LMFDB - Embedded newform 400.2.l.h.301.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(101,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			301.2
Root			$-0.296075 + 1.38287i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.h.101.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09971 + 0.889181i) q^{2} +(0.120009 + 0.120009i) q^{3} +(0.418713 - 1.95568i) q^{4} +(-0.238684 - 0.0252650i) q^{6} -2.66881i q^{7} +(1.27849 + 2.52299i) q^{8} -2.97120i q^{9} +(-3.49714 + 3.49714i) q^{11} +(0.284948 - 0.184450i) q^{12} +(-2.94072 - 2.94072i) q^{13} +(2.37306 + 2.93491i) q^{14} +(-3.64936 - 1.63774i) q^{16} -1.85116 q^{17} +(2.64193 + 3.26745i) q^{18} +(-3.44856 - 3.44856i) q^{19} +(0.320281 - 0.320281i) q^{21} +(0.736240 - 6.95543i) q^{22} +0.707288i q^{23} +(-0.149351 + 0.456211i) q^{24} +(5.84877 + 0.619099i) q^{26} +(0.716597 - 0.716597i) q^{27} +(-5.21934 - 1.11747i) q^{28} +(-3.49909 - 3.49909i) q^{29} +6.84272 q^{31} +(5.46947 - 1.44391i) q^{32} -0.839377 q^{33} +(2.03573 - 1.64601i) q^{34} +(-5.81070 - 1.24408i) q^{36} +(0.0975060 - 0.0975060i) q^{37} +(6.85881 + 0.726013i) q^{38} -0.705826i q^{39} -10.2052i q^{41} +(-0.0674276 + 0.637004i) q^{42} +(-4.43844 + 4.43844i) q^{43} +(5.37499 + 8.30359i) q^{44} +(-0.628908 - 0.777810i) q^{46} +1.89428 q^{47} +(-0.241413 - 0.634498i) q^{48} -0.122561 q^{49} +(-0.222155 - 0.222155i) q^{51} +(-6.98243 + 4.51979i) q^{52} +(7.43897 - 7.43897i) q^{53} +(-0.150862 + 1.42523i) q^{54} +(6.73338 - 3.41205i) q^{56} -0.827717i q^{57} +(6.95931 + 0.736651i) q^{58} +(0.959574 - 0.959574i) q^{59} +(6.49825 + 6.49825i) q^{61} +(-7.52499 + 6.08442i) q^{62} -7.92956 q^{63} +(-4.73092 + 6.45123i) q^{64} +(0.923069 - 0.746358i) q^{66} +(-3.49691 - 3.49691i) q^{67} +(-0.775103 + 3.62027i) q^{68} +(-0.0848809 + 0.0848809i) q^{69} +7.86777i q^{71} +(7.49629 - 3.79865i) q^{72} -15.6564i q^{73} +(-0.0205276 + 0.193929i) q^{74} +(-8.18824 + 5.30033i) q^{76} +(9.33322 + 9.33322i) q^{77} +(0.627607 + 0.776202i) q^{78} -6.70212 q^{79} -8.74159 q^{81} +(9.07431 + 11.2228i) q^{82} +(3.87327 + 3.87327i) q^{83} +(-0.492261 - 0.760473i) q^{84} +(0.934407 - 8.82755i) q^{86} -0.839845i q^{87} +(-13.2943 - 4.35218i) q^{88} +10.5055i q^{89} +(-7.84824 + 7.84824i) q^{91} +(1.38323 + 0.296151i) q^{92} +(0.821187 + 0.821187i) q^{93} +(-2.08316 + 1.68436i) q^{94} +(0.829667 + 0.483103i) q^{96} -4.79937 q^{97} +(0.134781 - 0.108979i) q^{98} +(10.3907 + 10.3907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.09971	+	0.889181i	−0.777611	+	0.628746i
$2$	−1.09971	+	0.889181i	−0.777611	+	0.628746i
$3$	0.120009	+	0.120009i	0.0692872	+	0.0692872i	0.740901	−	0.671614i	$-0.234399\pi$
$3$	0.120009	+	0.120009i	0.0692872	+	0.0692872i	−0.671614	+	0.740901i	$0.734399\pi$
$4$	0.418713	−	1.95568i	0.209357	−	0.977839i
$5$		0			0
$5$		0			0
$6$	−0.238684	−	0.0252650i	−0.0974425	−	0.0103144i
$7$		−	2.66881i		−	1.00872i	−0.863495	−	0.504358i	$-0.831729\pi$
$7$		−	2.66881i		−	1.00872i	0.863495	−	0.504358i	$-0.168271\pi$
$8$	1.27849	+	2.52299i	0.452015	+	0.892010i
$9$		−	2.97120i		−	0.990399i
$10$		0			0
$11$	−3.49714	+	3.49714i	−1.05443	+	1.05443i	−0.0559977	+	0.998431i	$0.517834\pi$
$11$	−3.49714	+	3.49714i	−1.05443	+	1.05443i	−0.998431	+	0.0559977i	$0.982166\pi$
$12$	0.284948	−	0.184450i	0.0822574	−	0.0532460i
$13$	−2.94072	−	2.94072i	−0.815610	−	0.815610i	0.169858	−	0.985468i	$-0.445669\pi$
$13$	−2.94072	−	2.94072i	−0.815610	−	0.815610i	−0.985468	+	0.169858i	$0.945669\pi$
$14$	2.37306	+	2.93491i	0.634227	+	0.784389i
$15$		0			0
$16$	−3.64936	−	1.63774i	−0.912340	−	0.409434i
$17$	−1.85116			−0.448971			−0.224486	−	0.974477i	$-0.572070\pi$
$17$	−1.85116			−0.448971			−0.224486	+	0.974477i	$0.572070\pi$
$18$	2.64193	+	3.26745i	0.622709	+	0.770144i
$19$	−3.44856	−	3.44856i	−0.791155	−	0.791155i	0.190527	−	0.981682i	$-0.438980\pi$
$19$	−3.44856	−	3.44856i	−0.791155	−	0.791155i	−0.981682	+	0.190527i	$0.938980\pi$
$20$		0			0
$21$	0.320281	−	0.320281i	0.0698911	−	0.0698911i
$22$	0.736240	−	6.95543i	0.156967	−	1.48290i
$23$			0.707288i			0.147480i	0.997278	+	0.0737399i	$0.0234935\pi$
$23$			0.707288i			0.147480i	−0.997278	+	0.0737399i	$0.976507\pi$
$24$	−0.149351	+	0.456211i	−0.0304860	+	0.0931237i
$25$		0			0
$26$	5.84877	+	0.619099i	1.14704	+	0.121415i
$27$	0.716597	−	0.716597i	0.137909	−	0.137909i
$28$	−5.21934	−	1.11747i	−0.986363	−	0.211181i
$29$	−3.49909	−	3.49909i	−0.649766	−	0.649766i	0.303171	−	0.952936i	$-0.401955\pi$
$29$	−3.49909	−	3.49909i	−0.649766	−	0.649766i	−0.952936	+	0.303171i	$0.901955\pi$
$30$		0			0
$31$	6.84272			1.22899			0.614494	−	0.788921i	$-0.289360\pi$
$31$	6.84272			1.22899			0.614494	+	0.788921i	$0.289360\pi$
$32$	5.46947	−	1.44391i	0.966875	−	0.255250i
$33$	−0.839377			−0.146117
$34$	2.03573	−	1.64601i	0.349125	−	0.282289i
$35$		0			0
$36$	−5.81070	−	1.24408i	−0.968451	−	0.207346i
$37$	0.0975060	−	0.0975060i	0.0160299	−	0.0160299i	−0.699046	−	0.715076i	$-0.746392\pi$
$37$	0.0975060	−	0.0975060i	0.0160299	−	0.0160299i	0.715076	+	0.699046i	$0.246392\pi$
$38$	6.85881	+	0.726013i	1.11265	+	0.117775i
$39$		−	0.705826i		−	0.113023i
$40$		0			0
$41$		−	10.2052i		−	1.59379i	−0.604117	−	0.796896i	$-0.706474\pi$
$41$		−	10.2052i		−	1.59379i	0.604117	−	0.796896i	$-0.293526\pi$
$42$	−0.0674276	+	0.637004i	−0.0104043	+	0.0982918i
$43$	−4.43844	+	4.43844i	−0.676855	+	0.676855i	−0.959287	−	0.282432i	$-0.908859\pi$
$43$	−4.43844	+	4.43844i	−0.676855	+	0.676855i	0.282432	+	0.959287i	$0.408859\pi$
$44$	5.37499	+	8.30359i	0.810310	+	1.25181i
$45$		0			0
$46$	−0.628908	−	0.777810i	−0.0927274	−	0.114682i
$47$	1.89428			0.276310			0.138155	−	0.990411i	$-0.455883\pi$
$47$	1.89428			0.276310			0.138155	+	0.990411i	$0.455883\pi$
$48$	−0.241413	−	0.634498i	−0.0348449	−	0.0915820i
$49$	−0.122561			−0.0175087
$50$		0			0
$51$	−0.222155	−	0.222155i	−0.0311079	−	0.0311079i
$52$	−6.98243	+	4.51979i	−0.968289	+	0.626782i
$53$	7.43897	−	7.43897i	1.02182	−	1.02182i	0.0220650	−	0.999757i	$-0.492976\pi$
$53$	7.43897	−	7.43897i	1.02182	−	1.02182i	0.999757	−	0.0220650i	$-0.00702407\pi$
$54$	−0.150862	+	1.42523i	−0.0205298	+	0.193949i
$55$		0			0
$56$	6.73338	−	3.41205i	0.899786	−	0.455955i
$57$		−	0.827717i		−	0.109634i
$58$	6.95931	+	0.736651i	0.913802	+	0.0967270i
$59$	0.959574	−	0.959574i	0.124926	−	0.124926i	−0.641880	−	0.766805i	$-0.721845\pi$
$59$	0.959574	−	0.959574i	0.124926	−	0.124926i	0.766805	+	0.641880i	$0.221845\pi$
$60$		0			0
$61$	6.49825	+	6.49825i	0.832015	+	0.832015i	0.987792	−	0.155777i	$-0.0497881\pi$
$61$	6.49825	+	6.49825i	0.832015	+	0.832015i	−0.155777	+	0.987792i	$0.549788\pi$
$62$	−7.52499	+	6.08442i	−0.955674	+	0.772722i
$63$	−7.92956			−0.999031
$64$	−4.73092	+	6.45123i	−0.591365	+	0.806404i
$65$		0			0
$66$	0.923069	−	0.746358i	0.113622	−	0.0918703i
$67$	−3.49691	−	3.49691i	−0.427216	−	0.427216i	0.460463	−	0.887679i	$-0.347683\pi$
$67$	−3.49691	−	3.49691i	−0.427216	−	0.427216i	−0.887679	+	0.460463i	$0.847683\pi$
$68$	−0.775103	+	3.62027i	−0.0939951	+	0.439022i
$69$	−0.0848809	+	0.0848809i	−0.0102185	+	0.0102185i
$70$		0			0
$71$			7.86777i			0.933733i	0.884328	+	0.466866i	$0.154617\pi$
$71$			7.86777i			0.933733i	−0.884328	+	0.466866i	$0.845383\pi$
$72$	7.49629	−	3.79865i	0.883446	−	0.447675i
$73$		−	15.6564i		−	1.83244i	−0.400675	−	0.916220i	$-0.631224\pi$
$73$		−	15.6564i		−	1.83244i	0.400675	−	0.916220i	$-0.368776\pi$
$74$	−0.0205276	+	0.193929i	−0.00238628	+	0.0225437i
$75$		0			0
$76$	−8.18824	+	5.30033i	−0.939256	+	0.607989i
$77$	9.33322	+	9.33322i	1.06362	+	1.06362i
$78$	0.627607	+	0.776202i	0.0710625	+	0.0878876i
$79$	−6.70212			−0.754047			−0.377024	−	0.926204i	$-0.623052\pi$
$79$	−6.70212			−0.754047			−0.377024	+	0.926204i	$0.623052\pi$
$80$		0			0
$81$	−8.74159			−0.971288
$82$	9.07431	+	11.2228i	1.00209	+	1.23935i
$83$	3.87327	+	3.87327i	0.425147	+	0.425147i	0.886971	−	0.461825i	$-0.152805\pi$
$83$	3.87327	+	3.87327i	0.425147	+	0.425147i	−0.461825	+	0.886971i	$0.652805\pi$
$84$	−0.492261	−	0.760473i	−0.0537101	−	0.0829744i
$85$		0			0
$86$	0.934407	−	8.82755i	0.100760	−	0.951900i
$87$		−	0.839845i		−	0.0900408i
$88$	−13.2943	−	4.35218i	−1.41718	−	0.463944i
$89$			10.5055i			1.11358i	0.830653	+	0.556790i	$0.187967\pi$
$89$			10.5055i			1.11358i	−0.830653	+	0.556790i	$0.812033\pi$
$90$		0			0
$91$	−7.84824	+	7.84824i	−0.822719	+	0.822719i
$92$	1.38323	+	0.296151i	0.144212	+	0.0308759i
$93$	0.821187	+	0.821187i	0.0851531	+	0.0851531i
$94$	−2.08316	+	1.68436i	−0.214861	+	0.173729i
$95$		0			0
$96$	0.829667	+	0.483103i	0.0846776	+	0.0493065i
$97$	−4.79937			−0.487303			−0.243651	−	0.969863i	$-0.578345\pi$
$97$	−4.79937			−0.487303			−0.243651	+	0.969863i	$0.578345\pi$
$98$	0.134781	−	0.108979i	0.0136150	−	0.0110085i
$99$	10.3907	+	10.3907i	1.04430	+	1.04430i
$100$		0			0
$101$	0.372979	−	0.372979i	0.0371128	−	0.0371128i	−0.688307	−	0.725420i	$-0.741646\pi$
$101$	0.372979	−	0.372979i	0.0371128	−	0.0371128i	0.725420	+	0.688307i	$0.241646\pi$
$102$	0.441842	+	0.0467695i	0.0437489	+	0.00463087i
$103$			10.3013i			1.01502i	0.861647	+	0.507508i	$0.169433\pi$
$103$			10.3013i			1.01502i	−0.861647	+	0.507508i	$0.830567\pi$
$104$	3.65972	−	11.1791i	0.358865	−	1.09620i
$105$		0			0
$106$	−1.56610	+	14.7953i	−0.152113	+	1.43705i
$107$	−14.5069	+	14.5069i	−1.40244	+	1.40244i	−0.610165	+	0.792274i	$0.708897\pi$
$107$	−14.5069	+	14.5069i	−1.40244	+	1.40244i	−0.792274	+	0.610165i	$0.791103\pi$
$108$	−1.10138	−	1.70148i	−0.105981	−	0.163725i
$109$	0.796284	+	0.796284i	0.0762701	+	0.0762701i	0.744213	−	0.667943i	$-0.232825\pi$
$109$	0.796284	+	0.796284i	0.0762701	+	0.0762701i	−0.667943	+	0.744213i	$0.732825\pi$
$110$		0			0
$111$	0.0234032			0.00222133
$112$	−4.37081	+	9.73945i	−0.413003	+	0.920292i
$113$	−0.842524			−0.0792580			−0.0396290	−	0.999214i	$-0.512618\pi$
$113$	−0.842524			−0.0792580			−0.0396290	+	0.999214i	$0.512618\pi$
$114$	0.735990	+	0.910246i	0.0689318	+	0.0852524i
$115$		0			0
$116$	−8.30822	+	5.37799i	−0.771399	+	0.499334i
$117$	−8.73747	+	8.73747i	−0.807779	+	0.807779i
$118$	−0.202015	+	1.90849i	−0.0185970	+	0.175690i
$119$			4.94039i			0.452885i
$120$		0			0
$121$		−	13.4600i		−	1.22364i
$122$	−12.9243	−	1.36805i	−1.17011	−	0.123858i
$123$	1.22472	−	1.22472i	0.110429	−	0.110429i
$124$	2.86513	−	13.3822i	0.257297	−	1.20175i
$125$		0			0
$126$	8.72020	−	7.05082i	0.776857	−	0.628137i
$127$	21.1693			1.87847			0.939234	−	0.343277i	$-0.111537\pi$
$127$	21.1693			1.87847			0.939234	+	0.343277i	$0.111537\pi$
$128$	−0.533685	−	11.3011i	−0.0471715	−	0.998887i
$129$	−1.06530			−0.0937947
$130$		0			0
$131$	4.67248	+	4.67248i	0.408237	+	0.408237i	0.881123	−	0.472887i	$-0.156788\pi$
$131$	4.67248	+	4.67248i	0.408237	+	0.408237i	−0.472887	+	0.881123i	$0.656788\pi$
$132$	−0.351458	+	1.64155i	−0.0305905	+	0.142879i
$133$	−9.20357	+	9.20357i	−0.798051	+	0.798051i
$134$	6.95497	+	0.736191i	0.600818	+	0.0635973i
$135$		0			0
$136$	−2.36669	−	4.67044i	−0.202942	−	0.400487i
$137$		−	10.2840i		−	0.878623i	−0.898335	−	0.439312i	$-0.855222\pi$
$137$		−	10.2840i		−	0.878623i	0.898335	−	0.439312i	$-0.144778\pi$
$138$	0.0178696	−	0.168819i	0.00152117	−	0.0143708i
$139$	4.98588	−	4.98588i	0.422897	−	0.422897i	−0.463303	−	0.886200i	$-0.653336\pi$
$139$	4.98588	−	4.98588i	0.422897	−	0.422897i	0.886200	+	0.463303i	$0.153336\pi$
$140$		0			0
$141$	0.227331	+	0.227331i	0.0191447	+	0.0191447i
$142$	−6.99588	−	8.65225i	−0.587081	−	0.726080i
$143$	20.5683			1.72001
$144$	−4.86604	+	10.8430i	−0.405503	+	0.903580i
$145$		0			0
$146$	13.9214	+	17.2174i	1.15214	+	1.42493i
$147$	−0.0147084	−	0.0147084i	−0.00121313	−	0.00121313i
$148$	−0.149863	−	0.231518i	−0.0123187	−	0.0190306i
$149$	8.79493	−	8.79493i	0.720509	−	0.720509i	−0.248200	−	0.968709i	$-0.579839\pi$
$149$	8.79493	−	8.79493i	0.720509	−	0.720509i	0.968709	+	0.248200i	$0.0798390\pi$
$150$		0			0
$151$		−	22.1838i		−	1.80529i	−0.430385	−	0.902645i	$-0.641622\pi$
$151$		−	22.1838i		−	1.80529i	0.430385	−	0.902645i	$-0.358378\pi$
$152$	4.29172	−	13.1096i	0.348105	−	1.06333i
$153$			5.50015i			0.444661i
$154$	−18.5627	−	1.96489i	−1.49583	−	0.158335i
$155$		0			0
$156$	−1.38037	−	0.295539i	−0.110518	−	0.0236620i
$157$	3.72187	+	3.72187i	0.297038	+	0.297038i	0.839852	−	0.542815i	$-0.182641\pi$
$157$	3.72187	+	3.72187i	0.297038	+	0.297038i	−0.542815	+	0.839852i	$0.682641\pi$
$158$	7.37037	−	5.95940i	0.586355	−	0.474104i
$159$	1.78549			0.141598
$160$		0			0
$161$	1.88762			0.148765
$162$	9.61319	−	7.77286i	0.755284	−	0.610694i
$163$	−2.11630	−	2.11630i	−0.165761	−	0.165761i	0.619352	−	0.785113i	$-0.287395\pi$
$163$	−2.11630	−	2.11630i	−0.165761	−	0.165761i	−0.785113	+	0.619352i	$0.787395\pi$
$164$	−19.9582	−	4.27307i	−1.55847	−	0.333671i
$165$		0			0
$166$	−7.70350	−	0.815425i	−0.597908	−	0.0632892i
$167$		−	18.1604i		−	1.40530i	−0.711538	−	0.702648i	$-0.752001\pi$
$167$		−	18.1604i		−	1.40530i	0.711538	−	0.702648i	$-0.247999\pi$
$168$	1.21754	+	0.398589i	0.0939354	+	0.0307518i
$169$			4.29572i			0.330440i
$170$		0			0
$171$	−10.2464	+	10.2464i	−0.783559	+	0.783559i
$172$	6.82172	+	10.5386i	0.520151	+	0.803560i
$173$	8.53542	+	8.53542i	0.648936	+	0.648936i	0.952736	−	0.303800i	$-0.0982555\pi$
$173$	8.53542	+	8.53542i	0.648936	+	0.648936i	−0.303800	+	0.952736i	$0.598255\pi$
$174$	0.746774	+	0.923584i	0.0566128	+	0.0700167i
$175$		0			0
$176$	18.4897	−	7.03493i	1.39372	−	0.530278i
$177$	0.230315			0.0173115
$178$	−9.34128	−	11.5530i	−0.700159	−	0.865931i
$179$	−2.42499	−	2.42499i	−0.181252	−	0.181252i	0.610649	−	0.791901i	$-0.290909\pi$
$179$	−2.42499	−	2.42499i	−0.181252	−	0.181252i	−0.791901	+	0.610649i	$0.790909\pi$
$180$		0			0
$181$	4.46593	−	4.46593i	0.331950	−	0.331950i	−0.521377	−	0.853327i	$-0.674581\pi$
$181$	4.46593	−	4.46593i	0.331950	−	0.331950i	0.853327	+	0.521377i	$0.174581\pi$
$182$	1.65226	−	15.6093i	0.122474	−	1.15704i
$183$			1.55970i			0.115296i
$184$	−1.78448	+	0.904262i	−0.131554	+	0.0666631i
$185$		0			0
$186$	−1.63325	−	0.172881i	−0.119756	−	0.0126763i
$187$	6.47376	−	6.47376i	0.473408	−	0.473408i
$188$	0.793162	−	3.70461i	0.0578473	−	0.270187i
$189$	−1.91246	−	1.91246i	−0.139111	−	0.139111i
$190$		0			0
$191$	7.75030			0.560792			0.280396	−	0.959884i	$-0.409534\pi$
$191$	7.75030			0.560792			0.280396	+	0.959884i	$0.409534\pi$
$192$	−1.34196	+	0.206453i	−0.0968475	+	0.0148994i
$193$	11.3388			0.816181			0.408091	−	0.912941i	$-0.366195\pi$
$193$	11.3388			0.816181			0.408091	+	0.912941i	$0.366195\pi$
$194$	5.27791	−	4.26751i	0.378932	−	0.306390i
$195$		0			0
$196$	−0.0513179	+	0.239690i	−0.00366557	+	0.0171207i
$197$	−1.10001	+	1.10001i	−0.0783725	+	0.0783725i	−0.745206	−	0.666834i	$-0.767649\pi$
$197$	−1.10001	+	1.10001i	−0.0783725	+	0.0783725i	0.666834	+	0.745206i	$0.267649\pi$
$198$	−20.6659	−	2.18751i	−1.46866	−	0.155460i
$199$			14.2722i			1.01173i	0.862614	+	0.505864i	$0.168826\pi$
$199$			14.2722i			1.01173i	−0.862614	+	0.505864i	$0.831174\pi$
$200$		0			0
$201$		−	0.839321i		−	0.0592012i
$202$	−0.0785219	+	0.741814i	−0.00552478	+	0.0521939i
$203$	−9.33843	+	9.33843i	−0.655429	+	0.655429i
$204$	−0.527483	+	0.341445i	−0.0369312	+	0.0239059i
$205$		0			0
$206$	−9.15971	−	11.3284i	−0.638187	−	0.789287i
$207$	2.10149			0.146064
$208$	5.91563	+	15.5479i	0.410175	+	1.07805i
$209$	24.1203			1.66843
$210$		0			0
$211$	−12.4716	−	12.4716i	−0.858577	−	0.858577i	0.132593	−	0.991171i	$-0.457670\pi$
$211$	−12.4716	−	12.4716i	−0.858577	−	0.858577i	−0.991171	+	0.132593i	$0.957670\pi$
$212$	−11.4334	−	17.6630i	−0.785252	−	1.21310i
$213$	−0.944203	+	0.944203i	−0.0646957	+	0.0646957i
$214$	3.05409	−	28.8527i	0.208773	−	1.97233i
$215$		0			0
$216$	2.72413	+	0.891801i	0.185353	+	0.0606794i
$217$		−	18.2619i		−	1.23970i
$218$	−1.58372	−	0.167639i	−0.107263	−	0.0113539i
$219$	1.87890	−	1.87890i	0.126965	−	0.126965i
$220$		0			0
$221$	5.44374	+	5.44374i	0.366186	+	0.366186i
$222$	−0.0257367	+	0.0208097i	−0.00172733	+	0.00139665i
$223$	−3.08673			−0.206703			−0.103351	−	0.994645i	$-0.532957\pi$
$223$	−3.08673			−0.206703			−0.103351	+	0.994645i	$0.532957\pi$
$224$	−3.85353	−	14.5970i	−0.257475	−	0.975303i
$225$		0			0
$226$	0.926530	−	0.749157i	0.0616319	−	0.0498332i
$227$	−8.31678	−	8.31678i	−0.552004	−	0.552004i	0.375015	−	0.927019i	$-0.377638\pi$
$227$	−8.31678	−	8.31678i	−0.552004	−	0.552004i	−0.927019	+	0.375015i	$0.877638\pi$
$228$	−1.61875	−	0.346576i	−0.107204	−	0.0229525i
$229$	−9.98910	+	9.98910i	−0.660098	+	0.660098i	−0.955403	−	0.295305i	$-0.904579\pi$
$229$	−9.98910	+	9.98910i	−0.660098	+	0.660098i	0.295305	+	0.955403i	$0.404579\pi$
$230$		0			0
$231$			2.24014i			0.147390i
$232$	4.35461	−	13.3017i	0.285894	−	0.873301i
$233$			13.9015i			0.910718i	0.890308	+	0.455359i	$0.150489\pi$
$233$			13.9015i			0.910718i	−0.890308	+	0.455359i	$0.849511\pi$
$234$	1.83947	−	17.3779i	0.120250	−	1.13603i
$235$		0			0
$236$	−1.47483	−	2.27840i	−0.0960034	−	0.148311i
$237$	−0.804314	−	0.804314i	−0.0522458	−	0.0522458i
$238$	−4.39290	−	5.43298i	−0.284750	−	0.352168i
$239$	−10.7687			−0.696569			−0.348284	−	0.937389i	$-0.613236\pi$
$239$	−10.7687			−0.696569			−0.348284	+	0.937389i	$0.613236\pi$
$240$		0			0
$241$	−12.4707			−0.803305			−0.401653	−	0.915792i	$-0.631564\pi$
$241$	−12.4707			−0.803305			−0.401653	+	0.915792i	$0.631564\pi$
$242$	11.9684	+	14.8021i	0.769358	+	0.951515i
$243$	−3.19886	−	3.19886i	−0.205207	−	0.205207i
$244$	15.4294	−	9.98758i	0.987765	−	0.639390i
$245$		0			0
$246$	−0.257836	+	2.43583i	−0.0164390	+	0.155303i
$247$			20.2826i			1.29055i
$248$	8.74835	+	17.2641i	0.555521	+	1.09627i
$249$			0.929654i			0.0589144i
$250$		0			0
$251$	3.69093	−	3.69093i	0.232969	−	0.232969i	−0.580962	−	0.813931i	$-0.697323\pi$
$251$	3.69093	−	3.69093i	0.232969	−	0.232969i	0.813931	+	0.580962i	$0.197323\pi$
$252$	−3.32021	+	15.5077i	−0.209154	+	0.976892i
$253$	−2.47349	−	2.47349i	−0.155507	−	0.155507i
$254$	−23.2800	+	18.8233i	−1.46072	+	1.18108i
$255$		0			0
$256$	10.6356	+	11.9534i	0.664727	+	0.747086i
$257$	−3.11011			−0.194003			−0.0970016	−	0.995284i	$-0.530925\pi$
$257$	−3.11011			−0.194003			−0.0970016	+	0.995284i	$0.530925\pi$
$258$	1.17152	−	0.947248i	0.0729358	−	0.0589731i
$259$	−0.260225	−	0.260225i	−0.0161696	−	0.0161696i
$260$		0			0
$261$	−10.3965	+	10.3965i	−0.643527	+	0.643527i
$262$	−9.29305	−	0.983680i	−0.574126	−	0.0607719i
$263$		−	17.9512i		−	1.10692i	−0.832877	−	0.553458i	$-0.813308\pi$
$263$		−	17.9512i		−	1.10692i	0.832877	−	0.553458i	$-0.186692\pi$
$264$	−1.07314	−	2.11774i	−0.0660469	−	0.130338i
$265$		0			0
$266$	1.93759	−	18.3049i	0.118801	−	1.12234i
$267$	−1.26075	+	1.26075i	−0.0771568	+	0.0771568i
$268$	−8.30304	+	5.37463i	−0.507189	+	0.328308i
$269$	1.62436	+	1.62436i	0.0990392	+	0.0990392i	0.754890	−	0.655851i	$-0.227690\pi$
$269$	1.62436	+	1.62436i	0.0990392	+	0.0990392i	−0.655851	+	0.754890i	$0.727690\pi$
$270$		0			0
$271$	18.1808			1.10440			0.552201	−	0.833711i	$-0.313788\pi$
$271$	18.1808			1.10440			0.552201	+	0.833711i	$0.313788\pi$
$272$	6.75553	+	3.03171i	0.409614	+	0.183824i
$273$	−1.88372			−0.114008
$274$	9.14436	+	11.3094i	0.552431	+	0.683227i
$275$		0			0
$276$	0.130459	+	0.201541i	0.00785271	+	0.0121313i
$277$	13.8675	−	13.8675i	0.833218	−	0.833218i	−0.154737	−	0.987956i	$-0.549453\pi$
$277$	13.8675	−	13.8675i	0.833218	−	0.833218i	0.987956	+	0.154737i	$0.0494531\pi$
$278$	−1.04966	+	9.91636i	−0.0629543	+	0.594744i
$279$		−	20.3310i		−	1.21719i
$280$		0			0
$281$			10.7377i			0.640556i	0.947324	+	0.320278i	$0.103776\pi$
$281$			10.7377i			0.640556i	−0.947324	+	0.320278i	$0.896224\pi$
$282$	−0.452136	−	0.0478591i	−0.0269243	−	0.00284997i
$283$	16.3679	−	16.3679i	0.972971	−	0.972971i	−0.0266735	−	0.999644i	$-0.508491\pi$
$283$	16.3679	−	16.3679i	0.972971	−	0.972971i	0.999644	+	0.0266735i	$0.00849143\pi$
$284$	15.3868	+	3.29434i	0.913041	+	0.195483i
$285$		0			0
$286$	−22.6191	+	18.2889i	−1.33749	+	1.08145i
$287$	−27.2359			−1.60768
$288$	−4.29014	−	16.2509i	−0.252799	−	0.957592i
$289$	−13.5732			−0.798425
$290$		0			0
$291$	−0.575968	−	0.575968i	−0.0337638	−	0.0337638i
$292$	−30.6188	−	6.55553i	−1.79183	−	0.383633i
$293$	4.22052	−	4.22052i	0.246566	−	0.246566i	−0.572994	−	0.819560i	$-0.694218\pi$
$293$	4.22052	−	4.22052i	0.246566	−	0.246566i	0.819560	+	0.572994i	$0.194218\pi$
$294$	0.0292534	+	0.00309651i	0.00170609	+	0.000180592i
$295$		0			0
$296$	0.370667	+	0.121346i	0.0215446	+	0.00705308i
$297$			5.01208i			0.290831i
$298$	−1.85156	+	17.4921i	−0.107258	+	1.01329i
$299$	2.07994	−	2.07994i	0.120286	−	0.120286i
$300$		0			0
$301$	11.8454	+	11.8454i	0.682755	+	0.682755i
$302$	19.7254	+	24.3957i	1.13507	+	1.40381i
$303$	0.0895217			0.00514289
$304$	6.93721	+	18.2329i	0.397876	+	1.04573i
$305$		0			0
$306$	−4.89063	−	6.04855i	−0.279579	−	0.345773i
$307$	12.6363	+	12.6363i	0.721190	+	0.721190i	0.968848	−	0.247658i	$-0.0796608\pi$
$307$	12.6363	+	12.6363i	0.721190	+	0.721190i	−0.247658	+	0.968848i	$0.579661\pi$
$308$	22.1607	−	14.3448i	1.26272	−	0.817373i
$309$	−1.23625	+	1.23625i	−0.0703276	+	0.0703276i
$310$		0			0
$311$		−	8.56815i		−	0.485855i	−0.970044	−	0.242928i	$-0.921892\pi$
$311$		−	8.56815i		−	0.485855i	0.970044	−	0.242928i	$-0.0781078\pi$
$312$	1.78079	−	0.902392i	0.100817	−	0.0510879i
$313$			19.1825i			1.08426i	0.840295	+	0.542129i	$0.182382\pi$
$313$			19.1825i			1.08426i	−0.840295	+	0.542129i	$0.817618\pi$
$314$	−7.40239	−	0.783551i	−0.417741	−	0.0442183i
$315$		0			0
$316$	−2.80626	+	13.1072i	−0.157865	+	0.737337i
$317$	9.41764	+	9.41764i	0.528947	+	0.528947i	0.920258	−	0.391311i	$-0.127978\pi$
$317$	9.41764	+	9.41764i	0.528947	+	0.528947i	−0.391311	+	0.920258i	$0.627978\pi$
$318$	−1.96351	+	1.58762i	−0.110108	+	0.0890293i
$319$	24.4737			1.37026
$320$		0			0
$321$	−3.48193			−0.194342
$322$	−2.07583	+	1.67844i	−0.115681	+	0.0935356i
$323$	6.38383	+	6.38383i	0.355206	+	0.355206i
$324$	−3.66022	+	17.0957i	−0.203345	+	0.949764i
$325$		0			0
$326$	4.20908	+	0.445536i	0.233120	+	0.0246760i
$327$			0.191122i			0.0105691i
$328$	25.7477	−	13.0473i	1.42168	−	0.720417i
$329$		−	5.05549i		−	0.278718i
$330$		0			0
$331$	12.8579	−	12.8579i	0.706733	−	0.706733i	−0.259114	−	0.965847i	$-0.583431\pi$
$331$	12.8579	−	12.8579i	0.706733	−	0.706733i	0.965847	+	0.259114i	$0.0834305\pi$
$332$	9.19666	−	5.95308i	0.504732	−	0.326718i
$333$	−0.289709	−	0.289709i	−0.0158760	−	0.0158760i
$334$	16.1479	+	19.9711i	0.883574	+	1.09277i
$335$		0			0
$336$	−1.69336	+	0.644285i	−0.0923802	+	0.0351486i
$337$	−3.31961			−0.180831			−0.0904153	−	0.995904i	$-0.528819\pi$
$337$	−3.31961			−0.180831			−0.0904153	+	0.995904i	$0.528819\pi$
$338$	−3.81967	−	4.72403i	−0.207763	−	0.256954i
$339$	−0.101110	−	0.101110i	−0.00549156	−	0.00549156i
$340$		0			0
$341$	−23.9300	+	23.9300i	−1.29588	+	1.29588i
$342$	2.15713	−	20.3789i	0.116644	−	1.10196i
$343$		−	18.3546i		−	0.991055i
$344$	−16.8726	−	5.52361i	−0.909710	−	0.297813i
$345$		0			0
$346$	−16.9760	−	1.79693i	−0.912635	−	0.0966035i
$347$	−17.8860	+	17.8860i	−0.960171	+	0.960171i	−0.999237	−	0.0390656i	$-0.987562\pi$
$347$	−17.8860	+	17.8860i	−0.960171	+	0.960171i	0.0390656	+	0.999237i	$0.487562\pi$
$348$	−1.64247	−	0.351654i	−0.0880455	−	0.0188506i
$349$	−3.68796	−	3.68796i	−0.197412	−	0.197412i	0.601478	−	0.798890i	$-0.294579\pi$
$349$	−3.68796	−	3.68796i	−0.197412	−	0.197412i	−0.798890	+	0.601478i	$0.794579\pi$
$350$		0			0
$351$	−4.21463			−0.224960
$352$	−14.0780	+	24.1771i	−0.750358	+	1.28864i
$353$	−33.0951			−1.76148			−0.880738	−	0.473604i	$-0.842953\pi$
$353$	−33.0951			−1.76148			−0.880738	+	0.473604i	$0.842953\pi$
$354$	−0.253279	+	0.204792i	−0.0134616	+	0.0108846i
$355$		0			0
$356$	20.5454	+	4.39879i	1.08890	+	0.233135i
$357$	−0.592891	+	0.592891i	−0.0313791	+	0.0313791i
$358$	4.82303	+	0.510524i	0.254905	+	0.0269820i
$359$		−	6.52522i		−	0.344388i	−0.985063	−	0.172194i	$-0.944914\pi$
$359$		−	6.52522i		−	0.344388i	0.985063	−	0.172194i	$-0.0550856\pi$
$360$		0			0
$361$			4.78519i			0.251852i
$362$	−0.940195	+	8.88224i	−0.0494156	+	0.466840i
$363$	1.61532	−	1.61532i	0.0847825	−	0.0847825i
$364$	12.0625	+	18.6348i	0.632246	+	0.976729i
$365$		0			0
$366$	−1.38685	−	1.71521i	−0.0724919	−	0.0896554i
$367$	11.0338			0.575959			0.287980	−	0.957636i	$-0.407016\pi$
$367$	11.0338			0.575959			0.287980	+	0.957636i	$0.407016\pi$
$368$	1.15835	−	2.58115i	0.0603833	−	0.134552i
$369$	−30.3218			−1.57849
$370$		0			0
$371$	−19.8532	−	19.8532i	−1.03073	−	1.03073i
$372$	1.94982	−	1.26214i	0.101093	−	0.0654387i
$373$	−6.84468	+	6.84468i	−0.354404	+	0.354404i	−0.861745	−	0.507341i	$-0.830628\pi$
$373$	−6.84468	+	6.84468i	−0.354404	+	0.354404i	0.507341	+	0.861745i	$0.330628\pi$
$374$	−1.36290	+	12.8756i	−0.0704737	+	0.665781i
$375$		0			0
$376$	2.42183	+	4.77925i	0.124896	+	0.246471i
$377$			20.5797i			1.05991i
$378$	3.80367	+	0.402623i	0.195640	+	0.0207087i
$379$	−10.1072	+	10.1072i	−0.519171	+	0.519171i	−0.917321	−	0.398150i	$-0.869653\pi$
$379$	−10.1072	+	10.1072i	−0.519171	+	0.519171i	0.398150	+	0.917321i	$0.369653\pi$
$380$		0			0
$381$	2.54050	+	2.54050i	0.130154	+	0.130154i
$382$	−8.52307	+	6.89143i	−0.436078	+	0.352596i
$383$	−29.5283			−1.50883			−0.754413	−	0.656400i	$-0.772078\pi$
$383$	−29.5283			−1.50883			−0.754413	+	0.656400i	$0.772078\pi$
$384$	1.29219	−	1.42028i	0.0659417	−	0.0724784i
$385$		0			0
$386$	−12.4693	+	10.0822i	−0.634671	+	0.513171i
$387$	13.1875	+	13.1875i	0.670356	+	0.670356i
$388$	−2.00956	+	9.38604i	−0.102020	+	0.476504i
$389$	0.990949	−	0.990949i	0.0502431	−	0.0502431i	−0.681539	−	0.731782i	$-0.738689\pi$
$389$	0.990949	−	0.990949i	0.0502431	−	0.0502431i	0.731782	+	0.681539i	$0.238689\pi$
$390$		0			0
$391$		−	1.30930i		−	0.0662142i
$392$	−0.156693	−	0.309220i	−0.00791420	−	0.0156180i
$393$			1.12148i			0.0565711i
$394$	0.231581	−	2.18780i	0.0116669	−	0.110220i
$395$		0			0
$396$	24.6716	−	15.9701i	1.23979	−	0.802530i
$397$	−17.0024	−	17.0024i	−0.853326	−	0.853326i	0.137216	−	0.990541i	$-0.456185\pi$
$397$	−17.0024	−	17.0024i	−0.853326	−	0.853326i	−0.990541	+	0.137216i	$0.956185\pi$
$398$	−12.6905	−	15.6952i	−0.636119	−	0.786730i
$399$	−2.20902			−0.110589
$400$		0			0
$401$	26.7791			1.33728			0.668642	−	0.743585i	$-0.266876\pi$
$401$	26.7791			1.33728			0.668642	+	0.743585i	$0.266876\pi$
$402$	0.746309	+	0.923008i	0.0372225	+	0.0460354i
$403$	−20.1225	−	20.1225i	−1.00238	−	1.00238i
$404$	−0.573256	−	0.885599i	−0.0285206	−	0.0440602i
$405$		0			0
$406$	1.96598	−	18.5731i	0.0975701	−	0.921767i
$407$			0.681985i			0.0338048i
$408$	0.276471	−	0.844518i	0.0136874	−	0.0418099i
$409$		−	13.1970i		−	0.652550i	−0.945275	−	0.326275i	$-0.894206\pi$
$409$		−	13.1970i		−	0.652550i	0.945275	−	0.326275i	$-0.105794\pi$
$410$		0			0
$411$	1.23417	−	1.23417i	0.0608773	−	0.0608773i
$412$	20.1460	+	4.31328i	0.992523	+	0.212500i
$413$	−2.56092	−	2.56092i	−0.126015	−	0.126015i
$414$	−2.31103	+	1.86861i	−0.113581	+	0.0918371i
$415$		0			0
$416$	−20.3304	−	11.8381i	−0.996777	−	0.580409i
$417$	1.19670			0.0586026
$418$	−26.5252	+	21.4473i	−1.29739	+	1.04902i
$419$	−9.92468	−	9.92468i	−0.484852	−	0.484852i	0.421825	−	0.906677i	$-0.361390\pi$
$419$	−9.92468	−	9.92468i	−0.484852	−	0.484852i	−0.906677	+	0.421825i	$0.861390\pi$
$420$		0			0
$421$	15.7930	−	15.7930i	0.769702	−	0.769702i	−0.208352	−	0.978054i	$-0.566810\pi$
$421$	15.7930	−	15.7930i	0.769702	−	0.769702i	0.978054	+	0.208352i	$0.0668100\pi$
$422$	24.8045	+	2.62559i	1.20747	+	0.127812i
$423$		−	5.62829i		−	0.273657i
$424$	28.2791	+	9.25777i	1.37335	+	0.449597i
$425$		0			0
$426$	0.198779	−	1.87791i	0.00963089	−	0.0909852i
$427$	17.3426	−	17.3426i	0.839268	−	0.839268i
$428$	22.2967	+	34.4452i	1.07775	+	1.66497i
$429$	2.46838	+	2.46838i	0.119174	+	0.119174i
$430$		0			0
$431$	−0.285215			−0.0137383			−0.00686917	−	0.999976i	$-0.502187\pi$
$431$	−0.285215			−0.0137383			−0.00686917	+	0.999976i	$0.502187\pi$
$432$	−3.78871	+	1.44152i	−0.182285	+	0.0693552i
$433$	18.1101			0.870318			0.435159	−	0.900354i	$-0.356692\pi$
$433$	18.1101			0.870318			0.435159	+	0.900354i	$0.356692\pi$
$434$	16.2382	+	20.0828i	0.779457	+	0.964004i
$435$		0			0
$436$	1.89069	−	1.22386i	0.0905476	−	0.0586123i
$437$	2.43913	−	2.43913i	0.116679	−	0.116679i
$438$	−0.395559	+	3.73693i	−0.0189005	+	0.178558i
$439$			11.5931i			0.553308i	0.960970	+	0.276654i	$0.0892256\pi$
$439$			11.5931i			0.553308i	−0.960970	+	0.276654i	$0.910774\pi$
$440$		0			0
$441$			0.364153i			0.0173406i
$442$	−10.8270	−	1.14605i	−0.514988	−	0.0545120i
$443$	22.6855	−	22.6855i	1.07782	−	1.07782i	0.0811145	−	0.996705i	$-0.474152\pi$
$443$	22.6855	−	22.6855i	1.07782	−	1.07782i	0.996705	−	0.0811145i	$-0.0258479\pi$
$444$	0.00979922	−	0.0457691i	0.000465050	−	0.00217211i
$445$		0			0
$446$	3.39450	−	2.74466i	0.160734	−	0.129963i
$447$	2.11094			0.0998440
$448$	17.2171	+	12.6259i	0.813433	+	0.596520i
$449$	12.1999			0.575747			0.287873	−	0.957669i	$-0.407052\pi$
$449$	12.1999			0.575747			0.287873	+	0.957669i	$0.407052\pi$
$450$		0			0
$451$	35.6892	+	35.6892i	1.68054	+	1.68054i
$452$	−0.352776	+	1.64771i	−0.0165932	+	0.0775016i
$453$	2.66225	−	2.66225i	0.125083	−	0.125083i
$454$	16.5411	+	1.75090i	0.776315	+	0.0821738i
$455$		0			0
$456$	2.08832	−	1.05823i	0.0977945	−	0.0495561i
$457$			1.70660i			0.0798314i	0.999203	+	0.0399157i	$0.0127089\pi$
$457$			1.70660i			0.0798314i	−0.999203	+	0.0399157i	$0.987291\pi$
$458$	2.10297	−	19.8672i	0.0982652	−	0.928334i
$459$	−1.32653	+	1.32653i	−0.0619172	+	0.0619172i
$460$		0			0
$461$	−4.74710	−	4.74710i	−0.221094	−	0.221094i	0.587865	−	0.808959i	$-0.299969\pi$
$461$	−4.74710	−	4.74710i	−0.221094	−	0.221094i	−0.808959	+	0.587865i	$0.799969\pi$
$462$	−1.99189	−	2.46350i	−0.0926711	−	0.114612i
$463$	11.1761			0.519398			0.259699	−	0.965690i	$-0.416377\pi$
$463$	11.1761			0.519398			0.259699	+	0.965690i	$0.416377\pi$
$464$	7.03886	+	18.5000i	0.326771	+	0.858843i
$465$		0			0
$466$	−12.3610	−	15.2876i	−0.572610	−	0.708184i
$467$	−2.06471	−	2.06471i	−0.0955435	−	0.0955435i	0.657719	−	0.753263i	$-0.271521\pi$
$467$	−2.06471	−	2.06471i	−0.0955435	−	0.0955435i	−0.753263	+	0.657719i	$0.771521\pi$
$468$	13.4292	+	20.7462i	0.620764	+	0.958992i
$469$	−9.33260	+	9.33260i	−0.430940	+	0.430940i
$470$		0			0
$471$			0.893315i			0.0411618i
$472$	3.64780	+	1.19419i	0.167904	+	0.0549668i
$473$		−	31.0437i		−	1.42739i
$474$	1.59969	+	0.169329i	0.0734762	+	0.00777754i
$475$		0			0
$476$	9.66181	+	2.06861i	0.442848	+	0.0948144i
$477$	−22.1026	−	22.1026i	−1.01201	−	1.01201i
$478$	11.8424	−	9.57532i	0.541659	−	0.437965i
$479$	−41.6214			−1.90173			−0.950864	−	0.309608i	$-0.899802\pi$
$479$	−41.6214			−1.90173			−0.950864	+	0.309608i	$0.899802\pi$
$480$		0			0
$481$	−0.573477			−0.0261483
$482$	13.7141	−	11.0887i	0.624659	−	0.505075i
$483$	0.226531	+	0.226531i	0.0103075	+	0.0103075i
$484$	−26.3235	−	5.63589i	−1.19652	−	0.256177i
$485$		0			0
$486$	6.36217	+	0.673443i	0.288594	+	0.0305480i
$487$		−	8.25627i		−	0.374127i	−0.982348	−	0.187064i	$-0.940103\pi$
$487$		−	8.25627i		−	0.374127i	0.982348	−	0.187064i	$-0.0598970\pi$
$488$	−8.08704	+	24.7029i	−0.366083	+	1.11825i
$489$		−	0.507950i		−	0.0229703i
$490$		0			0
$491$	4.28512	−	4.28512i	0.193385	−	0.193385i	−0.603772	−	0.797157i	$-0.706336\pi$
$491$	4.28512	−	4.28512i	0.193385	−	0.193385i	0.797157	+	0.603772i	$0.206336\pi$
$492$	−1.88235	−	2.90797i	−0.0848630	−	0.131101i
$493$	6.47737	+	6.47737i	0.291726	+	0.291726i
$494$	−18.0349	−	22.3049i	−0.811427	−	1.00354i
$495$		0			0
$496$	−24.9715	−	11.2066i	−1.12125	−	0.503190i
$497$	20.9976			0.941871
$498$	−0.826631	−	1.02235i	−0.0370422	−	0.0458125i
$499$	−15.1287	−	15.1287i	−0.677253	−	0.677253i	0.282125	−	0.959378i	$-0.408961\pi$
$499$	−15.1287	−	15.1287i	−0.677253	−	0.677253i	−0.959378	+	0.282125i	$0.908961\pi$
$500$		0			0
$501$	2.17941	−	2.17941i	0.0973689	−	0.0973689i
$502$	−0.777037	+	7.34084i	−0.0346808	+	0.327638i
$503$		−	18.6439i		−	0.831291i	−0.909527	−	0.415646i	$-0.863556\pi$
$503$		−	18.6439i		−	0.831291i	0.909527	−	0.415646i	$-0.136444\pi$
$504$	−10.1379	−	20.0062i	−0.451577	−	0.891146i
$505$		0			0
$506$	4.91950	+	0.520734i	0.218698	+	0.0231495i
$507$	−0.515524	+	0.515524i	−0.0228952	+	0.0228952i
$508$	8.86385	−	41.4003i	0.393270	−	1.83684i
$509$	11.6243	+	11.6243i	0.515239	+	0.515239i	0.916127	−	0.400888i	$-0.131298\pi$
$509$	11.6243	+	11.6243i	0.515239	+	0.515239i	−0.400888	+	0.916127i	$0.631298\pi$
$510$		0			0
$511$	−41.7839			−1.84841
$512$	−22.3248	−	3.68821i	−0.986627	−	0.162997i
$513$	−4.94246			−0.218215
$514$	3.42021	−	2.76545i	0.150859	−	0.121979i
$515$		0			0
$516$	−0.446057	+	2.08339i	−0.0196365	+	0.0917162i
$517$	−6.62459	+	6.62459i	−0.291349	+	0.291349i
$518$	0.517559	+	0.0547842i	0.0227402	+	0.00240708i
$519$			2.04865i			0.0899259i
$520$		0			0
$521$			36.9052i			1.61684i	0.588603	+	0.808422i	$0.299678\pi$
$521$			36.9052i			1.61684i	−0.588603	+	0.808422i	$0.700322\pi$
$522$	2.18873	−	20.6775i	0.0957983	−	0.905028i
$523$	−6.04158	+	6.04158i	−0.264180	+	0.264180i	−0.826750	−	0.562570i	$-0.809813\pi$
$523$	−6.04158	+	6.04158i	−0.264180	+	0.264180i	0.562570	+	0.826750i	$0.309813\pi$
$524$	11.0943	−	7.18144i	0.484657	−	0.313723i
$525$		0			0
$526$	15.9618	+	19.7410i	0.695969	+	0.860750i
$527$	−12.6669			−0.551780
$528$	3.06319	+	1.37468i	0.133308	+	0.0598252i
$529$	22.4997			0.978250
$530$		0			0
$531$	−2.85108	−	2.85108i	−0.123726	−	0.123726i
$532$	14.1456	+	21.8529i	0.613288	+	0.947443i
$533$	−30.0108	+	30.0108i	−1.29991	+	1.29991i
$534$	0.265421	−	2.50750i	0.0114859	−	0.108510i
$535$		0			0
$536$	4.35189	−	13.2934i	0.187973	−	0.574189i
$537$		−	0.582041i		−	0.0251169i
$538$	−3.23068	−	0.341971i	−0.139284	−	0.0147434i
$539$	0.428614	−	0.428614i	0.0184617	−	0.0184617i
$540$		0			0
$541$	−28.4222	−	28.4222i	−1.22197	−	1.22197i	−0.966932	−	0.255035i	$-0.917913\pi$
$541$	−28.4222	−	28.4222i	−1.22197	−	1.22197i	−0.255035	−	0.966932i	$-0.582087\pi$
$542$	−19.9935	+	16.1660i	−0.858795	+	0.694389i
$543$	1.07190			0.0459997
$544$	−10.1248	+	2.67290i	−0.434099	+	0.114600i
$545$		0			0
$546$	2.07154	−	1.67497i	0.0886537	−	0.0716820i
$547$	−23.3562	−	23.3562i	−0.998640	−	0.998640i	0.00135902	−	0.999999i	$-0.499567\pi$
$547$	−23.3562	−	23.3562i	−0.998640	−	0.998640i	−0.999999	+	0.00135902i	$0.999567\pi$
$548$	−20.1122	−	4.30605i	−0.859152	−	0.183945i
$549$	19.3076	−	19.3076i	0.824027	−	0.824027i
$550$		0			0
$551$			24.1337i			1.02813i
$552$	−0.322673	−	0.105634i	−0.0137339	−	0.00449608i
$553$			17.8867i			0.760620i
$554$	−2.91948	+	27.5810i	−0.124037	+	1.17180i
$555$		0			0
$556$	−7.66312	−	11.8384i	−0.324989	−	0.502061i
$557$	4.89520	+	4.89520i	0.207416	+	0.207416i	0.803168	−	0.595752i	$-0.203146\pi$
$557$	4.89520	+	4.89520i	0.207416	+	0.207416i	−0.595752	+	0.803168i	$0.703146\pi$
$558$	18.0780	+	22.3582i	0.765302	+	0.946498i
$559$	26.1044			1.10410
$560$		0			0
$561$	1.55382			0.0656022
$562$	−9.54774	−	11.8083i	−0.402747	−	0.498103i
$563$	−1.28613	−	1.28613i	−0.0542040	−	0.0542040i	0.679485	−	0.733689i	$-0.262203\pi$
$563$	−1.28613	−	1.28613i	−0.0542040	−	0.0542040i	−0.733689	+	0.679485i	$0.762203\pi$
$564$	0.539773	−	0.349400i	0.0227285	−	0.0147124i
$565$		0			0
$566$	−3.44587	+	32.5539i	−0.144841	+	1.36834i
$567$			23.3297i			0.979754i
$568$	−19.8503	+	10.0589i	−0.832899	+	0.422061i
$569$		−	11.4799i		−	0.481261i	−0.970617	−	0.240631i	$-0.922646\pi$
$569$		−	11.4799i		−	0.481261i	0.970617	−	0.240631i	$-0.0773543\pi$
$570$		0			0
$571$	28.7069	−	28.7069i	1.20134	−	1.20134i	0.227587	−	0.973758i	$-0.426917\pi$
$571$	28.7069	−	28.7069i	1.20134	−	1.20134i	0.973758	−	0.227587i	$-0.0730835\pi$
$572$	8.61221	−	40.2249i	0.360094	−	1.68189i
$573$	0.930105	+	0.930105i	0.0388557	+	0.0388557i
$574$	29.9515	−	24.2176i	1.25015	−	1.01082i
$575$		0			0
$576$	19.1679	+	14.0565i	0.798661	+	0.585687i
$577$	20.3419			0.846842			0.423421	−	0.905933i	$-0.360829\pi$
$577$	20.3419			0.846842			0.423421	+	0.905933i	$0.360829\pi$
$578$	14.9266	−	12.0691i	0.620864	−	0.502007i
$579$	1.36075	+	1.36075i	0.0565509	+	0.0565509i
$580$		0			0
$581$	10.3370	−	10.3370i	0.428852	−	0.428852i
$582$	1.14554	+	0.121256i	0.0474840	+	0.00502623i
$583$			52.0303i			2.15488i
$584$	39.5008	−	20.0165i	1.63456	−	0.828290i
$585$		0			0
$586$	−0.888530	+	8.39415i	−0.0367048	+	0.346759i
$587$	25.8136	−	25.8136i	1.06544	−	1.06544i	0.0677360	−	0.997703i	$-0.478422\pi$
$587$	25.8136	−	25.8136i	1.06544	−	1.06544i	0.997703	−	0.0677360i	$-0.0215775\pi$
$588$	−0.0349236	+	0.0226063i	−0.00144022	+	0.000932270i
$589$	−23.5975	−	23.5975i	−0.972320	−	0.972320i
$590$		0			0
$591$	−0.264022			−0.0108604
$592$	−0.515524	+	0.196145i	−0.0211879	+	0.00806152i
$593$	−4.02945			−0.165470			−0.0827349	−	0.996572i	$-0.526365\pi$
$593$	−4.02945			−0.165470			−0.0827349	+	0.996572i	$0.526365\pi$
$594$	−4.45665	−	5.51183i	−0.182859	−	0.226153i
$595$		0			0
$596$	−13.5175	−	20.8826i	−0.553699	−	0.855385i
$597$	−1.71279	+	1.71279i	−0.0700997	+	0.0700997i
$598$	−0.437882	+	4.13677i	−0.0179063	+	0.169165i
$599$		−	31.6701i		−	1.29400i	−0.762489	−	0.647002i	$-0.776023\pi$
$599$		−	31.6701i		−	1.29400i	0.762489	−	0.647002i	$-0.223977\pi$
$600$		0			0
$601$			19.4667i			0.794065i	0.917805	+	0.397032i	$0.129960\pi$
$601$			19.4667i			0.794065i	−0.917805	+	0.397032i	$0.870040\pi$
$602$	−23.5591	−	2.49376i	−0.960197	−	0.101638i
$603$	−10.3900	+	10.3900i	−0.423114	+	0.423114i
$604$	−43.3843	−	9.28864i	−1.76528	−	0.377949i
$605$		0			0
$606$	−0.0984477	+	0.0796010i	−0.00399916	+	0.00323357i
$607$	−13.6128			−0.552528			−0.276264	−	0.961082i	$-0.589096\pi$
$607$	−13.6128			−0.552528			−0.276264	+	0.961082i	$0.589096\pi$
$608$	−23.8412	−	13.8824i	−0.966890	−	0.563006i
$609$	−2.24139			−0.0908257
$610$		0			0
$611$	−5.57057	−	5.57057i	−0.225361	−	0.225361i
$612$	10.7565	+	2.30298i	0.434807	+	0.0930926i
$613$	11.1480	−	11.1480i	0.450265	−	0.450265i	−0.445177	−	0.895442i	$-0.646859\pi$
$613$	11.1480	−	11.1480i	0.450265	−	0.450265i	0.895442	+	0.445177i	$0.146859\pi$
$614$	−25.1321	−	2.66026i	−1.01425	−	0.107360i
$615$		0			0
$616$	−11.6152	+	35.4800i	−0.467988	+	1.42953i
$617$		−	1.96695i		−	0.0791863i	−0.999216	−	0.0395932i	$-0.987394\pi$
$617$		−	1.96695i		−	0.0791863i	0.999216	−	0.0395932i	$-0.0126062\pi$
$618$	0.260262	−	2.45876i	0.0104693	−	0.0989057i
$619$	7.84144	−	7.84144i	0.315174	−	0.315174i	−0.531736	−	0.846910i	$-0.678460\pi$
$619$	7.84144	−	7.84144i	0.315174	−	0.315174i	0.846910	+	0.531736i	$0.178460\pi$
$620$		0			0
$621$	0.506840	+	0.506840i	0.0203388	+	0.0203388i
$622$	7.61864	+	9.42246i	0.305480	+	0.377806i
$623$	28.0372			1.12329
$624$	−1.15596	+	2.57581i	−0.0462753	+	0.103115i
$625$		0			0
$626$	−17.0567	−	21.0951i	−0.681723	−	0.843131i
$627$	2.89464	+	2.89464i	0.115601	+	0.115601i
$628$	8.83718	−	5.72039i	0.352642	−	0.228268i
$629$	−0.180499	+	0.180499i	−0.00719696	+	0.00719696i
$630$		0			0
$631$			0.220729i			0.00878708i	0.999990	+	0.00439354i	$0.00139851\pi$
$631$			0.220729i			0.00878708i	−0.999990	+	0.00439354i	$0.998601\pi$
$632$	−8.56860	−	16.9093i	−0.340840	−	0.672618i
$633$		−	2.99339i		−	0.118977i
$634$	−18.7306	−	1.98266i	−0.743888	−	0.0787414i
$635$		0			0
$636$	0.747606	−	3.49184i	0.0296445	−	0.138460i
$637$	0.360418	+	0.360418i	0.0142803	+	0.0142803i
$638$	−26.9139	+	21.7615i	−1.06553	+	0.861547i
$639$	23.3767			0.924767
$640$		0			0
$641$	−19.2037			−0.758502			−0.379251	−	0.925294i	$-0.623818\pi$
$641$	−19.2037			−0.758502			−0.379251	+	0.925294i	$0.623818\pi$
$642$	3.82910	−	3.09606i	0.151122	−	0.122192i
$643$	7.17110	+	7.17110i	0.282801	+	0.282801i	0.834225	−	0.551424i	$-0.185915\pi$
$643$	7.17110	+	7.17110i	0.282801	+	0.282801i	−0.551424	+	0.834225i	$0.685915\pi$
$644$	0.790371	−	3.69158i	0.0311450	−	0.145469i
$645$		0			0
$646$	−12.6967	−	1.34396i	−0.499546	−	0.0528775i
$647$			26.4735i			1.04078i	0.853928	+	0.520391i	$0.174214\pi$
$647$			26.4735i			1.04078i	−0.853928	+	0.520391i	$0.825786\pi$
$648$	−11.1760	−	22.0549i	−0.439037	−	0.866399i
$649$			6.71153i			0.263451i
$650$		0			0
$651$	2.19159	−	2.19159i	0.0858953	−	0.0858953i
$652$	−5.02492	+	3.25268i	−0.196791	+	0.127385i
$653$	−10.5746	−	10.5746i	−0.413815	−	0.413815i	0.469250	−	0.883065i	$-0.344524\pi$
$653$	−10.5746	−	10.5746i	−0.413815	−	0.413815i	−0.883065	+	0.469250i	$0.844524\pi$
$654$	−0.169942	−	0.210179i	−0.00664527	−	0.00821863i
$655$		0			0
$656$	−16.7135	+	37.2426i	−0.652553	+	1.45408i
$657$	−46.5182			−1.81485
$658$	4.49525	+	5.55956i	0.175243	+	0.216734i
$659$	24.1291	+	24.1291i	0.939937	+	0.939937i	0.998296	−	0.0583584i	$-0.0185866\pi$
$659$	24.1291	+	24.1291i	0.939937	+	0.939937i	−0.0583584	+	0.998296i	$0.518587\pi$
$660$		0			0
$661$	23.4294	−	23.4294i	0.911299	−	0.911299i	−0.0850756	−	0.996374i	$-0.527113\pi$
$661$	23.4294	−	23.4294i	0.911299	−	0.911299i	0.996374	+	0.0850756i	$0.0271132\pi$
$662$	−2.70692	+	25.5729i	−0.105207	+	0.993919i
$663$			1.30659i			0.0507439i
$664$	−4.82027	+	14.7241i	−0.187063	+	0.571408i
$665$		0			0
$666$	0.576200	+	0.0609914i	0.0223273	+	0.00236337i
$667$	2.47487	−	2.47487i	0.0958273	−	0.0958273i
$668$	−35.5159	−	7.60401i	−1.37415	−	0.294208i
$669$	−0.370435	−	0.370435i	−0.0143218	−	0.0143218i
$670$		0			0
$671$	−45.4506			−1.75460
$672$	1.28931	−	2.21423i	0.0497363	−	0.0854157i
$673$	41.8069			1.61154			0.805769	−	0.592230i	$-0.201752\pi$
$673$	41.8069			1.61154			0.805769	+	0.592230i	$0.201752\pi$
$674$	3.65060	−	2.95173i	0.140616	−	0.113697i
$675$		0			0
$676$	8.40105	+	1.79867i	0.323117	+	0.0691798i
$677$	22.7350	−	22.7350i	0.873776	−	0.873776i	−0.119106	−	0.992882i	$-0.538003\pi$
$677$	22.7350	−	22.7350i	0.873776	−	0.873776i	0.992882	+	0.119106i	$0.0380027\pi$
$678$	0.201097	+	0.0212864i	0.00772310	+	0.000817499i
$679$			12.8086i			0.491550i
$680$		0			0
$681$		−	1.99617i		−	0.0764936i
$682$	5.03788	−	47.5940i	0.192911	−	1.82247i
$683$	−34.4402	+	34.4402i	−1.31782	+	1.31782i	−0.402315	+	0.915501i	$0.631794\pi$
$683$	−34.4402	+	34.4402i	−1.31782	+	1.31782i	−0.915501	+	0.402315i	$0.868206\pi$
$684$	15.7483	+	24.3289i	0.602151	+	0.930238i
$685$		0			0
$686$	16.3206	+	20.1847i	0.623122	+	0.770655i
$687$	−2.39756			−0.0914727
$688$	23.4664	−	8.92845i	0.894649	−	0.340394i
$689$	−43.7519			−1.66682
$690$		0			0
$691$	16.0991	+	16.0991i	0.612438	+	0.612438i	0.943581	−	0.331143i	$-0.107434\pi$
$691$	16.0991	+	16.0991i	0.612438	+	0.612438i	−0.331143	+	0.943581i	$0.607434\pi$
$692$	20.2664	−	13.1186i	0.770414	−	0.498696i
$693$	27.7308	−	27.7308i	1.05341	−	1.05341i
$694$	3.76547	−	35.5733i	0.142935	−	1.35034i
$695$		0			0
$696$	2.11892	−	1.07373i	0.0803174	−	0.0406998i
$697$			18.8915i			0.715567i
$698$	7.33495	+	0.776413i	0.277632	+	0.0293877i
$699$	−1.66830	+	1.66830i	−0.0631010	+	0.0631010i
$700$		0			0
$701$	−30.0507	−	30.0507i	−1.13500	−	1.13500i	−0.989334	−	0.145666i	$-0.953467\pi$
$701$	−30.0507	−	30.0507i	−1.13500	−	1.13500i	−0.145666	−	0.989334i	$-0.546533\pi$
$702$	4.63486	−	3.74757i	0.174931	−	0.141443i
$703$	−0.672512			−0.0253643
$704$	−6.01617	−	39.1056i	−0.226743	−	1.47385i
$705$		0			0
$706$	36.3950	−	29.4276i	1.36974	−	1.10752i
$707$	−0.995412	−	0.995412i	−0.0374363	−	0.0374363i
$708$	0.0964358	−	0.450422i	0.00362428	−	0.0169279i
$709$	−12.9188	+	12.9188i	−0.485176	+	0.485176i	−0.906780	−	0.421604i	$-0.861467\pi$
$709$	−12.9188	+	12.9188i	−0.485176	+	0.485176i	0.421604	+	0.906780i	$0.361467\pi$
$710$		0			0
$711$			19.9133i			0.746807i
$712$	−26.5052	+	13.4312i	−0.993325	+	0.503355i
$713$			4.83977i			0.181251i
$714$	0.124819	−	1.17919i	0.00467123	−	0.0441302i
$715$		0			0
$716$	−5.75788	+	3.72713i	−0.215182	+	0.139289i
$717$	−1.29234	−	1.29234i	−0.0482633	−	0.0482633i
$718$	5.80211	+	7.17584i	0.216533	+	0.267800i
$719$	17.0356			0.635319			0.317659	−	0.948205i	$-0.397103\pi$
$719$	17.0356			0.635319			0.317659	+	0.948205i	$0.397103\pi$
$720$		0			0
$721$	27.4922			1.02386
$722$	−4.25490	−	5.26231i	−0.158351	−	0.195843i
$723$	−1.49659	−	1.49659i	−0.0556588	−	0.0556588i
$724$	−6.86398	−	10.6039i	−0.255098	−	0.394090i
$725$		0			0
$726$	−0.340068	+	3.21270i	−0.0126211	+	0.119234i
$727$		−	31.7051i		−	1.17588i	−0.808905	−	0.587939i	$-0.799939\pi$
$727$		−	31.7051i		−	1.17588i	0.808905	−	0.587939i	$-0.200061\pi$
$728$	−29.8349	−	9.76710i	−1.10576	−	0.361993i
$729$			25.4570i			0.942852i
$730$		0			0
$731$	8.21624	−	8.21624i	0.303888	−	0.303888i
$732$	3.05026	+	0.653065i	0.112741	+	0.0241380i
$733$	−3.87657	−	3.87657i	−0.143184	−	0.143184i	0.631881	−	0.775065i	$-0.282283\pi$
$733$	−3.87657	−	3.87657i	−0.143184	−	0.143184i	−0.775065	+	0.631881i	$0.782283\pi$
$734$	−12.1339	+	9.81105i	−0.447872	+	0.362132i
$735$		0			0
$736$	1.02126	+	3.86849i	0.0376442	+	0.142595i
$737$	24.4584			0.900937
$738$	33.3451	−	26.9616i	1.22745	−	0.992469i
$739$	11.3024	+	11.3024i	0.415766	+	0.415766i	0.883742	−	0.467975i	$-0.155016\pi$
$739$	11.3024	+	11.3024i	0.415766	+	0.415766i	−0.467975	+	0.883742i	$0.655016\pi$
$740$		0			0
$741$	−2.43409	+	2.43409i	−0.0894184	+	0.0894184i
$742$	39.4859	+	4.17962i	1.44957	+	0.153439i
$743$			30.7210i			1.12704i	0.826102	+	0.563521i	$0.190554\pi$
$743$			30.7210i			1.12704i	−0.826102	+	0.563521i	$0.809446\pi$
$744$	−1.02196	+	3.12172i	−0.0374670	+	0.114448i
$745$		0			0
$746$	1.44098	−	13.6133i	0.0527582	−	0.498419i
$747$	11.5082	−	11.5082i	0.421065	−	0.421065i
$748$	−9.94995	−	15.3712i	−0.363806	−	0.562028i
$749$	38.7163	+	38.7163i	1.41466	+	1.41466i
$750$		0			0
$751$	16.4695			0.600981			0.300491	−	0.953785i	$-0.402850\pi$
$751$	16.4695			0.600981			0.300491	+	0.953785i	$0.402850\pi$
$752$	−6.91292	−	3.10234i	−0.252088	−	0.113131i
$753$	0.885888			0.0322836
$754$	−18.2991	−	22.6317i	−0.666415	−	0.824198i
$755$		0			0
$756$	−4.54093	+	2.93939i	−0.165152	+	0.106905i
$757$	−21.9737	+	21.9737i	−0.798649	+	0.798649i	−0.982883	−	0.184233i	$-0.941020\pi$
$757$	−21.9737	+	21.9737i	−0.798649	+	0.798649i	0.184233	+	0.982883i	$0.441020\pi$
$758$	2.12783	−	20.1021i	0.0772861	−	0.730140i
$759$		−	0.593681i		−	0.0215493i
$760$		0			0
$761$		−	5.91749i		−	0.214509i	−0.994232	−	0.107254i	$-0.965794\pi$
$761$		−	5.91749i		−	0.214509i	0.994232	−	0.107254i	$-0.0342060\pi$
$762$	−5.05277	−	0.534842i	−0.183043	−	0.0193753i
$763$	2.12513	−	2.12513i	0.0769349	−	0.0769349i
$764$	3.24515	−	15.1571i	0.117406	−	0.548365i
$765$		0			0
$766$	32.4725	−	26.2560i	1.17328	−	0.948668i
$767$	−5.64368			−0.203782
$768$	−0.158140	+	2.71088i	−0.00570640	+	0.0978206i
$769$	10.7206			0.386596			0.193298	−	0.981140i	$-0.438082\pi$
$769$	10.7206			0.386596			0.193298	+	0.981140i	$0.438082\pi$
$770$		0			0
$771$	−0.373240	−	0.373240i	−0.0134419	−	0.0134419i
$772$	4.74769	−	22.1750i	0.170873	−	0.798094i
$773$	16.8329	−	16.8329i	0.605438	−	0.605438i	−0.336312	−	0.941750i	$-0.609180\pi$
$773$	16.8329	−	16.8329i	0.605438	−	0.605438i	0.941750	+	0.336312i	$0.109180\pi$
$774$	−26.2284	−	2.77631i	−0.942760	−	0.0997922i
$775$		0			0
$776$	−6.13596	−	12.1088i	−0.220268	−	0.434679i
$777$		−	0.0624587i		−	0.00224069i
$778$	−0.208621	+	1.97089i	−0.00747941	+	0.0706597i
$779$	−35.1934	+	35.1934i	−1.26094	+	1.26094i
$780$		0			0
$781$	−27.5147	−	27.5147i	−0.984554	−	0.984554i
$782$	1.16421	+	1.43985i	0.0416319	+	0.0514889i
$783$	−5.01488			−0.179217
$784$	0.447269	+	0.200723i	0.0159739	+	0.00716867i
$785$		0			0
$786$	−0.997198	−	1.23330i	−0.0355689	−	0.0439903i
$787$	25.4619	+	25.4619i	0.907619	+	0.907619i	0.996080	−	0.0884603i	$-0.0281946\pi$
$787$	25.4619	+	25.4619i	0.907619	+	0.907619i	−0.0884603	+	0.996080i	$0.528195\pi$
$788$	1.69068	+	2.61186i	0.0602280	+	0.0930436i
$789$	2.15430	−	2.15430i	0.0766951	−	0.0766951i
$790$		0			0
$791$			2.24854i			0.0799489i
$792$	−12.9312	+	39.5000i	−0.459489	+	1.40357i
$793$		−	38.2191i		−	1.35720i
$794$	33.8159	+	3.57945i	1.20008	+	0.127030i
$795$		0			0
$796$	27.9118	+	5.97594i	0.989307	+	0.211812i
$797$	−7.14518	−	7.14518i	−0.253095	−	0.253095i	0.569143	−	0.822238i	$-0.307275\pi$
$797$	−7.14518	−	7.14518i	−0.253095	−	0.253095i	−0.822238	+	0.569143i	$0.807275\pi$
$798$	2.42928	−	1.96422i	0.0859955	−	0.0695326i
$799$	−3.50662			−0.124055
$800$		0			0
$801$	31.2139			1.10289
$802$	−29.4492	+	23.8115i	−1.03989	+	0.840812i
$803$	54.7526	+	54.7526i	1.93218	+	1.93218i
$804$	−1.64144	−	0.351435i	−0.0578892	−	0.0123941i
$805$		0			0
$806$	40.0215	+	4.23632i	1.40970	+	0.149218i
$807$			0.389876i			0.0137243i
$808$	1.41787	+	0.464171i	0.0498806	+	0.0163295i
$809$			12.4413i			0.437412i	0.975791	+	0.218706i	$0.0701835\pi$
$809$			12.4413i			0.437412i	−0.975791	+	0.218706i	$0.929817\pi$
$810$		0			0
$811$	−30.6494	+	30.6494i	−1.07624	+	1.07624i	−0.0794022	+	0.996843i	$0.525301\pi$
$811$	−30.6494	+	30.6494i	−1.07624	+	1.07624i	−0.996843	+	0.0794022i	$0.974699\pi$
$812$	14.3528	+	22.1731i	0.503686	+	0.778123i
$813$	2.18185	+	2.18185i	0.0765210	+	0.0765210i
$814$	−0.606409	−	0.749984i	−0.0212546	−	0.0262869i
$815$		0			0
$816$	0.446892	+	1.17456i	0.0156444	+	0.0411177i
$817$	30.6125			1.07099
$818$	11.7345	+	14.5129i	0.410288	+	0.507430i
$819$	23.3187	+	23.3187i	0.814820	+	0.814820i
$820$		0			0
$821$	8.84907	−	8.84907i	0.308835	−	0.308835i	−0.535623	−	0.844457i	$-0.679923\pi$
$821$	8.84907	−	8.84907i	0.308835	−	0.308835i	0.844457	+	0.535623i	$0.179923\pi$
$822$	−0.259826	+	2.45463i	−0.00906247	+	0.0856152i
$823$		−	11.7501i		−	0.409583i	−0.978806	−	0.204792i	$-0.934348\pi$
$823$		−	11.7501i		−	0.409583i	0.978806	−	0.204792i	$-0.0656516\pi$
$824$	−25.9900	+	13.1701i	−0.905405	+	0.458802i
$825$		0			0
$826$	5.09339	+	0.539141i	0.177222	+	0.0187591i
$827$	3.40407	−	3.40407i	0.118371	−	0.118371i	−0.645440	−	0.763811i	$-0.723326\pi$
$827$	3.40407	−	3.40407i	0.118371	−	0.118371i	0.763811	+	0.645440i	$0.223326\pi$
$828$	0.879922	−	4.10984i	0.0305794	−	0.142827i
$829$	24.8718	+	24.8718i	0.863834	+	0.863834i	0.991781	−	0.127947i	$-0.0408389\pi$
$829$	24.8718	+	24.8718i	0.863834	+	0.863834i	−0.127947	+	0.991781i	$0.540839\pi$
$830$		0			0
$831$	3.32845			0.115463
$832$	32.8836	−	5.05896i	1.14003	−	0.175388i
$833$	0.226880			0.00786092
$834$	−1.31602	+	1.06408i	−0.0455700	+	0.0368462i
$835$		0			0
$836$	10.0995	−	47.1715i	0.349297	−	1.63146i
$837$	4.90347	−	4.90347i	0.169489	−	0.169489i
$838$	19.7391	+	2.08940i	0.681875	+	0.0721773i
$839$			3.26196i			0.112615i	0.998413	+	0.0563076i	$0.0179328\pi$
$839$			3.26196i			0.112615i	−0.998413	+	0.0563076i	$0.982067\pi$
$840$		0			0
$841$		−	4.51268i		−	0.155610i
$842$	−3.32483	+	31.4104i	−0.114581	+	1.08248i
$843$	−1.28862	+	1.28862i	−0.0443823	+	0.0443823i
$844$	−29.6124	+	19.1683i	−1.01930	+	0.659802i
$845$		0			0
$846$	5.00457	+	6.18947i	0.172061	+	0.212798i
$847$	−35.9223			−1.23430
$848$	−39.3306	+	14.9644i	−1.35062	+	0.513880i
$849$	3.92859			0.134829
$850$		0			0
$851$	0.0689649	+	0.0689649i	0.00236409	+	0.00236409i
$852$	1.45121	+	2.24191i	0.0497175	+	0.0768065i
$853$	−4.02276	+	4.02276i	−0.137737	+	0.137737i	−0.772613	−	0.634877i	$-0.781051\pi$
$853$	−4.02276	+	4.02276i	−0.137737	+	0.137737i	0.634877	+	0.772613i	$0.281051\pi$
$854$	−3.65107	+	34.4925i	−0.124937	+	1.18031i
$855$		0			0
$856$	−55.1478	−	18.0538i	−1.88491	−	0.617067i
$857$			44.6563i			1.52543i	0.646736	+	0.762714i	$0.276134\pi$
$857$			44.6563i			1.52543i	−0.646736	+	0.762714i	$0.723866\pi$
$858$	−4.90932	−	0.519658i	−0.167602	−	0.0177408i
$859$	5.22864	−	5.22864i	0.178399	−	0.178399i	−0.612259	−	0.790658i	$-0.709739\pi$
$859$	5.22864	−	5.22864i	0.178399	−	0.178399i	0.790658	+	0.612259i	$0.209739\pi$
$860$		0			0
$861$	−3.26855	−	3.26855i	−0.111392	−	0.111392i
$862$	0.313653	−	0.253608i	0.0106831	−	0.00863793i
$863$	−36.9653			−1.25831			−0.629157	−	0.777278i	$-0.716600\pi$
$863$	−36.9653			−1.25831			−0.629157	+	0.777278i	$0.716600\pi$
$864$	2.88470	−	4.95411i	0.0981396	−	0.168542i
$865$		0			0
$866$	−19.9159	+	16.1032i	−0.676769	+	0.547209i
$867$	−1.62891	−	1.62891i	−0.0553206	−	0.0553206i
$868$	−35.7145	−	7.64651i	−1.21223	−	0.259539i
$869$	23.4383	−	23.4383i	0.795089	−	0.795089i
$870$		0			0
$871$			20.5669i			0.696883i
$872$	−0.990971	+	3.02705i	−0.0335585	+	0.102509i
$873$			14.2599i			0.482624i
$874$	−0.513501	+	4.85116i	−0.0173694	+	0.164093i
$875$		0			0
$876$	−2.88781	−	4.46126i	−0.0975701	−	0.150732i
$877$	−9.40192	−	9.40192i	−0.317480	−	0.317480i	0.530318	−	0.847799i	$-0.322072\pi$
$877$	−9.40192	−	9.40192i	−0.317480	−	0.317480i	−0.847799	+	0.530318i	$0.822072\pi$
$878$	−10.3084	−	12.7490i	−0.347890	−	0.430258i
$879$	1.01300			0.0341677
$880$		0			0
$881$	−10.3069			−0.347248			−0.173624	−	0.984812i	$-0.555548\pi$
$881$	−10.3069			−0.347248			−0.173624	+	0.984812i	$0.555548\pi$
$882$	−0.323798	−	0.400462i	−0.0109028	−	0.0134842i
$883$	−34.3375	−	34.3375i	−1.15555	−	1.15555i	−0.985422	−	0.170128i	$-0.945582\pi$
$883$	−34.3375	−	34.3375i	−1.15555	−	1.15555i	−0.170128	−	0.985422i	$-0.554418\pi$
$884$	12.9256	−	8.36684i	0.434734	−	0.281407i
$885$		0			0
$886$	−4.77589	+	45.1189i	−0.160449	+	1.51580i
$887$		−	6.79523i		−	0.228161i	−0.993471	−	0.114081i	$-0.963608\pi$
$887$		−	6.79523i		−	0.228161i	0.993471	−	0.114081i	$-0.0363922\pi$
$888$	0.0299208	+	0.0590459i	0.00100407	+	0.00198145i
$889$		−	56.4968i		−	1.89484i
$890$		0			0
$891$	30.5706	−	30.5706i	1.02415	−	1.02415i
$892$	−1.29245	+	6.03665i	−0.0432745	+	0.202122i
$893$	−6.53256	−	6.53256i	−0.218604	−	0.218604i
$894$	−2.32142	+	1.87701i	−0.0776398	+	0.0627766i
$895$		0			0
$896$	−30.1606	+	1.42431i	−1.00759	+	0.0475827i
$897$	0.499223			0.0166686
$898$	−13.4163	+	10.8479i	−0.447707	+	0.361998i
$899$	−23.9433	−	23.9433i	−0.798554	−	0.798554i
$900$		0			0
$901$	−13.7707	+	13.7707i	−0.458769	+	0.458769i
$902$	−70.9819	−	7.51351i	−2.36344	−	0.250173i
$903$			2.84310i			0.0946123i
$904$	−1.07716	−	2.12568i	−0.0358258	−	0.0706990i
$905$		0			0
$906$	−0.560473	+	5.29492i	−0.0186205	+	0.175912i
$907$	3.82391	−	3.82391i	0.126971	−	0.126971i	−0.640766	−	0.767737i	$-0.721383\pi$
$907$	3.82391	−	3.82391i	0.126971	−	0.126971i	0.767737	+	0.640766i	$0.221383\pi$
$908$	−19.7473	+	12.7826i	−0.655337	+	0.424206i
$909$	−1.10819	−	1.10819i	−0.0367565	−	0.0367565i
$910$		0			0
$911$	−18.9169			−0.626743			−0.313372	−	0.949631i	$-0.601459\pi$
$911$	−18.9169			−0.626743			−0.313372	+	0.949631i	$0.601459\pi$
$912$	−1.35558	+	3.02064i	−0.0448878	+	0.100023i
$913$	−27.0908			−0.896574
$914$	−1.51748	−	1.87676i	−0.0501937	−	0.0620777i
$915$		0			0
$916$	15.3529	+	23.7180i	0.507274	+	0.783666i
$917$	12.4700	−	12.4700i	0.411795	−	0.411795i
$918$	0.279270	−	2.63832i	0.00921727	−	0.0870777i
$919$			48.9075i			1.61331i	0.591022	+	0.806655i	$0.298724\pi$
$919$			48.9075i			1.61331i	−0.591022	+	0.806655i	$0.701276\pi$
$920$		0			0
$921$			3.03293i			0.0999384i
$922$	9.44144	+	0.999388i	0.310937	+	0.0329131i
$923$	23.1369	−	23.1369i	0.761562	−	0.761562i
$924$	4.38099	+	0.937976i	0.144124	+	0.0308571i
$925$		0			0
$926$	−12.2905	+	9.93759i	−0.403890	+	0.326570i
$927$	30.6071			1.00527
$928$	−24.1906	−	14.0858i	−0.794095	−	0.462390i
$929$	35.4660			1.16360			0.581801	−	0.813331i	$-0.302348\pi$
$929$	35.4660			1.16360			0.581801	+	0.813331i	$0.302348\pi$
$930$		0			0
$931$	0.422660	+	0.422660i	0.0138521	+	0.0138521i
$932$	27.1869	+	5.82074i	0.890536	+	0.190665i
$933$	1.02825	−	1.02825i	0.0336635	−	0.0336635i
$934$	4.10649	+	0.434676i	0.134368	+	0.0142230i
$935$		0			0
$936$	−33.2153	−	10.8737i	−1.08568	−	0.355419i
$937$			56.4991i			1.84575i	0.385105	+	0.922873i	$0.374165\pi$
$937$			56.4991i			1.84575i	−0.385105	+	0.922873i	$0.625835\pi$
$938$	1.96476	−	18.5615i	0.0641516	−	0.606055i
$939$	−2.30207	+	2.30207i	−0.0751252	+	0.0751252i
$940$		0			0
$941$	−2.86034	−	2.86034i	−0.0932445	−	0.0932445i	0.658946	−	0.752190i	$-0.271003\pi$
$941$	−2.86034	−	2.86034i	−0.0932445	−	0.0932445i	−0.752190	+	0.658946i	$0.771003\pi$
$942$	−0.794319	−	0.982385i	−0.0258803	−	0.0320078i
$943$	7.21805			0.235052
$944$	−5.07336	+	1.93030i	−0.165124	+	0.0628259i
$945$		0			0
$946$	27.6035	+	34.1390i	0.897466	+	1.10995i
$947$	−5.86681	−	5.86681i	−0.190646	−	0.190646i	0.605329	−	0.795975i	$-0.293041\pi$
$947$	−5.86681	−	5.86681i	−0.190646	−	0.190646i	−0.795975	+	0.605329i	$0.793041\pi$
$948$	−1.90976	+	1.23620i	−0.0620260	+	0.0401500i
$949$	−46.0411	+	46.0411i	−1.49456	+	1.49456i
$950$		0			0
$951$			2.26040i			0.0732985i
$952$	−12.4645	+	6.31624i	−0.403978	+	0.204711i
$953$			25.0238i			0.810599i	0.914184	+	0.405299i	$0.132833\pi$
$953$			25.0238i			0.810599i	−0.914184	+	0.405299i	$0.867167\pi$
$954$	43.9597	+	4.65318i	1.42325	+	0.150652i
$955$		0			0
$956$	−4.50899	+	21.0601i	−0.145831	+	0.681132i
$957$	2.93706	+	2.93706i	0.0949416	+	0.0949416i
$958$	45.7713	−	37.0089i	1.47880	−	1.19570i
$959$	−27.4461			−0.886281
$960$		0			0
$961$	15.8228			0.510412
$962$	0.630657	−	0.509925i	0.0203332	−	0.0164406i
$963$	43.1030	+	43.1030i	1.38897	+	1.38897i
$964$	−5.22163	+	24.3886i	−0.168177	+	0.785504i
$965$		0			0
$966$	−0.450545	−	0.0476907i	−0.0144961	−	0.00153442i
$967$			16.6523i			0.535502i	0.963488	+	0.267751i	$0.0862804\pi$
$967$			16.6523i			0.535502i	−0.963488	+	0.267751i	$0.913720\pi$
$968$	33.9595	−	17.2085i	1.09150	−	0.553103i
$969$			1.53223i			0.0492224i
$970$		0			0
$971$	−30.6552	+	30.6552i	−0.983771	+	0.983771i	−0.999870	−	0.0160991i	$-0.994875\pi$
$971$	−30.6552	+	30.6552i	−0.983771	+	0.983771i	0.0160991	+	0.999870i	$0.494875\pi$
$972$	−7.59534	+	4.91654i	−0.243621	+	0.157698i
$973$	−13.3064	−	13.3064i	−0.426583	−	0.426583i
$974$	7.34132	+	9.07948i	0.235231	+	0.290925i
$975$		0			0
$976$	−13.0720	−	34.3569i	−0.418425	−	1.09974i
$977$	13.4307			0.429687			0.214844	−	0.976648i	$-0.431076\pi$
$977$	13.4307			0.429687			0.214844	+	0.976648i	$0.431076\pi$
$978$	0.451659	+	0.558596i	0.0144425	+	0.0178619i
$979$	−36.7392	−	36.7392i	−1.17419	−	1.17419i
$980$		0			0
$981$	2.36591	−	2.36591i	0.0755378	−	0.0755378i
$982$	−0.902130	+	8.52263i	−0.0287881	+	0.271968i
$983$			7.94549i			0.253422i	0.991940	+	0.126711i	$0.0404420\pi$
$983$			7.94549i			0.253422i	−0.991940	+	0.126711i	$0.959558\pi$
$984$	4.65575	+	1.52416i	0.148420	+	0.0485884i
$985$		0			0
$986$	−12.8828	−	1.36366i	−0.410271	−	0.0434276i
$987$	0.606704	−	0.606704i	0.0193116	−	0.0193116i
$988$	39.6662	+	8.49257i	1.26195	+	0.270185i
$989$	−3.13925	−	3.13925i	−0.0998225	−	0.0998225i
$990$		0			0
$991$	−25.0787			−0.796652			−0.398326	−	0.917244i	$-0.630409\pi$
$991$	−25.0787			−0.796652			−0.398326	+	0.917244i	$0.630409\pi$
$992$	37.4260	−	9.88027i	1.18828	−	0.313699i
$993$	3.08612			0.0979350
$994$	−23.0912	+	18.6707i	−0.732409	+	0.592198i
$995$		0			0
$996$	1.81810	+	0.389258i	0.0576088	+	0.0123341i
$997$	−36.1819	+	36.1819i	−1.14589	+	1.14589i	−0.158539	+	0.987353i	$0.550678\pi$
$997$	−36.1819	+	36.1819i	−1.14589	+	1.14589i	−0.987353	+	0.158539i	$0.949322\pi$
$998$	30.0893	+	3.18498i	0.952459	+	0.100819i
$999$		−	0.139745i		−	0.00442134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.h.301.2		16
4.3	odd	2		1600.2.l.i.401.4		16
5.2	odd	4		400.2.q.g.349.3		16
5.3	odd	4		400.2.q.h.349.6		16
5.4	even	2		80.2.l.a.61.7	yes	16
15.14	odd	2		720.2.t.c.541.2		16
16.5	even	4	inner	400.2.l.h.101.2		16
16.11	odd	4		1600.2.l.i.1201.4		16
20.3	even	4		1600.2.q.g.849.5		16
20.7	even	4		1600.2.q.h.849.4		16
20.19	odd	2		320.2.l.a.81.5		16
40.19	odd	2		640.2.l.a.161.4		16
40.29	even	2		640.2.l.b.161.5		16
60.59	even	2		2880.2.t.c.721.6		16
80.19	odd	4		640.2.l.a.481.4		16
80.27	even	4		1600.2.q.g.49.5		16
80.29	even	4		640.2.l.b.481.5		16
80.37	odd	4		400.2.q.h.149.6		16
80.43	even	4		1600.2.q.h.49.4		16
80.53	odd	4		400.2.q.g.149.3		16
80.59	odd	4		320.2.l.a.241.5		16
80.69	even	4		80.2.l.a.21.7	✓	16
160.59	odd	8		5120.2.a.u.1.4		8
160.69	even	8		5120.2.a.s.1.5		8
160.139	odd	8		5120.2.a.t.1.5		8
160.149	even	8		5120.2.a.v.1.4		8
240.59	even	4		2880.2.t.c.2161.7		16
240.149	odd	4		720.2.t.c.181.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.7	✓	16	80.69	even	4
80.2.l.a.61.7	yes	16	5.4	even	2
320.2.l.a.81.5		16	20.19	odd	2
320.2.l.a.241.5		16	80.59	odd	4
400.2.l.h.101.2		16	16.5	even	4	inner
400.2.l.h.301.2		16	1.1	even	1	trivial
400.2.q.g.149.3		16	80.53	odd	4
400.2.q.g.349.3		16	5.2	odd	4
400.2.q.h.149.6		16	80.37	odd	4
400.2.q.h.349.6		16	5.3	odd	4
640.2.l.a.161.4		16	40.19	odd	2
640.2.l.a.481.4		16	80.19	odd	4
640.2.l.b.161.5		16	40.29	even	2
640.2.l.b.481.5		16	80.29	even	4
720.2.t.c.181.2		16	240.149	odd	4
720.2.t.c.541.2		16	15.14	odd	2
1600.2.l.i.401.4		16	4.3	odd	2
1600.2.l.i.1201.4		16	16.11	odd	4
1600.2.q.g.49.5		16	80.27	even	4
1600.2.q.g.849.5		16	20.3	even	4
1600.2.q.h.49.4		16	80.43	even	4
1600.2.q.h.849.4		16	20.7	even	4
2880.2.t.c.721.6		16	60.59	even	2
2880.2.t.c.2161.7		16	240.59	even	4
5120.2.a.s.1.5		8	160.69	even	8
5120.2.a.t.1.5		8	160.139	odd	8
5120.2.a.u.1.4		8	160.59	odd	8
5120.2.a.v.1.4		8	160.149	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09971 + 0.889181i) q^{2} +(0.120009 + 0.120009i) q^{3} +(0.418713 - 1.95568i) q^{4} +(-0.238684 - 0.0252650i) q^{6} -2.66881i q^{7} +(1.27849 + 2.52299i) q^{8} -2.97120i q^{9} +(-3.49714 + 3.49714i) q^{11} +(0.284948 - 0.184450i) q^{12} +(-2.94072 - 2.94072i) q^{13} +(2.37306 + 2.93491i) q^{14} +(-3.64936 - 1.63774i) q^{16} -1.85116 q^{17} +(2.64193 + 3.26745i) q^{18} +(-3.44856 - 3.44856i) q^{19} +(0.320281 - 0.320281i) q^{21} +(0.736240 - 6.95543i) q^{22} +0.707288i q^{23} +(-0.149351 + 0.456211i) q^{24} +(5.84877 + 0.619099i) q^{26} +(0.716597 - 0.716597i) q^{27} +(-5.21934 - 1.11747i) q^{28} +(-3.49909 - 3.49909i) q^{29} +6.84272 q^{31} +(5.46947 - 1.44391i) q^{32} -0.839377 q^{33} +(2.03573 - 1.64601i) q^{34} +(-5.81070 - 1.24408i) q^{36} +(0.0975060 - 0.0975060i) q^{37} +(6.85881 + 0.726013i) q^{38} -0.705826i q^{39} -10.2052i q^{41} +(-0.0674276 + 0.637004i) q^{42} +(-4.43844 + 4.43844i) q^{43} +(5.37499 + 8.30359i) q^{44} +(-0.628908 - 0.777810i) q^{46} +1.89428 q^{47} +(-0.241413 - 0.634498i) q^{48} -0.122561 q^{49} +(-0.222155 - 0.222155i) q^{51} +(-6.98243 + 4.51979i) q^{52} +(7.43897 - 7.43897i) q^{53} +(-0.150862 + 1.42523i) q^{54} +(6.73338 - 3.41205i) q^{56} -0.827717i q^{57} +(6.95931 + 0.736651i) q^{58} +(0.959574 - 0.959574i) q^{59} +(6.49825 + 6.49825i) q^{61} +(-7.52499 + 6.08442i) q^{62} -7.92956 q^{63} +(-4.73092 + 6.45123i) q^{64} +(0.923069 - 0.746358i) q^{66} +(-3.49691 - 3.49691i) q^{67} +(-0.775103 + 3.62027i) q^{68} +(-0.0848809 + 0.0848809i) q^{69} +7.86777i q^{71} +(7.49629 - 3.79865i) q^{72} -15.6564i q^{73} +(-0.0205276 + 0.193929i) q^{74} +(-8.18824 + 5.30033i) q^{76} +(9.33322 + 9.33322i) q^{77} +(0.627607 + 0.776202i) q^{78} -6.70212 q^{79} -8.74159 q^{81} +(9.07431 + 11.2228i) q^{82} +(3.87327 + 3.87327i) q^{83} +(-0.492261 - 0.760473i) q^{84} +(0.934407 - 8.82755i) q^{86} -0.839845i q^{87} +(-13.2943 - 4.35218i) q^{88} +10.5055i q^{89} +(-7.84824 + 7.84824i) q^{91} +(1.38323 + 0.296151i) q^{92} +(0.821187 + 0.821187i) q^{93} +(-2.08316 + 1.68436i) q^{94} +(0.829667 + 0.483103i) q^{96} -4.79937 q^{97} +(0.134781 - 0.108979i) q^{98} +(10.3907 + 10.3907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Introduction

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