754	+	0.550149i
$248$	−21.1648	+	15.3772i	−1.34397	+	0.976451i
$249$		0			0
$250$	10.4012	−	1.23463i	0.657827	−	0.0780846i
$251$	22.8068			1.43955			0.719776	−	0.694207i	$-0.244245\pi$
$251$	22.8068			1.43955			0.719776	+	0.694207i	$0.244245\pi$
$252$		0			0
$253$	−0.463011	+	1.42500i	−0.0291092	+	0.0895891i
$254$	4.54721	−	13.9949i	0.285317	−	0.878116i
$255$		0			0
$256$	−5.21218	−	16.0414i	−0.325761	−	1.00259i
$257$	−4.10576			−0.256110			−0.128055	−	0.991767i	$-0.540873\pi$
$257$	−4.10576			−0.256110			−0.128055	+	0.991767i	$0.540873\pi$
$258$		0			0
$259$	1.62962	+	1.18398i	0.101259	+	0.0735692i
$260$	−0.582721	+	8.90600i	−0.0361389	+	0.552327i
$261$		0			0
$262$	−6.70703	−	4.87294i	−0.414362	−	0.301051i
$263$	10.4168	+	7.56828i	0.642330	+	0.466680i	0.860650	−	0.509197i	$-0.170058\pi$
$263$	10.4168	+	7.56828i	0.642330	+	0.466680i	−0.218320	+	0.975877i	$0.570058\pi$
$264$		0			0
$265$	−5.82109	−	9.22356i	−0.357587	−	0.566599i
$266$	−5.30946	−	3.85755i	−0.325544	−	0.236521i
$267$		0			0
$268$	15.3911			0.940164
$269$	−2.27529	−	7.00263i	−0.138727	−	0.426958i	0.857424	−	0.514611i	$-0.172063\pi$
$269$	−2.27529	−	7.00263i	−0.138727	−	0.426958i	−0.996151	+	0.0876525i	$0.972063\pi$
$270$		0			0
$271$	−0.405027	+	1.24655i	−0.0246037	+	0.0757223i	−0.962604	−	0.270911i	$-0.912675\pi$
$271$	−0.405027	+	1.24655i	−0.0246037	+	0.0757223i	0.938001	+	0.346633i	$0.112675\pi$
$272$	−0.670178	+	2.06260i	−0.0406355	+	0.125063i
$273$		0			0
$274$	8.09017			0.488745
$275$	1.05923	+	1.00472i	0.0638741	+	0.0605868i
$276$		0			0
$277$	−9.25811	+	6.72641i	−0.556266	+	0.404151i	−0.830091	−	0.557629i	$-0.811711\pi$
$277$	−9.25811	+	6.72641i	−0.556266	+	0.404151i	0.273824	+	0.961780i	$0.411711\pi$
$278$	−2.32097	+	7.14321i	−0.139203	+	0.428422i
$279$		0			0
$280$	−16.6488	−	6.64004i	−0.994959	−	0.396818i
$281$	0.970352	+	2.98644i	0.0578864	+	0.178156i	0.975819	−	0.218581i	$-0.0701427\pi$
$281$	0.970352	+	2.98644i	0.0578864	+	0.178156i	−0.917933	+	0.396737i	$0.870143\pi$
$282$		0			0
$283$	5.65203	+	17.3951i	0.335978	+	1.03403i	0.966238	+	0.257650i	$0.0829482\pi$
$283$	5.65203	+	17.3951i	0.335978	+	1.03403i	−0.630260	+	0.776384i	$0.717052\pi$
$284$	−11.2664	−	8.18552i	−0.668538	−	0.485721i
$285$		0			0
$286$	0.787030	−	0.571811i	0.0465381	−	0.0338119i
$287$	−25.0386	−	18.1916i	−1.47798	−	1.07382i
$288$		0			0
$289$	−1.73256	+	1.25878i	−0.101915	+	0.0740458i
$290$	−18.2905	−	7.29478i	−1.07406	−	0.428364i
$291$		0			0
$292$	−1.57816	−	4.85708i	−0.0923550	−	0.284239i
$293$	12.2342			0.714727			0.357364	−	0.933965i	$-0.383676\pi$
$293$	12.2342			0.714727			0.357364	+	0.933965i	$0.383676\pi$
$294$		0			0
$295$	−11.0557	+	2.80911i	−0.643686	+	0.163553i
$296$	0.664424	−	2.04489i	0.0386188	−	0.118857i
$297$		0			0
$298$	9.76124	−	7.09195i	0.565453	−	0.410826i
$299$	18.2493			1.05539
$300$		0			0
$301$	0.685041			0.0394851
$302$	17.7005	−	12.8601i	1.01855	−	0.740018i
$303$		0			0
$304$	−0.391580	+	1.20516i	−0.0224587	+	0.0691206i
$305$	0.290733	−	4.44341i	0.0166473	−	0.254429i
$306$		0			0
$307$	34.8868			1.99110			0.995549	−	0.0942495i	$-0.0300451\pi$
$307$	34.8868			1.99110			0.995549	+	0.0942495i	$0.0300451\pi$
$308$	−0.277510	−	0.854088i	−0.0158126	−	0.0486662i
$309$		0			0
$310$	18.1584	−	4.61383i	1.03133	−	0.262048i
$311$	−7.74178	+	5.62473i	−0.438996	+	0.318949i	−0.785236	−	0.619197i	$-0.787458\pi$
$311$	−7.74178	+	5.62473i	−0.438996	+	0.318949i	0.346240	+	0.938146i	$0.387458\pi$
$312$		0			0
$313$	23.1535	+	16.8220i	1.30871	+	0.950834i	1.00000		0.000321264i	$-0.000102262\pi$
$313$	23.1535	+	16.8220i	1.30871	+	0.950834i	0.308711	+	0.951156i	$0.400102\pi$
$314$	−6.84365	+	4.97220i	−0.386209	+	0.280597i
$315$		0			0
$316$	6.85230	+	4.97848i	0.385472	+	0.280062i
$317$	3.99692	+	12.3012i	0.224489	+	0.690907i	0.998343	+	0.0575426i	$0.0183265\pi$
$317$	3.99692	+	12.3012i	0.224489	+	0.690907i	−0.773854	+	0.633364i	$0.781674\pi$
$318$		0			0
$319$	−0.848160	−	2.61037i	−0.0474879	−	0.146153i
$320$	−0.881378	+	13.4705i	−0.0492705	+	0.753024i
$321$		0			0
$322$	−4.07098	+	12.5292i	−0.226867	+	0.698225i
$323$	−9.04826	+	6.57395i	−0.503459	+	0.365784i
$324$		0			0
$325$	7.65160	−	16.0512i	0.424435	−	0.890362i
$326$	8.64674			0.478899
$327$		0			0
$328$	−10.2087	+	31.4191i	−0.563681	+	1.73483i
$329$	−2.44259	+	7.51751i	−0.134664	+	0.414454i
$330$		0			0
$331$	−4.36424	−	13.4318i	−0.239880	−	0.738276i	−0.996436	−	0.0843471i	$-0.973120\pi$
$331$	−4.36424	−	13.4318i	−0.239880	−	0.738276i	0.756556	−	0.653929i	$-0.226880\pi$
$332$	12.5277			0.687547
$333$		0			0
$334$	15.4016	+	11.1899i	0.842737	+	0.612284i
$335$	−28.4826	−	11.3597i	−1.55617	−	0.620646i
$336$		0			0
$337$	21.1034	+	15.3325i	1.14957	+	0.835214i	0.988424	−	0.151716i	$-0.0484800\pi$
$337$	21.1034	+	15.3325i	1.14957	+	0.835214i	0.161149	+	0.986930i	$0.448480\pi$
$338$	0.267118	+	0.194073i	0.0145293	+	0.0105562i
$339$		0			0
$340$	−7.01998	+	8.44254i	−0.380712	+	0.457861i
$341$	2.11269	+	1.53496i	0.114409	+	0.0831229i
$342$		0			0
$343$	−17.7860			−0.960356
$344$	−0.225961	−	0.695438i	−0.0121830	−	0.0374955i
$345$		0			0
$346$	−4.60891	+	14.1848i	−0.247776	+	0.762578i
$347$	10.3024	−	31.7076i	0.553063	−	1.70215i	−0.147943	−	0.988996i	$-0.547265\pi$
$347$	10.3024	−	31.7076i	0.553063	−	1.70215i	0.701005	−	0.713156i	$-0.252735\pi$
$348$		0			0
$349$	−2.42476			−0.129794			−0.0648972	−	0.997892i	$-0.520672\pi$
$349$	−2.42476			−0.129794			−0.0648972	+	0.997892i	$0.520672\pi$
$350$	9.31320	+	8.83390i	0.497811	+	0.472192i
$351$		0			0
$352$	−1.27227	+	0.924355i	−0.0678120	+	0.0492683i
$353$	7.92817	−	24.4004i	0.421974	−	1.29870i	−0.483888	−	0.875130i	$-0.660776\pi$
$353$	7.92817	−	24.4004i	0.421974	−	1.29870i	0.905862	−	0.423572i	$-0.139224\pi$
$354$		0			0
$355$	14.8080	+	23.4634i	0.785926	+	1.24531i
$356$	−2.77242	−	8.53264i	−0.146938	−	0.452229i
$357$		0			0
$358$	1.45616	+	4.48159i	0.0769602	+	0.236859i
$359$	−0.755429	−	0.548851i	−0.0398700	−	0.0289673i	0.567672	−	0.823255i	$-0.307844\pi$
$359$	−0.755429	−	0.548851i	−0.0398700	−	0.0289673i	−0.607542	+	0.794288i	$0.707844\pi$
$360$		0			0
$361$	10.0845	−	7.32681i	0.530763	−	0.385622i
$362$	2.15214	+	1.56362i	0.113114	+	0.0821820i
$363$		0			0
$364$	−8.84895	+	6.42914i	−0.463811	+	0.336978i
$365$	−0.664329	+	10.1532i	−0.0347726	+	0.531445i
$366$		0			0
$367$	−5.60428	−	17.2482i	−0.292541	−	0.900349i	−0.984036	−	0.177968i	$-0.943048\pi$
$367$	−5.60428	−	17.2482i	−0.292541	−	0.900349i	0.691495	−	0.722381i	$-0.256952\pi$
$368$	2.54368			0.132599
$369$		0			0
$370$	−0.984484	+	1.18398i	−0.0511809	+	0.0615524i
$371$	4.13052	−	12.7124i	0.214446	−	0.659997i
$372$		0			0
$373$	19.3335	−	14.0466i	1.00105	−	0.727304i	0.0387358	−	0.999249i	$-0.487667\pi$
$373$	19.3335	−	14.0466i	1.00105	−	0.727304i	0.962313	+	0.271945i	$0.0876669\pi$
$374$	1.19679			0.0618847
$375$		0			0
$376$	8.43729			0.435120
$377$	−27.0452	+	19.6495i	−1.39290	+	1.01200i
$378$		0			0
$379$	0.251135	−	0.772913i	0.0128999	−	0.0397019i	−0.944399	−	0.328801i	$-0.893356\pi$
$379$	0.251135	−	0.772913i	0.0128999	−	0.0397019i	0.957299	+	0.289099i	$0.0933556\pi$
$380$	−4.10172	+	4.93291i	−0.210414	+	0.253053i
$381$		0			0
$382$	−19.4683			−0.996086
$383$	7.22565	+	22.2383i	0.369214	+	1.13632i	0.947300	+	0.320347i	$0.103800\pi$
$383$	7.22565	+	22.2383i	0.369214	+	1.13632i	−0.578087	+	0.815975i	$0.696200\pi$
$384$		0			0
$385$	−0.116818	+	1.78538i	−0.00595360	+	0.0909916i
$386$	6.41264	−	4.65905i	0.326395	−	0.237140i
$387$		0			0
$388$	−14.9896	−	10.8906i	−0.760980	−	0.552884i
$389$	−9.31412	+	6.76711i	−0.472245	+	0.343106i	−0.798316	−	0.602239i	$-0.794275\pi$
$389$	−9.31412	+	6.76711i	−0.472245	+	0.343106i	0.326071	+	0.945345i	$0.394275\pi$
$390$		0			0
$391$	18.1631	+	13.1963i	0.918547	+	0.667363i
$392$	−0.460647	−	1.41772i	−0.0232662	−	0.0716059i
$393$		0			0
$394$	1.82520	+	5.61738i	0.0919522	+	0.283000i
$395$	−9.00631	−	14.2706i	−0.453157	−	0.718030i
$396$		0			0
$397$	1.47828	−	4.54967i	0.0741927	−	0.228342i	−0.907082	−	0.420953i	$-0.861696\pi$
$397$	1.47828	−	4.54967i	0.0741927	−	0.228342i	0.981275	+	0.192611i	$0.0616957\pi$
$398$	14.7180	−	10.6933i	0.737749	−	0.536006i
$399$		0			0
$400$	1.06652	−	2.23730i	0.0533259	−	0.111865i
$401$	−29.7663			−1.48646			−0.743228	−	0.669038i	$-0.766706\pi$
$401$	−29.7663			−1.48646			−0.743228	+	0.669038i	$0.766706\pi$
$402$		0			0
$403$	9.82877	−	30.2498i	0.489606	−	1.50685i
$404$	−3.40534	+	10.4806i	−0.169422	+	0.521428i
$405$		0			0
$406$	−7.45737	−	22.9514i	−0.370103	−	1.13906i
$407$	−0.214627			−0.0106387
$408$		0			0
$409$	4.84465	+	3.51985i	0.239553	+	0.174045i	0.701084	−	0.713079i	$-0.252700\pi$
$409$	4.84465	+	3.51985i	0.239553	+	0.174045i	−0.461531	+	0.887124i	$0.652700\pi$
$410$	15.1263	−	18.1916i	0.747036	−	0.898420i
$411$		0			0
$412$	4.47313	+	3.24992i	0.220375	+	0.160112i
$413$	−11.3097	−	8.21699i	−0.556515	−	0.404332i
$414$		0			0
$415$	−23.1836	−	9.24628i	−1.13804	−	0.453882i
$416$	15.4959	+	11.2584i	0.759747	+	0.551988i
$417$		0			0
$418$	0.699277			0.0342028
$419$	1.31544	+	4.04851i	0.0642635	+	0.197783i	0.978033	−	0.208451i	$-0.0668420\pi$
$419$	1.31544	+	4.04851i	0.0642635	+	0.197783i	−0.913769	+	0.406233i	$0.866842\pi$
$420$		0			0
$421$	−7.19046	+	22.1300i	−0.350441	+	1.07855i	0.608164	+	0.793811i	$0.291906\pi$
$421$	−7.19046	+	22.1300i	−0.350441	+	1.07855i	−0.958606	+	0.284737i	$0.908094\pi$
$422$	−4.99902	+	15.3854i	−0.243348	+	0.748950i
$423$		0			0
$424$	−14.2678			−0.692907
$425$	19.2222	−	10.4424i	0.932416	−	0.506533i
$426$		0			0
$427$	4.41494	−	3.20764i	0.213654	−	0.155229i
$428$	1.46631	−	4.51283i	0.0708766	−	0.218136i
$429$		0			0
$430$	−0.0341907	+	0.522553i	−0.00164882	+	0.0251997i
$431$	3.86801	+	11.9045i	0.186315	+	0.573420i	0.999969	−	0.00793088i	$-0.00252451\pi$
$431$	3.86801	+	11.9045i	0.186315	+	0.573420i	−0.813653	+	0.581351i	$0.802525\pi$
$432$		0			0
$433$	−5.85788	−	18.0287i	−0.281512	−	0.866403i	−0.987423	−	0.158103i	$-0.949462\pi$
$433$	−5.85788	−	18.0287i	−0.281512	−	0.866403i	0.705911	−	0.708300i	$-0.250538\pi$
$434$	18.5757	+	13.4960i	0.891661	+	0.647830i
$435$		0			0
$436$	−9.55880	+	6.94487i	−0.457783	+	0.332599i
$437$	10.6125	+	7.71047i	0.507667	+	0.368842i
$438$		0			0
$439$	5.90513	−	4.29033i	0.281836	−	0.204766i	−0.437882	−	0.899033i	$-0.644271\pi$
$439$	5.90513	−	4.29033i	0.281836	−	0.204766i	0.719718	+	0.694267i	$0.244271\pi$
$440$	1.85101	−	0.470320i	0.0882436	−	0.0224216i
$441$		0			0
$442$	−4.50442	−	13.8632i	−0.214254	−	0.659405i
$443$	−5.75210			−0.273291			−0.136645	−	0.990620i	$-0.543632\pi$
$443$	−5.75210			−0.273291			−0.136645	+	0.990620i	$0.543632\pi$
$444$		0			0
$445$	−1.16705	+	17.8366i	−0.0553236	+	0.845537i
$446$	0.412371	−	1.26915i	0.0195263	−	0.0600959i
$447$		0			0
$448$	−13.3842	+	9.72421i	−0.632345	+	0.459426i
$449$	−4.75061			−0.224195			−0.112098	−	0.993697i	$-0.535757\pi$
$449$	−4.75061			−0.224195			−0.112098	+	0.993697i	$0.535757\pi$
$450$		0			0
$451$	3.29769			0.155282
$452$	−10.6194	+	7.71542i	−0.499493	+	0.362903i
$453$		0			0
$454$	2.68318	−	8.25796i	0.125928	−	0.387565i
$455$	21.1209	−	5.36656i	0.990162	−	0.251588i
$456$		0			0
$457$	4.72678			0.221110			0.110555	−	0.993870i	$-0.464737\pi$
$457$	4.72678			0.221110			0.110555	+	0.993870i	$0.464737\pi$
$458$	−4.87039	−	14.9895i	−0.227579	−	0.700415i
$459$		0			0
$460$	11.9618	+	4.77071i	0.557722	+	0.222435i
$461$	−6.23775	+	4.53199i	−0.290521	+	0.211076i	−0.723493	−	0.690331i	$-0.757465\pi$
$461$	−6.23775	+	4.53199i	−0.290521	+	0.211076i	0.432972	+	0.901407i	$0.357465\pi$
$462$		0			0
$463$	3.09818	+	2.25096i	0.143985	+	0.104611i	0.657446	−	0.753502i	$-0.271637\pi$
$463$	3.09818	+	2.25096i	0.143985	+	0.104611i	−0.513461	+	0.858113i	$0.671637\pi$
$464$	−3.76970	+	2.73885i	−0.175004	+	0.127148i
$465$		0			0
$466$	−7.48372	−	5.43724i	−0.346677	−	0.251875i
$467$	6.14580	+	18.9148i	0.284394	+	0.875274i	0.986580	+	0.163281i	$0.0522076\pi$
$467$	6.14580	+	18.9148i	0.284394	+	0.875274i	−0.702186	+	0.711994i	$0.747792\pi$
$468$		0			0
$469$	−11.6129	−	35.7408i	−0.536233	−	1.65036i
$470$	−5.61248	−	2.23842i	−0.258885	−	0.103251i
$471$		0			0
$472$	−4.61118	+	14.1917i	−0.212247	+	0.653228i
$473$	−0.0590515	+	0.0429035i	−0.00271519	+	0.00197270i
$474$		0			0
$475$	11.2314	−	6.10144i	0.515332	−	0.279953i
$476$	−13.4561			−0.616760
$477$		0			0
$478$	−6.07613	+	18.7004i	−0.277916	+	0.855337i
$479$	−8.59722	+	26.4595i	−0.392817	+	1.20897i	0.537831	+	0.843052i	$0.319244\pi$
$479$	−8.59722	+	26.4595i	−0.392817	+	1.20897i	−0.930649	+	0.365914i	$0.880756\pi$
$480$		0			0
$481$	0.807801	+	2.48616i	0.0368326	+	0.113359i
$482$	0.561292			0.0255661
$483$		0			0
$484$	−9.91044	−	7.20036i	−0.450475	−	0.327289i
$485$	19.7015	+	31.2172i	0.894599	+	1.41750i
$486$		0			0
$487$	−25.6572	−	18.6411i	−1.16264	−	0.844708i	−0.172531	−	0.985004i	$-0.555195\pi$
$487$	−25.6572	−	18.6411i	−1.16264	−	0.844708i	−0.990110	+	0.140296i	$0.955195\pi$
$488$	−4.71260	−	3.42390i	−0.213329	−	0.154993i
$489$		0			0
$490$	−0.0697014	+	1.06528i	−0.00314879	+	0.0481244i
$491$	3.96526	+	2.88093i	0.178950	+	0.130015i	0.673654	−	0.739047i	$-0.264724\pi$
$491$	3.96526	+	2.88093i	0.178950	+	0.130015i	−0.494705	+	0.869061i	$0.664724\pi$
$492$		0			0
$493$	−41.1262			−1.85223
$494$	−2.63190	−	8.10016i	−0.118415	−	0.364443i
$495$		0			0
$496$	1.36998	−	4.21637i	0.0615140	−	0.189321i
$497$	−10.5074	+	32.3386i	−0.471323	+	1.45058i
$498$		0			0
$499$	3.13604			0.140389			0.0701943	−	0.997533i	$-0.477638\pi$
$499$	3.13604			0.140389			0.0701943	+	0.997533i	$0.477638\pi$
$500$	9.21145	−	8.52076i	0.411948	−	0.381060i
$501$		0			0
$502$	−17.2857	+	12.5588i	−0.771498	+	0.560526i
$503$	5.96362	−	18.3541i	0.265905	−	0.818370i	−0.725579	−	0.688139i	$-0.758428\pi$
$503$	5.96362	−	18.3541i	0.265905	−	0.818370i	0.991484	−	0.130231i	$-0.0415720\pi$
$504$		0			0
$505$	14.0372	−	16.8818i	0.624649	−	0.751231i
$506$	−0.433767	−	1.33500i	−0.0192833	−	0.0593478i
$507$		0			0
$508$	−5.44756	−	16.7659i	−0.241696	−	0.743865i
$509$	−33.7843	−	24.5458i	−1.49746	−	1.08797i	−0.971378	−	0.237541i	$-0.923659\pi$
$509$	−33.7843	−	24.5458i	−1.49746	−	1.08797i	−0.526087	−	0.850431i	$-0.676341\pi$
$510$		0			0
$511$	−10.0882	+	7.32951i	−0.446276	+	0.324238i
$512$	4.50601	+	3.27381i	0.199140	+	0.144683i
$513$		0			0
$514$	3.11183	−	2.26088i	0.137257	−	0.0997230i
$515$	−5.87925	−	9.31572i	−0.259071	−	0.410500i
$516$		0			0
$517$	−0.260260	−	0.800997i	−0.0114462	−	0.0352278i
$518$	−1.88709			−0.0829139
$519$		0			0
$520$	−12.4147	−	19.6713i	−0.544422	−	0.862642i
$521$	10.5179	−	32.3709i	0.460799	−	1.41819i	−0.403390	−	0.915028i	$-0.632168\pi$
$521$	10.5179	−	32.3709i	0.460799	−	1.41819i	0.864189	−	0.503167i	$-0.167832\pi$
$522$		0			0
$523$	6.47351	−	4.70328i	0.283067	−	0.205660i	−0.437187	−	0.899371i	$-0.644025\pi$
$523$	6.47351	−	4.70328i	0.283067	−	0.205660i	0.720254	+	0.693710i	$0.244025\pi$
$524$	−9.93184			−0.433874
$525$		0			0
$526$	−12.0627			−0.525957
$527$	31.6563	−	22.9996i	1.37897	−	1.00188i
$528$		0			0
$529$	1.02969	−	3.16907i	0.0447693	−	0.137786i
$530$	9.49095	+	3.78527i	0.412261	+	0.164421i
$531$		0			0
$532$	−7.86230			−0.340874
$533$	−12.4117	−	38.1991i	−0.537608	−	1.65459i
$534$		0			0
$535$	−6.04429	+	7.26914i	−0.261318	+	0.314272i
$536$	−32.4527	+	23.5783i	−1.40174	+	1.01843i
$537$		0			0
$538$	5.58056	+	4.05451i	0.240595	+	0.174802i
$539$	−0.120383	+	0.0874633i	−0.00518526	+	0.00376731i
$540$		0			0
$541$	−7.84390	−	5.69893i	−0.337235	−	0.245016i	0.406259	−	0.913758i	$-0.366833\pi$
$541$	−7.84390	−	5.69893i	−0.337235	−	0.245016i	−0.743495	+	0.668742i	$0.766833\pi$
$542$	−0.379445	−	1.16781i	−0.0162986	−	0.0501618i
$543$		0			0
$544$	7.28158	+	22.4104i	0.312195	+	0.960838i
$545$	22.8152	−	5.79705i	0.977294	−	0.248318i
$546$		0			0
$547$	−4.49631	+	13.8382i	−0.192248	+	0.591680i	0.807749	+	0.589526i	$0.200686\pi$
$547$	−4.49631	+	13.8382i	−0.192248	+	0.591680i	−0.999998	+	0.00215372i	$0.999314\pi$
$548$	7.84102	−	5.69683i	0.334952	−	0.243357i
$549$		0			0
$550$	−1.35607	−	0.178219i	−0.0578230	−	0.00759927i
$551$	−24.0297			−1.02370
$552$		0			0
$553$	6.39069	−	19.6685i	0.271760	−	0.836391i
$554$	3.31293	−	10.1961i	0.140753	−	0.433193i
$555$		0			0
$556$	2.78053	+	8.55758i	0.117921	+	0.362922i
$557$	17.8610			0.756795			0.378397	−	0.925643i	$-0.376475\pi$
$557$	17.8610			0.756795			0.378397	+	0.925643i	$0.376475\pi$
$558$		0			0
$559$	0.719232	+	0.522553i	0.0304203	+	0.0221016i
$560$	2.94393	−	0.748017i	0.124404	−	0.0316095i
$561$		0			0
$562$	−2.37996	−	1.72914i	−0.100393	−	0.0729394i
$563$	−17.5168	−	12.7267i	−0.738244	−	0.536365i	0.153917	−	0.988084i	$-0.450811\pi$
$563$	−17.5168	−	12.7267i	−0.738244	−	0.536365i	−0.892161	+	0.451718i	$0.850811\pi$
$564$		0			0
$565$	25.3466	−	6.44025i	1.06634	−	0.270943i
$566$	−13.8626	−	10.0718i	−0.582688	−	0.423348i
$567$		0			0
$568$	36.2953			1.52292
$569$	10.1244	+	31.1598i	0.424439	+	1.30629i	0.903531	+	0.428524i	$0.140966\pi$
$569$	10.1244	+	31.1598i	0.424439	+	1.30629i	−0.479092	+	0.877765i	$0.659034\pi$
$570$		0			0
$571$	−1.04981	+	3.23099i	−0.0439332	+	0.135213i	−0.970617	−	0.240629i	$-0.922646\pi$
$571$	−1.04981	+	3.23099i	−0.0439332	+	0.135213i	0.926684	+	0.375842i	$0.122646\pi$
$572$	0.360142	−	1.10840i	0.0150583	−	0.0463446i
$573$		0			0
$574$	28.9946			1.21021
$575$	−18.6152	−	17.6572i	−0.776309	−	0.736357i
$576$		0			0
$577$	−10.1669	+	7.38668i	−0.423253	+	0.307512i	−0.778945	−	0.627092i	$-0.784245\pi$
$577$	−10.1669	+	7.38668i	−0.423253	+	0.307512i	0.355692	+	0.934603i	$0.384245\pi$
$578$	0.619980	−	1.90810i	0.0257878	−	0.0793666i
$579$		0			0
$580$	−22.8640	+	5.80945i	−0.949375	+	0.241224i
$581$	−9.45237	−	29.0914i	−0.392150	−	1.20691i
$582$		0			0
$583$	0.440111	+	1.35452i	0.0182275	+	0.0560985i
$584$	10.7683	+	7.82366i	0.445597	+	0.323745i
$585$		0			0
$586$	−9.27249	+	6.73686i	−0.383043	+	0.278297i
$587$	29.4047	+	21.3638i	1.21366	+	0.881777i	0.995558	−	0.0941492i	$-0.0300131\pi$
$587$	29.4047	+	21.3638i	1.21366	+	0.881777i	0.218103	+	0.975926i	$0.430013\pi$
$588$		0			0
$589$	18.4965	−	13.4385i	0.762136	−	0.553724i
$590$	6.83244	−	8.21699i	0.281287	−	0.338288i
$591$		0			0
$592$	0.112595	+	0.346533i	0.00462764	+	0.0142424i
$593$	31.7555			1.30404			0.652022	−	0.758200i	$-0.273921\pi$
$593$	31.7555			1.30404			0.652022	+	0.758200i	$0.273921\pi$
$594$		0			0
$595$	24.9017	+	9.93151i	1.02087	+	0.407152i
$596$	4.46670	−	13.7471i	0.182963	−	0.563103i
$597$		0			0
$598$	−13.8315	+	10.0492i	−0.565612	+	0.410941i
$599$	−23.6306			−0.965519			−0.482759	−	0.875753i	$-0.660365\pi$
$599$	−23.6306			−0.965519			−0.482759	+	0.875753i	$0.660365\pi$
$600$		0			0
$601$	12.9840			0.529628			0.264814	−	0.964300i	$-0.414689\pi$
$601$	12.9840			0.529628			0.264814	+	0.964300i	$0.414689\pi$
$602$	−0.519205	+	0.377225i	−0.0211612	+	0.0153745i
$603$		0			0
$604$	8.09966	−	24.9282i	0.329570	−	1.01431i
$605$	13.0258	+	20.6395i	0.529573	+	0.839113i
$606$		0			0
$607$	9.23404			0.374798			0.187399	−	0.982284i	$-0.439994\pi$
$607$	9.23404			0.374798			0.187399	+	0.982284i	$0.439994\pi$
$608$	4.25457	+	13.0942i	0.172546	+	0.531041i
$609$		0			0
$610$	2.22645	+	3.52783i	0.0901465	+	0.142838i
$611$	−8.29889	+	6.02950i	−0.335737	+	0.243927i
$612$		0			0
$613$	−13.2902	−	9.65593i	−0.536788	−	0.389999i	0.286103	−	0.958199i	$-0.407640\pi$
$613$	−13.2902	−	9.65593i	−0.536788	−	0.389999i	−0.822891	+	0.568200i	$0.807640\pi$
$614$	−26.4414	+	19.2108i	−1.06709	+	0.775284i
$615$		0			0
$616$	1.89355	+	1.37574i	0.0762932	+	0.0554303i
$617$	2.44874	+	7.53645i	0.0985826	+	0.303406i	0.988171	−	0.153357i	$-0.0490086\pi$
$617$	2.44874	+	7.53645i	0.0985826	+	0.303406i	−0.889588	+	0.456764i	$0.849009\pi$
$618$		0			0
$619$	2.22540	+	6.84908i	0.0894465	+	0.275288i	0.985767	−	0.168120i	$-0.0537695\pi$
$619$	2.22540	+	6.84908i	0.0894465	+	0.275288i	−0.896320	+	0.443407i	$0.853769\pi$
$620$	14.3503	−	17.2583i	0.576321	−	0.693110i
$621$		0			0
$622$	2.77032	−	8.52618i	0.111080	−	0.341869i
$623$	−17.7224	+	12.8760i	−0.710031	+	0.515868i
$624$		0			0
$625$	−23.3355	+	8.96973i	−0.933419	+	0.358789i
$626$	−26.8116			−1.07161
$627$		0			0
$628$	−3.13162	+	9.63814i	−0.124965	+	0.384604i
$629$	−0.993779	+	3.05854i	−0.0396246	+	0.121952i
$630$		0			0
$631$	7.49118	+	23.0555i	0.298219	+	0.917824i	0.982121	+	0.188250i	$0.0602815\pi$
$631$	7.49118	+	23.0555i	0.298219	+	0.917824i	−0.683902	+	0.729574i	$0.739718\pi$
$632$	−22.0750			−0.878096
$633$		0			0
$634$	−9.80314	−	7.12240i	−0.389332	−	0.282867i
$635$	−2.29315	+	35.0473i	−0.0910010	+	1.39081i
$636$		0			0
$637$	1.46623	+	1.06528i	0.0580942	+	0.0422079i
$638$	2.08026	+	1.51140i	0.0823583	+	0.0598368i
$639$		0			0
$640$	6.10542	+	9.67409i	0.241338	+	0.382402i
$641$	−10.2590	−	7.45361i	−0.405207	−	0.294400i	0.366452	−	0.930437i	$-0.380573\pi$
$641$	−10.2590	−	7.45361i	−0.405207	−	0.294400i	−0.771659	+	0.636037i	$0.780573\pi$
$642$		0			0
$643$	25.2886			0.997287			0.498643	−	0.866807i	$-0.333832\pi$
$643$	25.2886			0.997287			0.498643	+	0.866807i	$0.333832\pi$
$644$	4.87704	+	15.0100i	0.192182	+	0.591476i
$645$		0			0
$646$	3.23783	−	9.96503i	0.127391	−	0.392069i
$647$	2.95787	−	9.10340i	0.116286	−	0.357892i	−0.875927	−	0.482444i	$-0.839749\pi$
$647$	2.95787	−	9.10340i	0.116286	−	0.357892i	0.992213	+	0.124552i	$0.0397494\pi$
$648$		0			0
$649$	1.48954			0.0584694
$650$	3.03948	+	16.3790i	0.119218	+	0.642435i
$651$		0			0
$652$	8.38045	−	6.08875i	0.328204	−	0.238454i
$653$	3.96525	−	12.2038i	0.155172	−	0.477571i	−0.843006	−	0.537904i	$-0.819216\pi$
$653$	3.96525	−	12.2038i	0.155172	−	0.477571i	0.998178	+	0.0603333i	$0.0192163\pi$
$654$		0			0
$655$	18.3797	+	7.33036i	0.718155	+	0.286421i
$656$	−1.73000	−	5.32438i	−0.0675450	−	0.207882i
$657$		0			0
$658$	−2.28831	−	7.04270i	−0.0892076	−	0.274553i
$659$	24.0347	+	17.4622i	0.936258	+	0.680231i	0.947517	−	0.319706i	$-0.103584\pi$
$659$	24.0347	+	17.4622i	0.936258	+	0.680231i	−0.0112594	+	0.999937i	$0.503584\pi$
$660$		0			0
$661$	18.5838	−	13.5019i	0.722825	−	0.525163i	−0.164461	−	0.986384i	$-0.552588\pi$
$661$	18.5838	−	13.5019i	0.722825	−	0.525163i	0.887285	+	0.461221i	$0.152588\pi$
$662$	10.7041	+	7.77696i	0.416025	+	0.302260i
$663$		0			0
$664$	−26.4150	+	19.1916i	−1.02510	+	0.744780i
$665$	14.5499	+	5.80290i	0.564219	+	0.225027i
$666$		0			0
$667$	14.9058	+	45.8753i	0.577155	+	1.77630i
$668$	22.8068			0.882423
$669$		0			0
$670$	27.8428	−	7.07452i	1.07566	−	0.273313i
$671$	−0.179683	+	0.553007i	−0.00693658	+	0.0213486i
$672$		0			0
$673$	−12.6360	+	9.18062i	−0.487084	+	0.353887i	−0.804062	−	0.594546i	$-0.797332\pi$
$673$	−12.6360	+	9.18062i	−0.487084	+	0.353887i	0.316978	+	0.948433i	$0.397332\pi$
$674$	−24.4376			−0.941301
$675$		0			0
$676$	0.395552			0.0152135
$677$	−0.169630	+	0.123244i	−0.00651942	+	0.00473664i	−0.591040	−	0.806642i	$-0.701283\pi$
$677$	−0.169630	+	0.123244i	−0.00651942	+	0.00473664i	0.584521	+	0.811379i	$0.301283\pi$
$678$		0			0
$679$	−13.9798	+	43.0253i	−0.536495	+	1.65116i
$680$	1.86839	−	28.5555i	0.0716496	−	1.09505i
$681$		0			0
$682$	−2.44649			−0.0936810
$683$	7.94768	+	24.4604i	0.304109	+	0.935953i	0.980008	+	0.198958i	$0.0637557\pi$
$683$	7.94768	+	24.4604i	0.304109	+	0.935953i	−0.675899	+	0.736995i	$0.736244\pi$
$684$		0			0
$685$	−18.7151	+	4.75528i	−0.715068	+	0.181690i
$686$	13.4804	−	9.79406i	0.514683	−	0.373939i
$687$		0			0
$688$	0.100250	+	0.0728360i	0.00382200	+	0.00277685i
$689$	14.0338	−	10.1961i	0.534645	−	0.388442i
$690$		0			0
$691$	21.6554	+	15.7336i	0.823812	+	0.598534i	0.917802	−	0.397039i	$-0.129962\pi$
$691$	21.6554	+	15.7336i	0.823812	+	0.598534i	−0.0939902	+	0.995573i	$0.529962\pi$
$692$	5.52148	+	16.9934i	0.209895	+	0.645991i
$693$		0			0
$694$	9.65170	+	29.7049i	0.366374	+	1.12758i
$695$	1.17046	−	17.8887i	0.0443983	−	0.678559i
$696$		0			0
$697$	15.2691	−	46.9936i	0.578360	−	1.78001i
$698$	1.83777	−	1.33522i	0.0695606	−	0.0505387i
$699$		0			0
$700$	15.2469	+	2.00380i	0.576280	+	0.0757364i
$701$	−19.6071			−0.740551			−0.370275	−	0.928922i	$-0.620737\pi$
$701$	−19.6071			−0.740551			−0.370275	+	0.928922i	$0.620737\pi$
$702$		0			0
$703$	−0.580657	+	1.78708i	−0.0218999	+	0.0674010i
$704$	0.544722	−	1.67648i	0.0205300	−	0.0631848i
$705$		0			0
$706$	7.42742	+	22.8592i	0.279534	+	0.860319i
$707$	26.9070			1.01194
$708$		0			0
$709$	−18.8375	−	13.6862i	−0.707456	−	0.513997i	0.174896	−	0.984587i	$-0.444041\pi$
$709$	−18.8375	−	13.6862i	−0.707456	−	0.513997i	−0.882352	+	0.470590i	$0.844041\pi$
$710$	−24.1436	−	9.62916i	−0.906093	−	0.361376i
$711$		0			0
$712$	18.9172	+	13.7441i	0.708952	+	0.515084i
$713$	−37.1291	−	26.9759i	−1.39050	−	1.01025i
$714$		0			0
$715$	−1.48455	+	1.78538i	−0.0555190	+	0.0667696i
$716$	4.56710	+	3.31819i	0.170680	+	0.124007i
$717$		0			0
$718$	0.874784			0.0326466
$719$	−5.03407	−	15.4933i	−0.187739	−	0.577802i	0.812246	−	0.583316i	$-0.198245\pi$
$719$	−5.03407	−	15.4933i	−0.187739	−	0.577802i	−0.999985	+	0.00551372i	$0.998245\pi$
$720$		0			0
$721$	4.17179	−	12.8395i	0.155366	−	0.478167i
$722$	−3.60864	+	11.1063i	−0.134300	+	0.413332i
$723$		0			0
$724$	3.18691			0.118441
$725$	46.5995	+	6.12425i	1.73066	+	0.227449i
$726$		0			0
$727$	21.0674	−	15.3064i	0.781346	−	0.567681i	−0.124036	−	0.992278i	$-0.539584\pi$
$727$	21.0674	−	15.3064i	0.781346	−	0.567681i	0.905383	+	0.424596i	$0.139584\pi$
$728$	8.80924	−	27.1121i	0.326492	−	1.00484i
$729$		0			0
$730$	−5.08748	−	8.06115i	−0.188296	−	0.298356i
$731$	0.337971	+	1.04017i	0.0125003	+	0.0384720i
$732$		0			0
$733$	7.47138	+	22.9946i	0.275962	+	0.849323i	0.988963	+	0.148161i	$0.0473353\pi$
$733$	7.47138	+	22.9946i	0.275962	+	0.849323i	−0.713001	+	0.701163i	$0.752665\pi$
$734$	13.7455	+	9.98668i	0.507355	+	0.368615i
$735$		0			0
$736$	22.3592	−	16.2449i	0.824169	−	0.598794i
$737$	3.23946	+	2.35360i	0.119327	+	0.0866961i
$738$		0			0
$739$	8.72996	−	6.34269i	0.321137	−	0.233320i	−0.415524	−	0.909582i	$-0.636402\pi$
$739$	8.72996	−	6.34269i	0.321137	−	0.233320i	0.736660	+	0.676263i	$0.236402\pi$
$740$	−0.120442	+	1.84076i	−0.00442752	+	0.0676678i
$741$		0			0
$742$	3.86963	+	11.9095i	0.142059	+	0.437212i
$743$	−23.8051			−0.873325			−0.436662	−	0.899625i	$-0.643840\pi$
$743$	−23.8051			−0.873325			−0.436662	+	0.899625i	$0.643840\pi$
$744$		0			0
$745$	−18.4123	+	22.1434i	−0.674574	+	0.811273i
$746$	−6.91829	+	21.2923i	−0.253297	+	0.779567i
$747$		0			0
$748$	1.15994	−	0.842743i	0.0424115	−	0.0308137i
$749$	−11.5859			−0.423339
$750$		0			0
$751$	−33.8662			−1.23580			−0.617898	−	0.786258i	$-0.712016\pi$
$751$	−33.8662			−1.23580			−0.617898	+	0.786258i	$0.712016\pi$
$752$	−1.15674	+	0.840421i	−0.0421820	+	0.0306470i
$753$		0			0
$754$	9.67788	−	29.7855i	0.352448	−	1.08472i
$755$	−33.3878	+	40.1537i	−1.21511	+	1.46134i
$756$		0			0
$757$	−26.4066			−0.959763			−0.479881	−	0.877333i	$-0.659320\pi$
$757$	−26.4066			−0.959763			−0.479881	+	0.877333i	$0.659320\pi$
$758$	0.235273	+	0.724095i	0.00854549	+	0.0263003i
$759$		0			0
$760$	1.09169	−	16.6848i	0.0395997	−	0.605220i
$761$	−16.2115	+	11.7783i	−0.587667	+	0.426965i	−0.841480	−	0.540288i	$-0.818315\pi$
$761$	−16.2115	+	11.7783i	−0.587667	+	0.426965i	0.253813	+	0.967253i	$0.418315\pi$
$762$		0			0
$763$	23.3394	+	16.9571i	0.844944	+	0.613888i
$764$	−18.8688	+	13.7090i	−0.682648	+	0.495973i
$765$		0			0
$766$	−17.7222	−	12.8759i	−0.640328	−	0.465226i
$767$	−5.60624	−	17.2542i	−0.202429	−	0.623014i
$768$		0			0
$769$	−5.06940	−	15.6020i	−0.182807	−	0.562623i	0.817096	−	0.576501i	$-0.195582\pi$
$769$	−5.06940	−	15.6020i	−0.182807	−	0.562623i	−0.999904	+	0.0138781i	$0.995582\pi$
$770$	−0.894601	−	1.41750i	−0.0322392	−	0.0510833i
$771$		0			0
$772$	2.93440	−	9.03114i	0.105611	−	0.325038i
$773$	9.26011	−	6.72786i	0.333063	−	0.241984i	−0.408666	−	0.912684i	$-0.634006\pi$
$773$	9.26011	−	6.72786i	0.333063	−	0.241984i	0.741729	+	0.670700i	$0.234006\pi$
$774$		0			0
$775$	−39.2942	+	21.3465i	−1.41149	+	0.766789i
$776$	48.2896			1.73349
$777$		0			0
$778$	3.33297	−	10.2578i	0.119493	−	0.367761i
$779$	8.92164	−	27.4580i	0.319651	−	0.983785i
$780$		0			0
$781$	−1.11958	−	3.44570i	−0.0400616	−	0.123297i
$782$	−21.0328			−0.752131
$783$		0			0
$784$	0.204371	+	0.148484i	0.00729895	+	0.00530300i
$785$	12.9089	−	15.5249i	0.460740	−	0.554106i
$786$		0			0
$787$	−5.26393	−	3.82447i	−0.187639	−	0.136328i	0.490000	−	0.871722i	$-0.336997\pi$
$787$	−5.26393	−	3.82447i	−0.187639	−	0.136328i	−0.677639	+	0.735395i	$0.736997\pi$
$788$	5.72457	+	4.15914i	0.203929	+	0.148163i
$789$		0			0
$790$	14.6843	+	5.85651i	0.522443	+	0.208365i
$791$	25.9290	+	18.8385i	0.921929	+	0.669821i
$792$		0			0
$793$	7.08210			0.251493
$794$	1.38491	+	4.26231i	0.0491486	+	0.151264i
$795$		0			0
$796$	6.73491	−	20.7279i	0.238713	−	0.734682i
$797$	−11.0243	+	33.9292i	−0.390500	+	1.20183i	0.541912	+	0.840435i	$0.317701\pi$
$797$	−11.0243	+	33.9292i	−0.390500	+	1.20183i	−0.932411	+	0.361399i	$0.882299\pi$
$798$		0			0
$799$	−12.6197			−0.446452
$800$	−4.91344	−	26.4772i	−0.173716	−	0.936111i
$801$		0			0
$802$	22.5604	−	16.3911i	0.796636	−	0.578790i
$803$	0.410578	−	1.26363i	0.0144890	−	0.0445925i
$804$		0			0
$805$	2.05299	−	31.3769i	0.0723585	−	1.10589i
$806$	9.20797	+	28.3392i	0.324337	+	0.998207i
$807$		0			0
$808$	−8.87530	−	27.3154i	−0.312232	−	0.960951i
$809$	−12.7855	−	9.28921i	−0.449514	−	0.326591i	0.339890	−	0.940465i	$-0.389610\pi$
$809$	−12.7855	−	9.28921i	−0.449514	−	0.326591i	−0.789404	+	0.613874i	$0.789610\pi$
$810$		0			0
$811$	−24.5451	+	17.8331i	−0.861895	+	0.626204i	−0.928400	−	0.371582i	$-0.878815\pi$
$811$	−24.5451	+	17.8331i	−0.861895	+	0.626204i	0.0665045	+	0.997786i	$0.478815\pi$
$812$	−23.3894	−	16.9934i	−0.820805	−	0.596350i
$813$		0			0
$814$	0.162670	−	0.118186i	0.00570157	−	0.00414243i
$815$	−20.0026	+	5.08243i	−0.700662	+	0.178030i
$816$		0			0
$817$	0.197474	+	0.607761i	0.00690873	+	0.0212629i
$818$	−5.61009			−0.196152
$819$		0			0
$820$	1.85055	−	28.2828i	0.0646241	−	0.987680i
$821$	9.71115	−	29.8878i	0.338921	−	1.04309i	−0.625837	−	0.779954i	$-0.715242\pi$
$821$	9.71115	−	29.8878i	0.338921	−	1.04309i	0.964758	−	0.263139i	$-0.0847576\pi$
$822$		0			0
$823$	−36.4329	+	26.4701i	−1.26997	+	0.922688i	−0.999201	−	0.0399555i	$-0.987278\pi$
$823$	−36.4329	+	26.4701i	−1.26997	+	0.922688i	−0.270770	+	0.962644i	$0.587278\pi$
$824$	−14.4104			−0.502010
$825$		0			0
$826$	13.0966			0.455690
$827$	−9.70541	+	7.05139i	−0.337490	+	0.245201i	−0.743602	−	0.668622i	$-0.766884\pi$
$827$	−9.70541	+	7.05139i	−0.337490	+	0.245201i	0.406112	+	0.913823i	$0.366884\pi$
$828$		0			0
$829$	−9.57479	+	29.4682i	−0.332546	+	1.02347i	0.635372	+	0.772206i	$0.280847\pi$
$829$	−9.57479	+	29.4682i	−0.332546	+	1.02347i	−0.967918	+	0.251266i	$0.919153\pi$
$830$	22.6628	−	5.75834i	0.786638	−	0.199875i
$831$		0			0
$832$	−21.4699			−0.744335
$833$	0.688989	+	2.12049i	0.0238721	+	0.0734706i
$834$		0			0
$835$	−42.2060	−	16.8330i	−1.46060	−	0.582529i
$836$	0.677741	−	0.492408i	0.0234402	−	0.0170303i
$837$		0			0
$838$	−3.22635	−	2.34408i	−0.111452	−	0.0809749i
$839$	29.2884	−	21.2792i	1.01115	−	0.734641i	0.0466971	−	0.998909i	$-0.485130\pi$
$839$	29.2884	−	21.2792i	1.01115	−	0.734641i	0.964449	+	0.264268i	$0.0851305\pi$
$840$		0			0
$841$	−48.0239	−	34.8914i	−1.65600	−	1.20315i
$842$	−6.73630	−	20.7322i	−0.232148	−	0.714479i
$843$		0			0
$844$	5.98883	+	18.4317i	0.206144	+	0.634446i
$845$	−0.732002	−	0.291944i	−0.0251816	−	0.0100432i
$846$		0			0
$847$	−9.24282	+	28.4465i	−0.317587	+	0.977433i
$848$	1.95610	−	1.42119i	0.0671727	−	0.0488038i
$849$		0			0
$850$	−8.81866	+	18.4994i	−0.302477	+	0.634525i
$851$	3.77191			0.129300
$852$		0			0
$853$	10.0778	−	31.0162i	0.345056	−	1.06197i	−0.616498	−	0.787357i	$-0.711449\pi$
$853$	10.0778	−	31.0162i	0.345056	−	1.06197i	0.961554	−	0.274616i	$-0.0885509\pi$
$854$	−1.57985	+	4.86226i	−0.0540612	+	0.166383i
$855$		0			0
$856$	3.82161	+	11.7617i	0.130620	+	0.402007i
$857$	−4.85223			−0.165749			−0.0828744	−	0.996560i	$-0.526410\pi$
$857$	−4.85223			−0.165749			−0.0828744	+	0.996560i	$0.526410\pi$
$858$		0			0
$859$	26.1972	+	19.0334i	0.893836	+	0.649410i	0.936875	−	0.349663i	$-0.113704\pi$
$859$	26.1972	+	19.0334i	0.893836	+	0.649410i	−0.0430393	+	0.999073i	$0.513704\pi$
$860$	0.334827	+	0.530536i	0.0114175	+	0.0180911i
$861$		0			0
$862$	−9.48696	−	6.89268i	−0.323127	−	0.234766i
$863$	17.7578	+	12.9018i	0.604481	+	0.439181i	0.847467	−	0.530849i	$-0.178127\pi$
$863$	17.7578	+	12.9018i	0.604481	+	0.439181i	−0.242986	+	0.970030i	$0.578127\pi$
$864$		0			0
$865$	2.32427	−	35.5229i	0.0790276	−	1.20781i
$866$	14.3675	+	10.4386i	0.488226	+	0.354717i
$867$		0			0
$868$	27.5071			0.933650
$869$	0.680933	+	2.09570i	0.0230991	+	0.0710917i
$870$		0			0
$871$	15.0707	−	46.3830i	0.510653	−	1.57163i
$872$	9.51591	−	29.2869i	0.322249	−	0.991781i
$873$		0			0
$874$	−12.2893			−0.415691
$875$	−26.7368	−	14.9615i	−0.903869	−	0.505789i
$876$		0			0
$877$	−3.45609	+	2.51100i	−0.116704	+	0.0847904i	−0.644606	−	0.764515i	$-0.722979\pi$
$877$	−3.45609	+	2.51100i	−0.116704	+	0.0847904i	0.527902	+	0.849305i	$0.322979\pi$
$878$	−2.11309	+	6.50344i	−0.0713135	+	0.219480i
$879$		0			0
$880$	−0.206924	+	0.248856i	−0.00697540	+	0.00838893i
$881$	−9.00341	−	27.7096i	−0.303332	−	0.933561i	−0.980294	−	0.197543i	$-0.936704\pi$
$881$	−9.00341	−	27.7096i	−0.303332	−	0.933561i	0.676962	−	0.736018i	$-0.263296\pi$
$882$		0			0
$883$	15.1896	+	46.7489i	0.511172	+	1.57322i	0.790141	+	0.612925i	$0.210007\pi$
$883$	15.1896	+	46.7489i	0.511172	+	1.57322i	−0.278970	+	0.960300i	$0.589993\pi$
$884$	−14.1277	−	10.2644i	−0.475166	−	0.345228i
$885$		0			0
$886$	4.35962	−	3.16745i	0.146464	−	0.106413i
$887$	−24.6252	−	17.8912i	−0.826832	−	0.600728i	0.0918294	−	0.995775i	$-0.470729\pi$
$887$	−24.6252	−	17.8912i	−0.826832	−	0.600728i	−0.918661	+	0.395046i	$0.870729\pi$
$888$		0			0
$889$	−34.8228	+	25.3003i	−1.16792	+	0.848543i
$890$	−8.93738	−	14.1613i	−0.299582	−	0.474689i
$891$		0			0
$892$	−0.494021	−	1.52044i	−0.0165411	−	0.0509081i
$893$	−7.37357			−0.246747
$894$		0			0
$895$	−6.00276	−	9.51142i	−0.200650	−	0.317932i
$896$	−4.33228	+	13.3334i	−0.144731	+	0.445437i
$897$		0			0
$898$	3.60058	−	2.61597i	0.120153	−	0.0872961i
$899$	84.0704			2.80391
$900$		0			0
$901$	21.3404			0.710952
$902$	−2.49938	+	1.81590i	−0.0832202	+	0.0604630i
$903$		0			0
$904$	10.5717	−	32.5364i	0.351610	−	1.08214i
$905$	−5.89765	−	2.35215i	−0.196044	−	0.0781882i
$906$		0			0
$907$	−14.9403			−0.496084			−0.248042	−	0.968749i	$-0.579787\pi$
$907$	−14.9403			−0.496084			−0.248042	+	0.968749i	$0.579787\pi$
$908$	−3.21445	−	9.89305i	−0.106675	−	0.328312i
$909$		0			0
$910$	−13.0528	+	15.6978i	−0.432695	+	0.520378i
$911$	9.57024	−	6.95319i	0.317076	−	0.230369i	−0.417851	−	0.908516i	$-0.637216\pi$
$911$	9.57024	−	6.95319i	0.317076	−	0.230369i	0.734927	+	0.678146i	$0.237216\pi$
$912$		0			0
$913$	2.63677	+	1.91573i	0.0872645	+	0.0634013i
$914$	−3.58251	+	2.60285i	−0.118499	+	0.0860946i
$915$		0			0
$916$	−15.2755	−	11.0983i	−0.504718	−	0.366699i
$917$	7.49374	+	23.0634i	0.247465	+	0.761620i
$918$		0			0
$919$	−9.47476	−	29.1603i	−0.312543	−	0.961910i	−0.976754	−	0.214364i	$-0.931232\pi$
$919$	−9.47476	−	29.1603i	−0.312543	−	0.961910i	0.664210	−	0.747546i	$-0.268768\pi$
$920$	−32.5302	+	8.26553i	−1.07249	+	0.272506i
$921$		0			0
$922$	2.23212	−	6.86975i	0.0735109	−	0.226243i
$923$	−35.6999	+	25.9375i	−1.17508	+	0.853743i
$924$		0			0
$925$	1.58149	−	3.31760i	0.0519992	−	0.109082i
$926$	−3.58768			−0.117898
$927$		0			0
$928$	−15.6447	+	48.1494i	−0.513562	+	1.58058i
$929$	−1.99749	+	6.14763i	−0.0655354	+	0.201697i	−0.978462	−	0.206426i	$-0.933817\pi$
$929$	−1.99749	+	6.14763i	−0.0655354	+	0.201697i	0.912927	+	0.408123i	$0.133817\pi$
$930$		0			0
$931$	0.402571	+	1.23899i	0.0131937	+	0.0406061i
$932$	−11.0820			−0.363002
$933$		0			0
$934$	−15.0737	−	10.9517i	−0.493225	−	0.358349i
$935$	−2.76856	+	0.703457i	−0.0905416	+	0.0230055i
$936$		0			0
$937$	9.90312	+	7.19504i	0.323521	+	0.235052i	0.737676	−	0.675154i	$-0.235923\pi$
$937$	9.90312	+	7.19504i	0.323521	+	0.235052i	−0.414155	+	0.910206i	$0.635923\pi$
$938$	28.4826	+	20.6938i	0.929991	+	0.675678i
$939$		0			0
$940$	−7.01586	+	1.78264i	−0.228832	+	0.0581434i
$941$	−5.98241	−	4.34647i	−0.195021	−	0.141691i	0.485990	−	0.873965i	$-0.338459\pi$
$941$	−5.98241	−	4.34647i	−0.195021	−	0.141691i	−0.681011	+	0.732274i	$0.738459\pi$
$942$		0			0
$943$	−57.9545			−1.88726
$944$	−0.781425	−	2.40498i	−0.0254332	−	0.0782754i
$945$		0			0
$946$	0.0211310	−	0.0650346i	0.000687029	−	0.00211446i
$947$	8.95927	−	27.5738i	0.291137	−	0.896028i	−0.693355	−	0.720596i	$-0.743868\pi$
$947$	8.95927	−	27.5738i	0.291137	−	0.896028i	0.984492	−	0.175431i	$-0.0561319\pi$
$948$		0			0
$949$	−16.1827			−0.525312
$950$	−5.15267	+	10.8091i	−0.167175	+	0.350693i
$951$		0			0
$952$	28.3726	−	20.6139i	0.919561	−	0.668100i
$953$	−13.3073	+	40.9558i	−0.431067	+	1.32669i	0.465997	+	0.884786i	$0.345696\pi$
$953$	−13.3073	+	40.9558i	−0.431067	+	1.32669i	−0.897064	+	0.441901i	$0.854304\pi$
$954$		0			0
$955$	45.0364	−	11.4432i	1.45734	−	0.370293i
$956$	7.27921	+	22.4031i	0.235427	+	0.724568i
$957$		0			0
$958$	−8.05421	−	24.7883i	−0.260220	−	0.800874i
$959$	−19.1452	−	13.9098i	−0.618230	−	0.449170i
$960$		0			0
$961$	−39.6324	+	28.7946i	−1.27847	+	0.928859i
$962$	−1.98127	−	1.43948i	−0.0638788	−	0.0464107i
$963$		0			0
$964$	0.544006	−	0.395243i	0.0175212	−	0.0127299i
$965$	−12.0959	+	14.5471i	−0.389382	+	0.468288i
$966$		0			0
$967$	9.86384	+	30.3578i	0.317200	+	0.976240i	0.974840	+	0.222908i	$0.0715549\pi$
$967$	9.86384	+	30.3578i	0.317200	+	0.976240i	−0.657640	+	0.753333i	$0.728445\pi$
$968$	31.9270			1.02617
$969$		0			0
$970$	−32.1222	−	12.8113i	−1.03138	−	0.411345i
$971$	3.65314	−	11.2432i	0.117235	−	0.360812i	−0.875172	−	0.483812i	$-0.839252\pi$
$971$	3.65314	−	11.2432i	0.117235	−	0.360812i	0.992407	+	0.123001i	$0.0392517\pi$
$972$		0			0
$973$	17.7742	−	12.9137i	0.569813	−	0.413994i
$974$	29.7110			0.952001
$975$		0			0
$976$	0.987138			0.0315975
$977$	12.7718	−	9.27927i	0.408607	−	0.296870i	−0.364431	−	0.931231i	$-0.618736\pi$
$977$	12.7718	−	9.27927i	0.408607	−	0.296870i	0.773038	+	0.634360i	$0.218736\pi$
$978$		0			0
$979$	0.721279	−	2.21987i	0.0230522	−	0.0709473i
$980$	0.682580	+	1.08155i	0.0218042	+	0.0345490i
$981$		0			0
$982$	−4.59176			−0.146529
$983$	7.89312	+	24.2925i	0.251751	+	0.774811i	0.994452	+	0.105188i	$0.0335444\pi$
$983$	7.89312	+	24.2925i	0.251751	+	0.774811i	−0.742701	+	0.669623i	$0.766456\pi$
$984$		0			0
$985$	−7.52408	−	11.9220i	−0.239737	−	0.379865i
$986$	31.1703	−	22.6465i	0.992664	−	0.721213i
$987$		0			0
$988$	−8.25471	−	5.99740i	−0.262617	−	0.190803i
$989$	1.03779	−	0.753997i	0.0329997	−	0.0239757i
$990$		0			0
$991$	1.07727	+	0.782683i	0.0342207	+	0.0248628i	0.604764	−	0.796405i	$-0.293267\pi$
$991$	1.07727	+	0.782683i	0.0342207	+	0.0248628i	−0.570543	+	0.821267i	$0.693267\pi$
$992$	−14.8851	−	45.8115i	−0.472601	−	1.45452i
$993$		0			0
$994$	−9.84378	−	30.2960i	−0.312226	−	0.960932i
$995$	−27.7621	+	33.3880i	−0.880119	+	1.05847i
$996$		0			0
$997$	15.9754	−	49.1673i	0.505947	−	1.55714i	−0.293227	−	0.956043i	$-0.594729\pi$
$997$	15.9754	−	49.1673i	0.505947	−	1.55714i	0.799173	−	0.601101i	$-0.205271\pi$
$998$	−2.37687	+	1.72689i	−0.0752384	+	0.0546639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.e.136.2	yes	16
3.2	odd	2	inner	225.2.h.e.136.3	yes	16
25.4	even	10		5625.2.a.v.1.3		8
25.16	even	5	inner	225.2.h.e.91.2	✓	16
25.21	even	5		5625.2.a.w.1.6		8
75.29	odd	10		5625.2.a.v.1.6		8
75.41	odd	10	inner	225.2.h.e.91.3	yes	16
75.71	odd	10		5625.2.a.w.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.h.e.91.2	✓	16	25.16	even	5	inner
225.2.h.e.91.3	yes	16	75.41	odd	10	inner
225.2.h.e.136.2	yes	16	1.1	even	1	trivial
225.2.h.e.136.3	yes	16	3.2	odd	2	inner
5625.2.a.v.1.3		8	25.4	even	10
5625.2.a.v.1.6		8	75.29	odd	10
5625.2.a.w.1.3		8	75.71	odd	10
5625.2.a.w.1.6		8	25.21	even	5

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.757918 + 0.550660i) q^{2} +(-0.346820 + 1.06740i) q^{4} +(1.42964 - 1.71934i) q^{5} +2.74037 q^{7} +(-0.903913 - 2.78196i) q^{8} +O(q^{10})\)	\(q+(-0.757918 + 0.550660i) q^{2} +(-0.346820 + 1.06740i) q^{4} +(1.42964 - 1.71934i) q^{5} +2.74037 q^{7} +(-0.903913 - 2.78196i) q^{8} +(-0.136773 + 2.09036i) q^{10} +(-0.236224 + 0.171627i) q^{11} +(2.87714 + 2.09036i) q^{13} +(-2.07697 + 1.50901i) q^{14} +(0.401030 + 0.291365i) q^{16} +(1.35198 + 4.16097i) q^{17} +(0.789953 + 2.43123i) q^{19} +(1.33941 + 2.12230i) q^{20} +(0.0845304 - 0.260158i) q^{22} +(4.15146 - 3.01621i) q^{23} +(-0.912286 - 4.91607i) q^{25} -3.33172 q^{26} +(-0.950415 + 2.92508i) q^{28} +(-2.90477 + 8.93997i) q^{29} +(-2.76373 - 8.50589i) q^{31} +5.38585 q^{32} +(-3.31597 - 2.40920i) q^{34} +(3.91773 - 4.71163i) q^{35} +(0.594670 + 0.432053i) q^{37} +(-1.93750 - 1.40767i) q^{38} +(-6.07541 - 2.42305i) q^{40} +(-9.13695 - 6.63838i) q^{41} +0.249982 q^{43} +(-0.101267 - 0.311669i) q^{44} +(-1.48556 + 4.57209i) q^{46} +(-0.891336 + 2.74325i) q^{47} +0.509614 q^{49} +(3.39852 + 3.22362i) q^{50} +(-3.22911 + 2.34609i) q^{52} +(1.50729 - 4.63896i) q^{53} +(-0.0426286 + 0.651513i) q^{55} +(-2.47705 - 7.62358i) q^{56} +(-2.72130 - 8.37531i) q^{58} +(-4.12708 - 2.99850i) q^{59} +(1.61108 - 1.17052i) q^{61} +(6.77853 + 4.92489i) q^{62} +(-4.88410 + 3.54850i) q^{64} +(7.70732 - 1.95833i) q^{65} +(-4.23771 - 13.0423i) q^{67} -4.91033 q^{68} +(-0.374808 + 5.72837i) q^{70} +(-3.83432 + 11.8008i) q^{71} +(-3.68133 + 2.67464i) q^{73} -0.688626 q^{74} -2.86907 q^{76} +(-0.647340 + 0.470320i) q^{77} +(2.33206 - 7.17733i) q^{79} +(1.07428 - 0.272962i) q^{80} +10.5806 q^{82} +(-3.44931 - 10.6159i) q^{83} +(9.08699 + 3.62415i) q^{85} +(-0.189466 + 0.137655i) q^{86} +(0.690983 + 0.502029i) q^{88} +(-6.46715 + 4.69866i) q^{89} +(7.88442 + 5.72837i) q^{91} +(1.77970 + 5.47736i) q^{92} +(-0.835038 - 2.56998i) q^{94} +(5.30946 + 2.11756i) q^{95} +(-5.10143 + 15.7006i) q^{97} +(-0.386246 + 0.280624i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

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