LMFDB - Embedded newform 400.2.q.g.149.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(149,400)] 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, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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			149.3
Root			$-0.296075 + 1.38287i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.g.349.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$	−0.889181	+	1.09971i	−0.628746	+	0.777611i
$2$	−0.889181	+	1.09971i	−0.628746	+	0.777611i
$3$	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
$7$	2.66881			1.00872			0.504358	−	0.863495i	$-0.331729\pi$
$7$	2.66881			1.00872			0.504358	+	0.863495i	$0.331729\pi$
$8$	2.52299	+	1.27849i	0.892010	+	0.452015i
$9$		−	2.97120i		−	0.990399i
$10$		0			0
$11$	−3.49714	−	3.49714i	−1.05443	−	1.05443i	−0.998431	−	0.0559977i	$-0.982166\pi$
$11$	−3.49714	−	3.49714i	−1.05443	−	1.05443i	−0.0559977	−	0.998431i	$-0.517834\pi$
$12$	0.184450	−	0.284948i	0.0532460	−	0.0822574i
$13$	−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
$17$			1.85116i			0.448971i	0.974477	+	0.224486i	$0.0720702\pi$
$17$			1.85116i			0.448971i	−0.974477	+	0.224486i	$0.927930\pi$
$18$	3.26745	+	2.64193i	0.770144	+	0.622709i
$19$	3.44856	−	3.44856i	0.791155	−	0.791155i	−0.190527	−	0.981682i	$-0.561020\pi$
$19$	3.44856	−	3.44856i	0.791155	−	0.791155i	0.981682	+	0.190527i	$0.0610197\pi$
$20$		0			0
$21$	0.320281	+	0.320281i	0.0698911	+	0.0698911i
$22$	6.95543	−	0.736240i	1.48290	−	0.156967i
$23$	0.707288			0.147480			0.0737399	−	0.997278i	$-0.476507\pi$
$23$	0.707288			0.147480			0.0737399	+	0.997278i	$0.476507\pi$
$24$	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
$28$	−1.11747	−	5.21934i	−0.211181	−	0.986363i
$29$	3.49909	−	3.49909i	0.649766	−	0.649766i	−0.303171	−	0.952936i	$-0.598045\pi$
$29$	3.49909	−	3.49909i	0.649766	−	0.649766i	0.952936	+	0.303171i	$0.0980452\pi$
$30$		0			0
$31$	6.84272			1.22899			0.614494	−	0.788921i	$-0.289360\pi$
$31$	6.84272			1.22899			0.614494	+	0.788921i	$0.289360\pi$
$32$	1.44391	−	5.46947i	0.255250	−	0.966875i
$33$		−	0.839377i		−	0.146117i
$34$	−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	$0.246392\pi$
$38$	0.726013	+	6.85881i	0.117775	+	1.11265i
$39$		−	0.705826i		−	0.113023i
$40$		0			0
$41$			10.2052i			1.59379i	0.604117	+	0.796896i	$0.293526\pi$
$41$			10.2052i			1.59379i	−0.604117	+	0.796896i	$0.706474\pi$
$42$	−0.637004	+	0.0674276i	−0.0982918	+	0.0104043i
$43$	4.43844	−	4.43844i	0.676855	−	0.676855i	−0.282432	−	0.959287i	$-0.591141\pi$
$43$	4.43844	−	4.43844i	0.676855	−	0.676855i	0.959287	+	0.282432i	$0.0911412\pi$
$44$	−5.37499	+	8.30359i	−0.810310	+	1.25181i
$45$		0			0
$46$	−0.628908	+	0.777810i	−0.0927274	+	0.114682i
$47$		−	1.89428i		−	0.276310i	−0.990411	−	0.138155i	$-0.955883\pi$
$47$		−	1.89428i		−	0.276310i	0.990411	−	0.138155i	$-0.0441172\pi$
$48$	−0.634498	−	0.241413i	−0.0915820	−	0.0348449i
$49$	0.122561			0.0175087
$50$		0			0
$51$	−0.222155	+	0.222155i	−0.0311079	+	0.0311079i
$52$	−4.51979	+	6.98243i	−0.626782	+	0.968289i
$53$	−7.43897	+	7.43897i	−1.02182	+	1.02182i	−0.0220650	+	0.999757i	$0.507024\pi$
$53$	−7.43897	+	7.43897i	−1.02182	+	1.02182i	−0.999757	+	0.0220650i	$0.992976\pi$
$54$	0.150862	+	1.42523i	0.0205298	+	0.193949i
$55$		0			0
$56$	6.73338	+	3.41205i	0.899786	+	0.455955i
$57$	0.827717			0.109634
$58$	0.736651	+	6.95931i	0.0967270	+	0.913802i
$59$	−0.959574	−	0.959574i	−0.124926	−	0.124926i	0.641880	−	0.766805i	$-0.278155\pi$
$59$	−0.959574	−	0.959574i	−0.124926	−	0.124926i	−0.766805	+	0.641880i	$0.778155\pi$
$60$		0			0
$61$	6.49825	−	6.49825i	0.832015	−	0.832015i	−0.155777	−	0.987792i	$-0.549788\pi$
$61$	6.49825	−	6.49825i	0.832015	−	0.832015i	0.987792	+	0.155777i	$0.0497881\pi$
$62$	−6.08442	+	7.52499i	−0.772722	+	0.955674i
$63$		−	7.92956i		−	0.999031i
$64$	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	0.887679	−	0.460463i	$-0.152317\pi$
$67$	3.49691	+	3.49691i	0.427216	+	0.427216i	−0.460463	+	0.887679i	$0.652317\pi$
$68$	3.62027	−	0.775103i	0.439022	−	0.0939951i
$69$	0.0848809	+	0.0848809i	0.0102185	+	0.0102185i
$70$		0			0
$71$		−	7.86777i		−	0.933733i	−0.884328	−	0.466866i	$-0.845383\pi$
$71$		−	7.86777i		−	0.933733i	0.884328	−	0.466866i	$-0.154617\pi$
$72$	3.79865	−	7.49629i	0.447675	−	0.883446i
$73$	−15.6564			−1.83244			−0.916220	−	0.400675i	$-0.868776\pi$
$73$	−15.6564			−1.83244			−0.916220	+	0.400675i	$0.868776\pi$
$74$	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
$78$	0.776202	+	0.627607i	0.0878876	+	0.0710625i
$79$	6.70212			0.754047			0.377024	−	0.926204i	$-0.376948\pi$
$79$	6.70212			0.754047			0.377024	+	0.926204i	$0.376948\pi$
$80$		0			0
$81$	−8.74159			−0.971288
$82$	−11.2228	−	9.07431i	−1.23935	−	1.00209i
$83$	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
$87$	0.839845			0.0900408
$88$	−4.35218	−	13.2943i	−0.463944	−	1.41718i
$89$			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
$92$	−0.296151	−	1.38323i	−0.0308759	−	0.144212i
$93$	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
$97$			4.79937i			0.487303i	0.969863	+	0.243651i	$0.0783453\pi$
$97$			4.79937i			0.487303i	−0.969863	+	0.243651i	$0.921655\pi$
$98$	−0.108979	+	0.134781i	−0.0110085	+	0.0136150i
$99$	−10.3907	+	10.3907i	−1.04430	+	1.04430i
$100$		0			0
$101$	0.372979	+	0.372979i	0.0371128	+	0.0371128i	0.725420	−	0.688307i	$-0.241646\pi$
$101$	0.372979	+	0.372979i	0.0371128	+	0.0371128i	−0.688307	+	0.725420i	$0.741646\pi$
$102$	−0.0467695	−	0.441842i	−0.00463087	−	0.0437489i
$103$	10.3013			1.01502			0.507508	−	0.861647i	$-0.330567\pi$
$103$	10.3013			1.01502			0.507508	+	0.861647i	$0.330567\pi$
$104$	−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	$0.791103\pi$
$108$	−1.70148	−	1.10138i	−0.163725	−	0.105981i
$109$	−0.796284	+	0.796284i	−0.0762701	+	0.0762701i	−0.744213	−	0.667943i	$-0.767175\pi$
$109$	−0.796284	+	0.796284i	−0.0762701	+	0.0762701i	0.667943	+	0.744213i	$0.267175\pi$
$110$		0			0
$111$	0.0234032			0.00222133
$112$	−9.73945	+	4.37081i	−0.920292	+	0.413003i
$113$		−	0.842524i		−	0.0792580i	−0.999214	−	0.0396290i	$-0.987382\pi$
$113$		−	0.842524i		−	0.0792580i	0.999214	−	0.0396290i	$-0.0126176\pi$
$114$	−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
$118$	1.90849	−	0.202015i	0.175690	−	0.0185970i
$119$			4.94039i			0.452885i
$120$		0			0
$121$			13.4600i			1.22364i
$122$	1.36805	+	12.9243i	0.123858	+	1.17011i
$123$	−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
$127$		−	21.1693i		−	1.87847i	−0.343277	−	0.939234i	$-0.611537\pi$
$127$		−	21.1693i		−	1.87847i	0.343277	−	0.939234i	$-0.388463\pi$
$128$	−11.3011	−	0.533685i	−0.998887	−	0.0471715i
$129$	1.06530			0.0937947
$130$		0			0
$131$	4.67248	−	4.67248i	0.408237	−	0.408237i	−0.472887	−	0.881123i	$-0.656788\pi$
$131$	4.67248	−	4.67248i	0.408237	−	0.408237i	0.881123	+	0.472887i	$0.156788\pi$
$132$	−1.64155	+	0.351458i	−0.142879	+	0.0305905i
$133$	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
$137$	10.2840			0.878623			0.439312	−	0.898335i	$-0.355222\pi$
$137$	10.2840			0.878623			0.439312	+	0.898335i	$0.355222\pi$
$138$	−0.168819	+	0.0178696i	−0.0143708	+	0.00152117i
$139$	−4.98588	−	4.98588i	−0.422897	−	0.422897i	0.463303	−	0.886200i	$-0.346664\pi$
$139$	−4.98588	−	4.98588i	−0.422897	−	0.422897i	−0.886200	+	0.463303i	$0.846664\pi$
$140$		0			0
$141$	0.227331	−	0.227331i	0.0191447	−	0.0191447i
$142$	8.65225	+	6.99588i	0.726080	+	0.587081i
$143$			20.5683i			1.72001i
$144$	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
$148$	−0.231518	−	0.149863i	−0.0190306	−	0.0123187i
$149$	−8.79493	−	8.79493i	−0.720509	−	0.720509i	0.248200	−	0.968709i	$-0.420161\pi$
$149$	−8.79493	−	8.79493i	−0.720509	−	0.720509i	−0.968709	+	0.248200i	$0.920161\pi$
$150$		0			0
$151$			22.1838i			1.80529i	0.430385	+	0.902645i	$0.358378\pi$
$151$			22.1838i			1.80529i	−0.430385	+	0.902645i	$0.641622\pi$
$152$	13.1096	−	4.29172i	1.06333	−	0.348105i
$153$	5.50015			0.444661
$154$	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	0.542815	−	0.839852i	$-0.317359\pi$
$157$	−3.72187	−	3.72187i	−0.297038	−	0.297038i	−0.839852	+	0.542815i	$0.817359\pi$
$158$	−5.95940	+	7.37037i	−0.474104	+	0.586355i
$159$	−1.78549			−0.141598
$160$		0			0
$161$	1.88762			0.148765
$162$	7.77286	−	9.61319i	0.610694	−	0.755284i
$163$	−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
$167$	18.1604			1.40530			0.702648	−	0.711538i	$-0.252001\pi$
$167$	18.1604			1.40530			0.702648	+	0.711538i	$0.252001\pi$
$168$	0.398589	+	1.21754i	0.0307518	+	0.0939354i
$169$			4.29572i			0.330440i
$170$		0			0
$171$	−10.2464	−	10.2464i	−0.783559	−	0.783559i
$172$	−10.5386	−	6.82172i	−0.803560	−	0.520151i
$173$	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
$177$		−	0.230315i		−	0.0173115i
$178$	−11.5530	−	9.34128i	−0.865931	−	0.700159i
$179$	2.42499	−	2.42499i	0.181252	−	0.181252i	−0.610649	−	0.791901i	$-0.709091\pi$
$179$	2.42499	−	2.42499i	0.181252	−	0.181252i	0.791901	+	0.610649i	$0.209091\pi$
$180$		0			0
$181$	4.46593	+	4.46593i	0.331950	+	0.331950i	0.853327	−	0.521377i	$-0.174581\pi$
$181$	4.46593	+	4.46593i	0.331950	+	0.331950i	−0.521377	+	0.853327i	$0.674581\pi$
$182$	15.6093	−	1.65226i	1.15704	−	0.122474i
$183$	1.55970			0.115296
$184$	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
$188$	−3.70461	+	0.793162i	−0.270187	+	0.0578473i
$189$	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	$0.409534\pi$
$192$	−0.206453	+	1.34196i	−0.0148994	+	0.0968475i
$193$			11.3388i			0.816181i	0.912941	+	0.408091i	$0.133805\pi$
$193$			11.3388i			0.816181i	−0.912941	+	0.408091i	$0.866195\pi$
$194$	−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	$0.267649\pi$
$198$	−2.18751	−	20.6659i	−0.155460	−	1.46866i
$199$			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
$202$	−0.741814	+	0.0785219i	−0.0521939	+	0.00552478i
$203$	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
$207$		−	2.10149i		−	0.146064i
$208$	15.5479	+	5.91563i	1.07805	+	0.410175i
$209$	−24.1203			−1.66843
$210$		0			0
$211$	−12.4716	+	12.4716i	−0.858577	+	0.858577i	−0.991171	−	0.132593i	$-0.957670\pi$
$211$	−12.4716	+	12.4716i	−0.858577	+	0.858577i	0.132593	+	0.991171i	$0.457670\pi$
$212$	17.6630	+	11.4334i	1.21310	+	0.785252i
$213$	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
$217$	18.2619			1.23970
$218$	−0.167639	−	1.58372i	−0.0113539	−	0.107263i
$219$	−1.87890	−	1.87890i	−0.126965	−	0.126965i
$220$		0			0
$221$	5.44374	−	5.44374i	0.366186	−	0.366186i
$222$	−0.0208097	+	0.0257367i	−0.00139665	+	0.00172733i
$223$		−	3.08673i		−	0.206703i	−0.994645	−	0.103351i	$-0.967043\pi$
$223$		−	3.08673i		−	0.206703i	0.994645	−	0.103351i	$-0.0329566\pi$
$224$	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	0.927019	−	0.375015i	$-0.122362\pi$
$227$	8.31678	+	8.31678i	0.552004	+	0.552004i	−0.375015	+	0.927019i	$0.622362\pi$
$228$	−0.346576	−	1.61875i	−0.0229525	−	0.107204i
$229$	9.98910	+	9.98910i	0.660098	+	0.660098i	0.955403	−	0.295305i	$-0.0954212\pi$
$229$	9.98910	+	9.98910i	0.660098	+	0.660098i	−0.295305	+	0.955403i	$0.595421\pi$
$230$		0			0
$231$		−	2.24014i		−	0.147390i
$232$	13.3017	−	4.35461i	0.873301	−	0.285894i
$233$	13.9015			0.910718			0.455359	−	0.890308i	$-0.349511\pi$
$233$	13.9015			0.910718			0.455359	+	0.890308i	$0.349511\pi$
$234$	−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
$238$	−5.43298	−	4.39290i	−0.352168	−	0.284750i
$239$	10.7687			0.696569			0.348284	−	0.937389i	$-0.386764\pi$
$239$	10.7687			0.696569			0.348284	+	0.937389i	$0.386764\pi$
$240$		0			0
$241$	−12.4707			−0.803305			−0.401653	−	0.915792i	$-0.631564\pi$
$241$	−12.4707			−0.803305			−0.401653	+	0.915792i	$0.631564\pi$
$242$	−14.8021	−	11.9684i	−0.951515	−	0.769358i
$243$	−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
$247$	−20.2826			−1.29055
$248$	17.2641	+	8.74835i	1.09627	+	0.555521i
$249$			0.929654i			0.0589144i
$250$		0			0
$251$	3.69093	+	3.69093i	0.232969	+	0.232969i	0.813931	−	0.580962i	$-0.197323\pi$
$251$	3.69093	+	3.69093i	0.232969	+	0.232969i	−0.580962	+	0.813931i	$0.697323\pi$
$252$	−15.5077	+	3.32021i	−0.976892	+	0.209154i
$253$	−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
$257$			3.11011i			0.194003i	0.995284	+	0.0970016i	$0.0309252\pi$
$257$			3.11011i			0.194003i	−0.995284	+	0.0970016i	$0.969075\pi$
$258$	−0.947248	+	1.17152i	−0.0589731	+	0.0729358i
$259$	0.260225	−	0.260225i	0.0161696	−	0.0161696i
$260$		0			0
$261$	−10.3965	−	10.3965i	−0.643527	−	0.643527i
$262$	0.983680	+	9.29305i	0.0607719	+	0.574126i
$263$	−17.9512			−1.10692			−0.553458	−	0.832877i	$-0.686692\pi$
$263$	−17.9512			−1.10692			−0.553458	+	0.832877i	$0.686692\pi$
$264$	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
$268$	5.37463	−	8.30304i	0.328308	−	0.507189i
$269$	−1.62436	+	1.62436i	−0.0990392	+	0.0990392i	−0.754890	−	0.655851i	$-0.772310\pi$
$269$	−1.62436	+	1.62436i	−0.0990392	+	0.0990392i	0.655851	+	0.754890i	$0.272310\pi$
$270$		0			0
$271$	18.1808			1.10440			0.552201	−	0.833711i	$-0.313788\pi$
$271$	18.1808			1.10440			0.552201	+	0.833711i	$0.313788\pi$
$272$	−3.03171	−	6.75553i	−0.183824	−	0.409614i
$273$		−	1.88372i		−	0.114008i
$274$	−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	$0.0494531\pi$
$278$	9.91636	−	1.04966i	0.594744	−	0.0629543i
$279$		−	20.3310i		−	1.21719i
$280$		0			0
$281$		−	10.7377i		−	0.640556i	−0.947324	−	0.320278i	$-0.896224\pi$
$281$		−	10.7377i		−	0.640556i	0.947324	−	0.320278i	$-0.103776\pi$
$282$	0.0478591	+	0.452136i	0.00284997	+	0.0269243i
$283$	−16.3679	+	16.3679i	−0.972971	+	0.972971i	−0.999644	−	0.0266735i	$-0.991509\pi$
$283$	−16.3679	+	16.3679i	−0.972971	+	0.972971i	0.0266735	+	0.999644i	$0.491509\pi$
$284$	−15.3868	+	3.29434i	−0.913041	+	0.195483i
$285$		0			0
$286$	−22.6191	−	18.2889i	−1.33749	−	1.08145i
$287$			27.2359i			1.60768i
$288$	−16.2509	−	4.29014i	−0.957592	−	0.252799i
$289$	13.5732			0.798425
$290$		0			0
$291$	−0.575968	+	0.575968i	−0.0337638	+	0.0337638i
$292$	6.55553	+	30.6188i	0.383633	+	1.79183i
$293$	−4.22052	+	4.22052i	−0.246566	+	0.246566i	−0.819560	−	0.572994i	$-0.805782\pi$
$293$	−4.22052	+	4.22052i	−0.246566	+	0.246566i	0.572994	+	0.819560i	$0.305782\pi$
$294$	−0.0292534	+	0.00309651i	−0.00170609	+	0.000180592i
$295$		0			0
$296$	0.370667	−	0.121346i	0.0215446	−	0.00705308i
$297$	−5.01208			−0.290831
$298$	17.4921	−	1.85156i	1.01329	−	0.107258i
$299$	−2.07994	−	2.07994i	−0.120286	−	0.120286i
$300$		0			0
$301$	11.8454	−	11.8454i	0.682755	−	0.682755i
$302$	−24.3957	−	19.7254i	−1.40381	−	1.13507i
$303$			0.0895217i			0.00514289i
$304$	−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	0.247658	−	0.968848i	$-0.420339\pi$
$307$	−12.6363	−	12.6363i	−0.721190	−	0.721190i	−0.968848	+	0.247658i	$0.920339\pi$
$308$	−14.3448	+	22.1607i	−0.817373	+	1.26272i
$309$	1.23625	+	1.23625i	0.0703276	+	0.0703276i
$310$		0			0
$311$			8.56815i			0.485855i	0.970044	+	0.242928i	$0.0781078\pi$
$311$			8.56815i			0.485855i	−0.970044	+	0.242928i	$0.921892\pi$
$312$	0.902392	−	1.78079i	0.0510879	−	0.100817i
$313$	19.1825			1.08426			0.542129	−	0.840295i	$-0.317618\pi$
$313$	19.1825			1.08426			0.542129	+	0.840295i	$0.317618\pi$
$314$	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	0.391311	−	0.920258i	$-0.372022\pi$
$317$	−9.41764	−	9.41764i	−0.528947	−	0.528947i	−0.920258	+	0.391311i	$0.872022\pi$
$318$	1.58762	−	1.96351i	0.0890293	−	0.110108i
$319$	−24.4737			−1.37026
$320$		0			0
$321$	−3.48193			−0.194342
$322$	−1.67844	+	2.07583i	−0.0935356	+	0.115681i
$323$	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
$327$	−0.191122			−0.0105691
$328$	−13.0473	+	25.7477i	−0.720417	+	1.42168i
$329$		−	5.05549i		−	0.278718i
$330$		0			0
$331$	12.8579	+	12.8579i	0.706733	+	0.706733i	0.965847	−	0.259114i	$-0.0834305\pi$
$331$	12.8579	+	12.8579i	0.706733	+	0.706733i	−0.259114	+	0.965847i	$0.583431\pi$
$332$	5.95308	−	9.19666i	0.326718	−	0.504732i
$333$	−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
$337$			3.31961i			0.180831i	0.995904	+	0.0904153i	$0.0288194\pi$
$337$			3.31961i			0.180831i	−0.995904	+	0.0904153i	$0.971181\pi$
$338$	−4.72403	−	3.81967i	−0.256954	−	0.207763i
$339$	0.101110	−	0.101110i	0.00549156	−	0.00549156i
$340$		0			0
$341$	−23.9300	−	23.9300i	−1.29588	−	1.29588i
$342$	20.3789	−	2.15713i	1.10196	−	0.116644i
$343$	−18.3546			−0.991055
$344$	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	$0.487562\pi$
$348$	−0.351654	−	1.64247i	−0.0188506	−	0.0880455i
$349$	3.68796	−	3.68796i	0.197412	−	0.197412i	−0.601478	−	0.798890i	$-0.705421\pi$
$349$	3.68796	−	3.68796i	0.197412	−	0.197412i	0.798890	+	0.601478i	$0.205421\pi$
$350$		0			0
$351$	−4.21463			−0.224960
$352$	−24.1771	+	14.0780i	−1.28864	+	0.750358i
$353$		−	33.0951i		−	1.76148i	−0.473604	−	0.880738i	$-0.657047\pi$
$353$		−	33.0951i		−	1.76148i	0.473604	−	0.880738i	$-0.342953\pi$
$354$	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
$358$	0.510524	+	4.82303i	0.0269820	+	0.254905i
$359$		−	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
$362$	−8.88224	+	0.940195i	−0.466840	+	0.0494156i
$363$	−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
$367$		−	11.0338i		−	0.575959i	−0.957636	−	0.287980i	$-0.907016\pi$
$367$		−	11.0338i		−	0.575959i	0.957636	−	0.287980i	$-0.0929836\pi$
$368$	−2.58115	+	1.15835i	−0.134552	+	0.0603833i
$369$	30.3218			1.57849
$370$		0			0
$371$	−19.8532	+	19.8532i	−1.03073	+	1.03073i
$372$	1.26214	−	1.94982i	0.0654387	−	0.101093i
$373$	6.84468	−	6.84468i	0.354404	−	0.354404i	−0.507341	−	0.861745i	$-0.669372\pi$
$373$	6.84468	−	6.84468i	0.354404	−	0.354404i	0.861745	+	0.507341i	$0.169372\pi$
$374$	1.36290	+	12.8756i	0.0704737	+	0.665781i
$375$		0			0
$376$	2.42183	−	4.77925i	0.124896	−	0.246471i
$377$	−20.5797			−1.05991
$378$	0.402623	+	3.80367i	0.0207087	+	0.195640i
$379$	10.1072	+	10.1072i	0.519171	+	0.519171i	0.917321	−	0.398150i	$-0.130347\pi$
$379$	10.1072	+	10.1072i	0.519171	+	0.519171i	−0.398150	+	0.917321i	$0.630347\pi$
$380$		0			0
$381$	2.54050	−	2.54050i	0.130154	−	0.130154i
$382$	−6.89143	+	8.52307i	−0.352596	+	0.436078i
$383$		−	29.5283i		−	1.50883i	−0.656400	−	0.754413i	$-0.727922\pi$
$383$		−	29.5283i		−	1.50883i	0.656400	−	0.754413i	$-0.272078\pi$
$384$	−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
$388$	9.38604	−	2.00956i	0.476504	−	0.102020i
$389$	−0.990949	−	0.990949i	−0.0502431	−	0.0502431i	0.681539	−	0.731782i	$-0.261311\pi$
$389$	−0.990949	−	0.990949i	−0.0502431	−	0.0502431i	−0.731782	+	0.681539i	$0.761311\pi$
$390$		0			0
$391$			1.30930i			0.0662142i
$392$	0.309220	+	0.156693i	0.0156180	+	0.00791420i
$393$	1.12148			0.0565711
$394$	−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	0.990541	−	0.137216i	$-0.0438153\pi$
$397$	17.0024	+	17.0024i	0.853326	+	0.853326i	−0.137216	+	0.990541i	$0.543815\pi$
$398$	−15.6952	−	12.6905i	−0.786730	−	0.636119i
$399$	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	$0.266876\pi$
$402$	−0.923008	−	0.746309i	−0.0460354	−	0.0372225i
$403$	−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
$407$	−0.681985			−0.0338048
$408$	−0.844518	+	0.276471i	−0.0418099	+	0.0136874i
$409$		−	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
$412$	−4.31328	−	20.1460i	−0.212500	−	0.992523i
$413$	−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
$417$		−	1.19670i		−	0.0586026i
$418$	21.4473	−	26.5252i	1.04902	−	1.29739i
$419$	9.92468	−	9.92468i	0.484852	−	0.484852i	−0.421825	−	0.906677i	$-0.638610\pi$
$419$	9.92468	−	9.92468i	0.484852	−	0.484852i	0.906677	+	0.421825i	$0.138610\pi$
$420$		0			0
$421$	15.7930	+	15.7930i	0.769702	+	0.769702i	0.978054	−	0.208352i	$-0.0668100\pi$
$421$	15.7930	+	15.7930i	0.769702	+	0.769702i	−0.208352	+	0.978054i	$0.566810\pi$
$422$	−2.62559	−	24.8045i	−0.127812	−	1.20747i
$423$	−5.62829			−0.273657
$424$	−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
$428$	34.4452	+	22.2967i	1.66497	+	1.07775i
$429$	−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	$0.502187\pi$
$432$	−1.44152	+	3.78871i	−0.0693552	+	0.182285i
$433$			18.1101i			0.870318i	0.900354	+	0.435159i	$0.143308\pi$
$433$			18.1101i			0.870318i	−0.900354	+	0.435159i	$0.856692\pi$
$434$	−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
$438$	3.73693	−	0.395559i	0.178558	−	0.0189005i
$439$			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
$442$	1.14605	+	10.8270i	0.0545120	+	0.514988i
$443$	−22.6855	+	22.6855i	−1.07782	+	1.07782i	−0.0811145	+	0.996705i	$0.525848\pi$
$443$	−22.6855	+	22.6855i	−1.07782	+	1.07782i	−0.996705	+	0.0811145i	$0.974152\pi$
$444$	−0.00979922	−	0.0457691i	−0.000465050	−	0.00217211i
$445$		0			0
$446$	3.39450	+	2.74466i	0.160734	+	0.129963i
$447$		−	2.11094i		−	0.0998440i
$448$	12.6259	+	17.2171i	0.596520	+	0.813433i
$449$	−12.1999			−0.575747			−0.287873	−	0.957669i	$-0.592948\pi$
$449$	−12.1999			−0.575747			−0.287873	+	0.957669i	$0.592948\pi$
$450$		0			0
$451$	35.6892	−	35.6892i	1.68054	−	1.68054i
$452$	−1.64771	+	0.352776i	−0.0775016	+	0.0165932i
$453$	−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
$457$	−1.70660			−0.0798314			−0.0399157	−	0.999203i	$-0.512709\pi$
$457$	−1.70660			−0.0798314			−0.0399157	+	0.999203i	$0.512709\pi$
$458$	−19.8672	+	2.10297i	−0.928334	+	0.0982652i
$459$	1.32653	+	1.32653i	0.0619172	+	0.0619172i
$460$		0			0
$461$	−4.74710	+	4.74710i	−0.221094	+	0.221094i	−0.808959	−	0.587865i	$-0.799969\pi$
$461$	−4.74710	+	4.74710i	−0.221094	+	0.221094i	0.587865	+	0.808959i	$0.299969\pi$
$462$	2.46350	+	1.99189i	0.114612	+	0.0926711i
$463$			11.1761i			0.519398i	0.965690	+	0.259699i	$0.0836234\pi$
$463$			11.1761i			0.519398i	−0.965690	+	0.259699i	$0.916377\pi$
$464$	−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	0.753263	−	0.657719i	$-0.228479\pi$
$467$	2.06471	+	2.06471i	0.0955435	+	0.0955435i	−0.657719	+	0.753263i	$0.728479\pi$
$468$	20.7462	+	13.4292i	0.958992	+	0.620764i
$469$	9.33260	+	9.33260i	0.430940	+	0.430940i
$470$		0			0
$471$		−	0.893315i		−	0.0411618i
$472$	−1.19419	−	3.64780i	−0.0549668	−	0.167904i
$473$	−31.0437			−1.42739
$474$	−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
$478$	−9.57532	+	11.8424i	−0.437965	+	0.541659i
$479$	41.6214			1.90173			0.950864	−	0.309608i	$-0.100198\pi$
$479$	41.6214			1.90173			0.950864	+	0.309608i	$0.100198\pi$
$480$		0			0
$481$	−0.573477			−0.0261483
$482$	11.0887	−	13.7141i	0.505075	−	0.624659i
$483$	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
$487$	8.25627			0.374127			0.187064	−	0.982348i	$-0.440103\pi$
$487$	8.25627			0.374127			0.187064	+	0.982348i	$0.440103\pi$
$488$	24.7029	−	8.08704i	1.11825	−	0.366083i
$489$		−	0.507950i		−	0.0229703i
$490$		0			0
$491$	4.28512	+	4.28512i	0.193385	+	0.193385i	0.797157	−	0.603772i	$-0.206336\pi$
$491$	4.28512	+	4.28512i	0.193385	+	0.193385i	−0.603772	+	0.797157i	$0.706336\pi$
$492$	2.90797	+	1.88235i	0.131101	+	0.0848630i
$493$	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
$497$		−	20.9976i		−	0.941871i
$498$	−1.02235	−	0.826631i	−0.0458125	−	0.0370422i
$499$	15.1287	−	15.1287i	0.677253	−	0.677253i	−0.282125	−	0.959378i	$-0.591039\pi$
$499$	15.1287	−	15.1287i	0.677253	−	0.677253i	0.959378	+	0.282125i	$0.0910392\pi$
$500$		0			0
$501$	2.17941	+	2.17941i	0.0973689	+	0.0973689i
$502$	−7.34084	+	0.777037i	−0.327638	+	0.0346808i
$503$	−18.6439			−0.831291			−0.415646	−	0.909527i	$-0.636444\pi$
$503$	−18.6439			−0.831291			−0.415646	+	0.909527i	$0.636444\pi$
$504$	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
$508$	−41.4003	+	8.86385i	−1.83684	+	0.393270i
$509$	−11.6243	+	11.6243i	−0.515239	+	0.515239i	−0.916127	−	0.400888i	$-0.868702\pi$
$509$	−11.6243	+	11.6243i	−0.515239	+	0.515239i	0.400888	+	0.916127i	$0.368702\pi$
$510$		0			0
$511$	−41.7839			−1.84841
$512$	3.68821	+	22.3248i	0.162997	+	0.986627i
$513$		−	4.94246i		−	0.218215i
$514$	−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
$518$	0.0547842	+	0.517559i	0.00240708	+	0.0227402i
$519$			2.04865i			0.0899259i
$520$		0			0
$521$		−	36.9052i		−	1.61684i	−0.588603	−	0.808422i	$-0.700322\pi$
$521$		−	36.9052i		−	1.61684i	0.588603	−	0.808422i	$-0.299678\pi$
$522$	20.6775	−	2.18873i	0.905028	−	0.0957983i
$523$	6.04158	−	6.04158i	0.264180	−	0.264180i	−0.562570	−	0.826750i	$-0.690187\pi$
$523$	6.04158	−	6.04158i	0.264180	−	0.264180i	0.826750	+	0.562570i	$0.190187\pi$
$524$	−11.0943	−	7.18144i	−0.484657	−	0.313723i
$525$		0			0
$526$	15.9618	−	19.7410i	0.695969	−	0.860750i
$527$			12.6669i			0.551780i
$528$	1.37468	+	3.06319i	0.0598252	+	0.133308i
$529$	−22.4997			−0.978250
$530$		0			0
$531$	−2.85108	+	2.85108i	−0.123726	+	0.123726i
$532$	−21.8529	−	14.1456i	−0.947443	−	0.613288i
$533$	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
$537$	0.582041			0.0251169
$538$	−0.341971	−	3.23068i	−0.0147434	−	0.139284i
$539$	−0.428614	−	0.428614i	−0.0184617	−	0.0184617i
$540$		0			0
$541$	−28.4222	+	28.4222i	−1.22197	+	1.22197i	−0.255035	+	0.966932i	$0.582087\pi$
$541$	−28.4222	+	28.4222i	−1.22197	+	1.22197i	−0.966932	+	0.255035i	$0.917913\pi$
$542$	−16.1660	+	19.9935i	−0.694389	+	0.858795i
$543$			1.07190i			0.0459997i
$544$	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	0.999999	−	0.00135902i	$-0.000432589\pi$
$547$	23.3562	+	23.3562i	0.998640	+	0.998640i	−0.00135902	+	0.999999i	$0.500433\pi$
$548$	−4.30605	−	20.1122i	−0.183945	−	0.859152i
$549$	−19.3076	−	19.3076i	−0.824027	−	0.824027i
$550$		0			0
$551$		−	24.1337i		−	1.02813i
$552$	0.105634	+	0.322673i	0.00449608	+	0.0137339i
$553$	17.8867			0.760620
$554$	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	0.595752	−	0.803168i	$-0.296854\pi$
$557$	−4.89520	−	4.89520i	−0.207416	−	0.207416i	−0.803168	+	0.595752i	$0.796854\pi$
$558$	22.3582	+	18.0780i	0.946498	+	0.765302i
$559$	−26.1044			−1.10410
$560$		0			0
$561$	1.55382			0.0656022
$562$	11.8083	+	9.54774i	0.498103	+	0.402747i
$563$	−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
$567$	−23.3297			−0.979754
$568$	10.0589	−	19.8503i	0.422061	−	0.832899i
$569$		−	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	0.973758	+	0.227587i	$0.0730835\pi$
$571$	28.7069	+	28.7069i	1.20134	+	1.20134i	0.227587	+	0.973758i	$0.426917\pi$
$572$	40.2249	−	8.61221i	1.68189	−	0.360094i
$573$	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
$577$		−	20.3419i		−	0.846842i	−0.905933	−	0.423421i	$-0.860829\pi$
$577$		−	20.3419i		−	0.846842i	0.905933	−	0.423421i	$-0.139171\pi$
$578$	−12.0691	+	14.9266i	−0.502007	+	0.620864i
$579$	−1.36075	+	1.36075i	−0.0565509	+	0.0565509i
$580$		0			0
$581$	10.3370	+	10.3370i	0.428852	+	0.428852i
$582$	−0.121256	−	1.14554i	−0.00502623	−	0.0474840i
$583$	52.0303			2.15488
$584$	−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	$-0.0215775\pi$
$588$	0.0226063	−	0.0349236i	0.000932270	−	0.00144022i
$589$	23.5975	−	23.5975i	0.972320	−	0.972320i
$590$		0			0
$591$	−0.264022			−0.0108604
$592$	−0.196145	+	0.515524i	−0.00806152	+	0.0211879i
$593$		−	4.02945i		−	0.165470i	−0.996572	−	0.0827349i	$-0.973635\pi$
$593$		−	4.02945i		−	0.165470i	0.996572	−	0.0827349i	$-0.0263655\pi$
$594$	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
$598$	4.13677	−	0.437882i	0.169165	−	0.0179063i
$599$		−	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	$-0.870040\pi$
$601$		−	19.4667i		−	0.794065i	0.917805	−	0.397032i	$-0.129960\pi$
$602$	2.49376	+	23.5591i	0.101638	+	0.960197i
$603$	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
$607$			13.6128i			0.552528i	0.961082	+	0.276264i	$0.0890965\pi$
$607$			13.6128i			0.552528i	−0.961082	+	0.276264i	$0.910904\pi$
$608$	−13.8824	−	23.8412i	−0.563006	−	0.966890i
$609$	2.24139			0.0908257
$610$		0			0
$611$	−5.57057	+	5.57057i	−0.225361	+	0.225361i
$612$	−2.30298	−	10.7565i	−0.0930926	−	0.434807i
$613$	−11.1480	+	11.1480i	−0.450265	+	0.450265i	−0.895442	−	0.445177i	$-0.853141\pi$
$613$	−11.1480	+	11.1480i	−0.450265	+	0.450265i	0.445177	+	0.895442i	$0.353141\pi$
$614$	25.1321	−	2.66026i	1.01425	−	0.107360i
$615$		0			0
$616$	−11.6152	−	35.4800i	−0.467988	−	1.42953i
$617$	1.96695			0.0791863			0.0395932	−	0.999216i	$-0.487394\pi$
$617$	1.96695			0.0791863			0.0395932	+	0.999216i	$0.487394\pi$
$618$	−2.45876	+	0.260262i	−0.0989057	+	0.0104693i
$619$	−7.84144	−	7.84144i	−0.315174	−	0.315174i	0.531736	−	0.846910i	$-0.321540\pi$
$619$	−7.84144	−	7.84144i	−0.315174	−	0.315174i	−0.846910	+	0.531736i	$0.821540\pi$
$620$		0			0
$621$	0.506840	−	0.506840i	0.0203388	−	0.0203388i
$622$	−9.42246	−	7.61864i	−0.377806	−	0.305480i
$623$			28.0372i			1.12329i
$624$	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
$628$	−5.72039	+	8.83718i	−0.228268	+	0.352642i
$629$	0.180499	+	0.180499i	0.00719696	+	0.00719696i
$630$		0			0
$631$		−	0.220729i		−	0.00878708i	−0.999990	−	0.00439354i	$-0.998601\pi$
$631$		−	0.220729i		−	0.00878708i	0.999990	−	0.00439354i	$-0.00139851\pi$
$632$	16.9093	+	8.56860i	0.672618	+	0.340840i
$633$	−2.99339			−0.118977
$634$	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
$638$	21.7615	−	26.9139i	0.861547	−	1.06553i
$639$	−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	$0.623818\pi$
$642$	3.09606	−	3.82910i	0.122192	−	0.151122i
$643$	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
$647$	−26.4735			−1.04078			−0.520391	−	0.853928i	$-0.674214\pi$
$647$	−26.4735			−1.04078			−0.520391	+	0.853928i	$0.674214\pi$
$648$	−22.0549	−	11.1760i	−0.866399	−	0.439037i
$649$			6.71153i			0.263451i
$650$		0			0
$651$	2.19159	+	2.19159i	0.0858953	+	0.0858953i
$652$	−3.25268	+	5.02492i	−0.127385	+	0.196791i
$653$	−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
$657$			46.5182i			1.81485i
$658$	5.55956	+	4.49525i	0.216734	+	0.175243i
$659$	−24.1291	+	24.1291i	−0.939937	+	0.939937i	−0.998296	−	0.0583584i	$-0.981413\pi$
$659$	−24.1291	+	24.1291i	−0.939937	+	0.939937i	0.0583584	+	0.998296i	$0.481413\pi$
$660$		0			0
$661$	23.4294	+	23.4294i	0.911299	+	0.911299i	0.996374	−	0.0850756i	$-0.0271132\pi$
$661$	23.4294	+	23.4294i	0.911299	+	0.911299i	−0.0850756	+	0.996374i	$0.527113\pi$
$662$	−25.5729	+	2.70692i	−0.993919	+	0.105207i
$663$	1.30659			0.0507439
$664$	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
$668$	−7.60401	−	35.5159i	−0.294208	−	1.37415i
$669$	0.370435	−	0.370435i	0.0143218	−	0.0143218i
$670$		0			0
$671$	−45.4506			−1.75460
$672$	2.21423	−	1.28931i	0.0854157	−	0.0497363i
$673$			41.8069i			1.61154i	0.592230	+	0.805769i	$0.298248\pi$
$673$			41.8069i			1.61154i	−0.592230	+	0.805769i	$0.701752\pi$
$674$	−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	$0.0380027\pi$
$678$	0.0212864	+	0.201097i	0.000817499	+	0.00772310i
$679$			12.8086i			0.491550i
$680$		0			0
$681$			1.99617i			0.0764936i
$682$	47.5940	−	5.03788i	1.82247	−	0.192911i
$683$	34.4402	−	34.4402i	1.31782	−	1.31782i	0.402315	−	0.915501i	$-0.368206\pi$
$683$	34.4402	−	34.4402i	1.31782	−	1.31782i	0.915501	−	0.402315i	$-0.131794\pi$
$684$	−15.7483	+	24.3289i	−0.602151	+	0.930238i
$685$		0			0
$686$	16.3206	−	20.1847i	0.623122	−	0.770655i
$687$			2.39756i			0.0914727i
$688$	−8.92845	+	23.4664i	−0.340394	+	0.894649i
$689$	43.7519			1.66682
$690$		0			0
$691$	16.0991	−	16.0991i	0.612438	−	0.612438i	−0.331143	−	0.943581i	$-0.607434\pi$
$691$	16.0991	−	16.0991i	0.612438	−	0.612438i	0.943581	+	0.331143i	$0.107434\pi$
$692$	13.1186	−	20.2664i	0.498696	−	0.770414i
$693$	−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
$697$	−18.8915			−0.715567
$698$	0.776413	+	7.33495i	0.0293877	+	0.277632i
$699$	1.66830	+	1.66830i	0.0631010	+	0.0631010i
$700$		0			0
$701$	−30.0507	+	30.0507i	−1.13500	+	1.13500i	−0.145666	+	0.989334i	$0.546533\pi$
$701$	−30.0507	+	30.0507i	−1.13500	+	1.13500i	−0.989334	+	0.145666i	$0.953467\pi$
$702$	3.74757	−	4.63486i	0.141443	−	0.174931i
$703$		−	0.672512i		−	0.0253643i
$704$	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
$708$	−0.450422	+	0.0964358i	−0.0169279	+	0.00362428i
$709$	12.9188	+	12.9188i	0.485176	+	0.485176i	0.906780	−	0.421604i	$-0.138533\pi$
$709$	12.9188	+	12.9188i	0.485176	+	0.485176i	−0.421604	+	0.906780i	$0.638533\pi$
$710$		0			0
$711$		−	19.9133i		−	0.746807i
$712$	−13.4312	+	26.5052i	−0.503355	+	0.993325i
$713$	4.83977			0.181251
$714$	−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
$718$	7.17584	+	5.80211i	0.267800	+	0.216533i
$719$	−17.0356			−0.635319			−0.317659	−	0.948205i	$-0.602897\pi$
$719$	−17.0356			−0.635319			−0.317659	+	0.948205i	$0.602897\pi$
$720$		0			0
$721$	27.4922			1.02386
$722$	5.26231	+	4.25490i	0.195843	+	0.158351i
$723$	−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
$727$	31.7051			1.17588			0.587939	−	0.808905i	$-0.299939\pi$
$727$	31.7051			1.17588			0.587939	+	0.808905i	$0.299939\pi$
$728$	−9.76710	−	29.8349i	−0.361993	−	1.10576i
$729$			25.4570i			0.942852i
$730$		0			0
$731$	8.21624	+	8.21624i	0.303888	+	0.303888i
$732$	−0.653065	−	3.05026i	−0.0241380	−	0.112741i
$733$	−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
$737$		−	24.4584i		−	0.900937i
$738$	−26.9616	+	33.3451i	−0.992469	+	1.22745i
$739$	−11.3024	+	11.3024i	−0.415766	+	0.415766i	−0.883742	−	0.467975i	$-0.844984\pi$
$739$	−11.3024	+	11.3024i	−0.415766	+	0.415766i	0.467975	+	0.883742i	$0.344984\pi$
$740$		0			0
$741$	−2.43409	−	2.43409i	−0.0894184	−	0.0894184i
$742$	−4.17962	−	39.4859i	−0.153439	−	1.44957i
$743$	30.7210			1.12704			0.563521	−	0.826102i	$-0.309446\pi$
$743$	30.7210			1.12704			0.563521	+	0.826102i	$0.309446\pi$
$744$	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
$748$	−15.3712	−	9.94995i	−0.562028	−	0.363806i
$749$	−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	$0.402850\pi$
$752$	3.10234	+	6.91292i	0.113131	+	0.252088i
$753$			0.885888i			0.0322836i
$754$	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	$0.441020\pi$
$758$	−20.1021	+	2.12783i	−0.730140	+	0.0772861i
$759$		−	0.593681i		−	0.0215493i
$760$		0			0
$761$			5.91749i			0.214509i	0.994232	+	0.107254i	$0.0342060\pi$
$761$			5.91749i			0.214509i	−0.994232	+	0.107254i	$0.965794\pi$
$762$	0.534842	+	5.05277i	0.0193753	+	0.183043i
$763$	−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
$767$			5.64368i			0.203782i
$768$	2.71088	−	0.158140i	0.0978206	−	0.00570640i
$769$	−10.7206			−0.386596			−0.193298	−	0.981140i	$-0.561918\pi$
$769$	−10.7206			−0.386596			−0.193298	+	0.981140i	$0.561918\pi$
$770$		0			0
$771$	−0.373240	+	0.373240i	−0.0134419	+	0.0134419i
$772$	22.1750	−	4.74769i	0.798094	−	0.170873i
$773$	−16.8329	+	16.8329i	−0.605438	+	0.605438i	−0.941750	−	0.336312i	$-0.890820\pi$
$773$	−16.8329	+	16.8329i	−0.605438	+	0.605438i	0.336312	+	0.941750i	$0.390820\pi$
$774$	26.2284	−	2.77631i	0.942760	−	0.0997922i
$775$		0			0
$776$	−6.13596	+	12.1088i	−0.220268	+	0.434679i
$777$	0.0624587			0.00224069
$778$	1.97089	−	0.208621i	0.0706597	−	0.00747941i
$779$	35.1934	+	35.1934i	1.26094	+	1.26094i
$780$		0			0
$781$	−27.5147	+	27.5147i	−0.984554	+	0.984554i
$782$	−1.43985	−	1.16421i	−0.0514889	−	0.0416319i
$783$		−	5.01488i		−	0.179217i
$784$	−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	0.0884603	−	0.996080i	$-0.471805\pi$
$787$	−25.4619	−	25.4619i	−0.907619	−	0.907619i	−0.996080	+	0.0884603i	$0.971805\pi$
$788$	2.61186	+	1.69068i	0.0930436	+	0.0602280i
$789$	−2.15430	−	2.15430i	−0.0766951	−	0.0766951i
$790$		0			0
$791$		−	2.24854i		−	0.0799489i
$792$	−39.5000	+	12.9312i	−1.40357	+	0.459489i
$793$	−38.2191			−1.35720
$794$	−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	0.822238	−	0.569143i	$-0.192725\pi$
$797$	7.14518	+	7.14518i	0.253095	+	0.253095i	−0.569143	+	0.822238i	$0.692725\pi$
$798$	−1.96422	+	2.42928i	−0.0695326	+	0.0859955i
$799$	3.50662			0.124055
$800$		0			0
$801$	31.2139			1.10289
$802$	−23.8115	+	29.4492i	−0.840812	+	1.03989i
$803$	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
$807$	−0.389876			−0.0137243
$808$	0.464171	+	1.41787i	0.0163295	+	0.0498806i
$809$			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	−0.996843	−	0.0794022i	$-0.974699\pi$
$811$	−30.6494	−	30.6494i	−1.07624	−	1.07624i	−0.0794022	−	0.996843i	$-0.525301\pi$
$812$	−22.1731	−	14.3528i	−0.778123	−	0.503686i
$813$	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
$817$		−	30.6125i		−	1.07099i
$818$	14.5129	+	11.7345i	0.507430	+	0.410288i
$819$	−23.3187	+	23.3187i	−0.814820	+	0.814820i
$820$		0			0
$821$	8.84907	+	8.84907i	0.308835	+	0.308835i	0.844457	−	0.535623i	$-0.179923\pi$
$821$	8.84907	+	8.84907i	0.308835	+	0.308835i	−0.535623	+	0.844457i	$0.679923\pi$
$822$	−2.45463	+	0.259826i	−0.0856152	+	0.00906247i
$823$	−11.7501			−0.409583			−0.204792	−	0.978806i	$-0.565652\pi$
$823$	−11.7501			−0.409583			−0.204792	+	0.978806i	$0.565652\pi$
$824$	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	$0.223326\pi$
$828$	−4.10984	+	0.879922i	−0.142827	+	0.0305794i
$829$	−24.8718	+	24.8718i	−0.863834	+	0.863834i	−0.991781	−	0.127947i	$-0.959161\pi$
$829$	−24.8718	+	24.8718i	−0.863834	+	0.863834i	0.127947	+	0.991781i	$0.459161\pi$
$830$		0			0
$831$	3.32845			0.115463
$832$	5.05896	−	32.8836i	0.175388	−	1.14003i
$833$			0.226880i			0.00786092i
$834$	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
$838$	2.08940	+	19.7391i	0.0721773	+	0.681875i
$839$			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
$842$	−31.4104	+	3.32483i	−1.08248	+	0.114581i
$843$	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
$847$			35.9223i			1.23430i
$848$	14.9644	−	39.3306i	0.513880	−	1.35062i
$849$	−3.92859			−0.134829
$850$		0			0
$851$	0.0689649	−	0.0689649i	0.00236409	−	0.00236409i
$852$	−2.24191	−	1.45121i	−0.0768065	−	0.0497175i
$853$	4.02276	−	4.02276i	0.137737	−	0.137737i	−0.634877	−	0.772613i	$-0.718949\pi$
$853$	4.02276	−	4.02276i	0.137737	−	0.137737i	0.772613	+	0.634877i	$0.218949\pi$
$854$	3.65107	+	34.4925i	0.124937	+	1.18031i
$855$		0			0
$856$	−55.1478	+	18.0538i	−1.88491	+	0.617067i
$857$	−44.6563			−1.52543			−0.762714	−	0.646736i	$-0.776134\pi$
$857$	−44.6563			−1.52543			−0.762714	+	0.646736i	$0.776134\pi$
$858$	−0.519658	−	4.90932i	−0.0177408	−	0.167602i
$859$	−5.22864	−	5.22864i	−0.178399	−	0.178399i	0.612259	−	0.790658i	$-0.290261\pi$
$859$	−5.22864	−	5.22864i	−0.178399	−	0.178399i	−0.790658	+	0.612259i	$0.790261\pi$
$860$		0			0
$861$	−3.26855	+	3.26855i	−0.111392	+	0.111392i
$862$	0.253608	−	0.313653i	0.00863793	−	0.0106831i
$863$		−	36.9653i		−	1.25831i	−0.777278	−	0.629157i	$-0.783400\pi$
$863$		−	36.9653i		−	1.25831i	0.777278	−	0.629157i	$-0.216600\pi$
$864$	−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
$868$	−7.64651	−	35.7145i	−0.259539	−	1.21223i
$869$	−23.4383	−	23.4383i	−0.795089	−	0.795089i
$870$		0			0
$871$		−	20.5669i		−	0.696883i
$872$	−3.02705	+	0.990971i	−0.102509	+	0.0335585i
$873$	14.2599			0.482624
$874$	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	0.847799	−	0.530318i	$-0.177928\pi$
$877$	9.40192	+	9.40192i	0.317480	+	0.317480i	−0.530318	+	0.847799i	$0.677928\pi$
$878$	−12.7490	−	10.3084i	−0.430258	−	0.347890i
$879$	−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	$0.555548\pi$
$882$	0.400462	+	0.323798i	0.0134842	+	0.0109028i
$883$	−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
$887$	6.79523			0.228161			0.114081	−	0.993471i	$-0.463608\pi$
$887$	6.79523			0.228161			0.114081	+	0.993471i	$0.463608\pi$
$888$	0.0590459	+	0.0299208i	0.00198145	+	0.00100407i
$889$		−	56.4968i		−	1.89484i
$890$		0			0
$891$	30.5706	+	30.5706i	1.02415	+	1.02415i
$892$	−6.03665	+	1.29245i	−0.202122	+	0.0432745i
$893$	−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
$897$		−	0.499223i		−	0.0166686i
$898$	10.8479	−	13.4163i	0.361998	−	0.447707i
$899$	23.9433	−	23.9433i	0.798554	−	0.798554i
$900$		0			0
$901$	−13.7707	−	13.7707i	−0.458769	−	0.458769i
$902$	7.51351	+	70.9819i	0.250173	+	2.36344i
$903$	2.84310			0.0946123
$904$	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	$0.221383\pi$
$908$	12.7826	−	19.7473i	0.424206	−	0.655337i
$909$	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	$0.601459\pi$
$912$	−3.02064	+	1.35558i	−0.100023	+	0.0448878i
$913$		−	27.0908i		−	0.896574i
$914$	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
$918$	−2.63832	+	0.279270i	−0.0870777	+	0.00921727i
$919$			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
$922$	−0.999388	−	9.44144i	−0.0329131	−	0.310937i
$923$	−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
$927$		−	30.6071i		−	1.00527i
$928$	−14.0858	−	24.1906i	−0.462390	−	0.794095i
$929$	−35.4660			−1.16360			−0.581801	−	0.813331i	$-0.697652\pi$
$929$	−35.4660			−1.16360			−0.581801	+	0.813331i	$0.697652\pi$
$930$		0			0
$931$	0.422660	−	0.422660i	0.0138521	−	0.0138521i
$932$	−5.82074	−	27.1869i	−0.190665	−	0.890536i
$933$	−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
$937$	−56.4991			−1.84575			−0.922873	−	0.385105i	$-0.874165\pi$
$937$	−56.4991			−1.84575			−0.922873	+	0.385105i	$0.874165\pi$
$938$	−18.5615	+	1.96476i	−0.606055	+	0.0641516i
$939$	2.30207	+	2.30207i	0.0751252	+	0.0751252i
$940$		0			0
$941$	−2.86034	+	2.86034i	−0.0932445	+	0.0932445i	−0.752190	−	0.658946i	$-0.771003\pi$
$941$	−2.86034	+	2.86034i	−0.0932445	+	0.0932445i	0.658946	+	0.752190i	$0.271003\pi$
$942$	0.982385	+	0.794319i	0.0320078	+	0.0258803i
$943$			7.21805i			0.235052i
$944$	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	0.795975	−	0.605329i	$-0.206959\pi$
$947$	5.86681	+	5.86681i	0.190646	+	0.190646i	−0.605329	+	0.795975i	$0.706959\pi$
$948$	1.23620	−	1.90976i	0.0401500	−	0.0620260i
$949$	46.0411	+	46.0411i	1.49456	+	1.49456i
$950$		0			0
$951$		−	2.26040i		−	0.0732985i
$952$	−6.31624	+	12.4645i	−0.204711	+	0.403978i
$953$	25.0238			0.810599			0.405299	−	0.914184i	$-0.367167\pi$
$953$	25.0238			0.810599			0.405299	+	0.914184i	$0.367167\pi$
$954$	−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
$958$	−37.0089	+	45.7713i	−1.19570	+	1.47880i
$959$	27.4461			0.886281
$960$		0			0
$961$	15.8228			0.510412
$962$	0.509925	−	0.630657i	0.0164406	−	0.0203332i
$963$	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
$967$	−16.6523			−0.535502			−0.267751	−	0.963488i	$-0.586280\pi$
$967$	−16.6523			−0.535502			−0.267751	+	0.963488i	$0.586280\pi$
$968$	−17.2085	+	33.9595i	−0.553103	+	1.09150i
$969$			1.53223i			0.0492224i
$970$		0			0
$971$	−30.6552	−	30.6552i	−0.983771	−	0.983771i	0.0160991	−	0.999870i	$-0.494875\pi$
$971$	−30.6552	−	30.6552i	−0.983771	−	0.983771i	−0.999870	+	0.0160991i	$0.994875\pi$
$972$	−4.91654	+	7.59534i	−0.157698	+	0.243621i
$973$	−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
$977$		−	13.4307i		−	0.429687i	−0.976648	−	0.214844i	$-0.931076\pi$
$977$		−	13.4307i		−	0.429687i	0.976648	−	0.214844i	$-0.0689242\pi$
$978$	0.558596	+	0.451659i	0.0178619	+	0.0144425i
$979$	36.7392	−	36.7392i	1.17419	−	1.17419i
$980$		0			0
$981$	2.36591	+	2.36591i	0.0755378	+	0.0755378i
$982$	−8.52263	+	0.902130i	−0.271968	+	0.0287881i
$983$	7.94549			0.253422			0.126711	−	0.991940i	$-0.459558\pi$
$983$	7.94549			0.253422			0.126711	+	0.991940i	$0.459558\pi$
$984$	−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
$988$	8.49257	+	39.6662i	0.270185	+	1.26195i
$989$	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	$0.630409\pi$
$992$	9.88027	−	37.4260i	0.313699	−	1.18828i
$993$			3.08612i			0.0979350i
$994$	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	$0.949322\pi$
$998$	3.18498	+	30.0893i	0.100819	+	0.952459i
$999$		−	0.139745i		−	0.00442134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.g.149.3		16
4.3	odd	2		1600.2.q.h.49.4		16
5.2	odd	4		400.2.l.h.101.2		16
5.3	odd	4		80.2.l.a.21.7	✓	16
5.4	even	2		400.2.q.h.149.6		16
15.8	even	4		720.2.t.c.181.2		16
16.3	odd	4		1600.2.q.g.849.5		16
16.13	even	4		400.2.q.h.349.6		16
20.3	even	4		320.2.l.a.241.5		16
20.7	even	4		1600.2.l.i.1201.4		16
20.19	odd	2		1600.2.q.g.49.5		16
40.3	even	4		640.2.l.a.481.4		16
40.13	odd	4		640.2.l.b.481.5		16
60.23	odd	4		2880.2.t.c.2161.7		16
80.3	even	4		320.2.l.a.81.5		16
80.13	odd	4		80.2.l.a.61.7	yes	16
80.19	odd	4		1600.2.q.h.849.4		16
80.29	even	4	inner	400.2.q.g.349.3		16
80.43	even	4		640.2.l.a.161.4		16
80.53	odd	4		640.2.l.b.161.5		16
80.67	even	4		1600.2.l.i.401.4		16
80.77	odd	4		400.2.l.h.301.2		16
160.3	even	8		5120.2.a.t.1.5		8
160.13	odd	8		5120.2.a.s.1.5		8
160.83	even	8		5120.2.a.u.1.4		8
160.93	odd	8		5120.2.a.v.1.4		8
240.83	odd	4		2880.2.t.c.721.6		16
240.173	even	4		720.2.t.c.541.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.7	✓	16	5.3	odd	4
80.2.l.a.61.7	yes	16	80.13	odd	4
320.2.l.a.81.5		16	80.3	even	4
320.2.l.a.241.5		16	20.3	even	4
400.2.l.h.101.2		16	5.2	odd	4
400.2.l.h.301.2		16	80.77	odd	4
400.2.q.g.149.3		16	1.1	even	1	trivial
400.2.q.g.349.3		16	80.29	even	4	inner
400.2.q.h.149.6		16	5.4	even	2
400.2.q.h.349.6		16	16.13	even	4
640.2.l.a.161.4		16	80.43	even	4
640.2.l.a.481.4		16	40.3	even	4
640.2.l.b.161.5		16	80.53	odd	4
640.2.l.b.481.5		16	40.13	odd	4
720.2.t.c.181.2		16	15.8	even	4
720.2.t.c.541.2		16	240.173	even	4
1600.2.l.i.401.4		16	80.67	even	4
1600.2.l.i.1201.4		16	20.7	even	4
1600.2.q.g.49.5		16	20.19	odd	2
1600.2.q.g.849.5		16	16.3	odd	4
1600.2.q.h.49.4		16	4.3	odd	2
1600.2.q.h.849.4		16	80.19	odd	4
2880.2.t.c.721.6		16	240.83	odd	4
2880.2.t.c.2161.7		16	60.23	odd	4
5120.2.a.s.1.5		8	160.13	odd	8
5120.2.a.t.1.5		8	160.3	even	8
5120.2.a.u.1.4		8	160.83	even	8
5120.2.a.v.1.4		8	160.93	odd	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.q (of order \(4\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more