LMFDB - Embedded newform 80.2.l.a.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.638803216170$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.7
Root			$-0.296075 + 1.38287i$ of defining polynomial
Character	$\chi$	$=$	80.61
Dual form			80.2.l.a.21.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09971 - 0.889181i) q^{2} +(-0.120009 - 0.120009i) q^{3} +(0.418713 - 1.95568i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.238684 - 0.0252650i) q^{6} +2.66881i q^{7} +(-1.27849 - 2.52299i) q^{8} -2.97120i q^{9} +O(q^{10})$	\(q+(1.09971 - 0.889181i) q^{2} +(-0.120009 - 0.120009i) q^{3} +(0.418713 - 1.95568i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.238684 - 0.0252650i) q^{6} +2.66881i q^{7} +(-1.27849 - 2.52299i) q^{8} -2.97120i q^{9} +(-0.148864 + 1.40636i) q^{10} +(-3.49714 + 3.49714i) q^{11} +(-0.284948 + 0.184450i) q^{12} +(2.94072 + 2.94072i) q^{13} +(2.37306 + 2.93491i) q^{14} +0.169718 q^{15} +(-3.64936 - 1.63774i) q^{16} +1.85116 q^{17} +(-2.64193 - 3.26745i) q^{18} +(-3.44856 - 3.44856i) q^{19} +(1.08680 + 1.67895i) q^{20} +(0.320281 - 0.320281i) q^{21} +(-0.736240 + 6.95543i) q^{22} -0.707288i q^{23} +(-0.149351 + 0.456211i) q^{24} -1.00000i q^{25} +(5.84877 + 0.619099i) q^{26} +(-0.716597 + 0.716597i) q^{27} +(5.21934 + 1.11747i) q^{28} +(-3.49909 - 3.49909i) q^{29} +(0.186640 - 0.150910i) q^{30} +6.84272 q^{31} +(-5.46947 + 1.44391i) q^{32} +0.839377 q^{33} +(2.03573 - 1.64601i) q^{34} +(-1.88714 - 1.88714i) q^{35} +(-5.81070 - 1.24408i) q^{36} +(-0.0975060 + 0.0975060i) q^{37} +(-6.85881 - 0.726013i) q^{38} -0.705826i q^{39} +(2.68805 + 0.879991i) q^{40} -10.2052i q^{41} +(0.0674276 - 0.637004i) q^{42} +(4.43844 - 4.43844i) q^{43} +(5.37499 + 8.30359i) q^{44} +(2.10095 + 2.10095i) q^{45} +(-0.628908 - 0.777810i) q^{46} -1.89428 q^{47} +(0.241413 + 0.634498i) q^{48} -0.122561 q^{49} +(-0.889181 - 1.09971i) q^{50} +(-0.222155 - 0.222155i) q^{51} +(6.98243 - 4.51979i) q^{52} +(-7.43897 + 7.43897i) q^{53} +(-0.150862 + 1.42523i) q^{54} -4.94571i q^{55} +(6.73338 - 3.41205i) q^{56} +0.827717i q^{57} +(-6.95931 - 0.736651i) q^{58} +(0.959574 - 0.959574i) q^{59} +(0.0710632 - 0.331914i) q^{60} +(6.49825 + 6.49825i) q^{61} +(7.52499 - 6.08442i) q^{62} +7.92956 q^{63} +(-4.73092 + 6.45123i) q^{64} -4.15881 q^{65} +(0.923069 - 0.746358i) q^{66} +(3.49691 + 3.49691i) q^{67} +(0.775103 - 3.62027i) q^{68} +(-0.0848809 + 0.0848809i) q^{69} +(-3.75330 - 0.397291i) q^{70} +7.86777i q^{71} +(-7.49629 + 3.79865i) q^{72} +15.6564i q^{73} +(-0.0205276 + 0.193929i) q^{74} +(-0.120009 + 0.120009i) q^{75} +(-8.18824 + 5.30033i) q^{76} +(-9.33322 - 9.33322i) q^{77} +(-0.627607 - 0.776202i) q^{78} -6.70212 q^{79} +(3.73854 - 1.42243i) q^{80} -8.74159 q^{81} +(-9.07431 - 11.2228i) q^{82} +(-3.87327 - 3.87327i) q^{83} +(-0.492261 - 0.760473i) q^{84} +(-1.30896 + 1.30896i) q^{85} +(0.934407 - 8.82755i) q^{86} +0.839845i q^{87} +(13.2943 + 4.35218i) q^{88} +10.5055i q^{89} +(4.17856 + 0.442305i) q^{90} +(-7.84824 + 7.84824i) q^{91} +(-1.38323 - 0.296151i) q^{92} +(-0.821187 - 0.821187i) q^{93} +(-2.08316 + 1.68436i) q^{94} +4.87701 q^{95} +(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}+O(q^{10}) $ 16 * q - 4 * q^4 - 12 * q^6	$ 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 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} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 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 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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	0.671614	−	0.740901i	$-0.265601\pi$
$3$	−0.120009	−	0.120009i	−0.0692872	−	0.0692872i	−0.740901	+	0.671614i	$0.765601\pi$
$4$	0.418713	−	1.95568i	0.209357	−	0.977839i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.238684	−	0.0252650i	−0.0974425	−	0.0103144i
$7$			2.66881i			1.00872i	0.863495	+	0.504358i	$0.168271\pi$
$7$			2.66881i			1.00872i	−0.863495	+	0.504358i	$0.831729\pi$
$8$	−1.27849	−	2.52299i	−0.452015	−	0.892010i
$9$		−	2.97120i		−	0.990399i
$10$	−0.148864	+	1.40636i	−0.0470751	+	0.444729i
$11$	−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	0.985468	−	0.169858i	$-0.0543310\pi$
$13$	2.94072	+	2.94072i	0.815610	+	0.815610i	−0.169858	+	0.985468i	$0.554331\pi$
$14$	2.37306	+	2.93491i	0.634227	+	0.784389i
$15$	0.169718			0.0438211
$16$	−3.64936	−	1.63774i	−0.912340	−	0.409434i
$17$	1.85116			0.448971			0.224486	−	0.974477i	$-0.427930\pi$
$17$	1.85116			0.448971			0.224486	+	0.974477i	$0.427930\pi$
$18$	−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	$0.938980\pi$
$20$	1.08680	+	1.67895i	0.243016	+	0.375424i
$21$	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	$-0.976507\pi$
$23$		−	0.707288i		−	0.147480i	0.997278	−	0.0737399i	$-0.0234935\pi$
$24$	−0.149351	+	0.456211i	−0.0304860	+	0.0931237i
$25$		−	1.00000i		−	0.200000i
$26$	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	$0.901955\pi$
$30$	0.186640	−	0.150910i	0.0340757	−	0.0275523i
$31$	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
$35$	−1.88714	−	1.88714i	−0.318984	−	0.318984i
$36$	−5.81070	−	1.24408i	−0.968451	−	0.207346i
$37$	−0.0975060	+	0.0975060i	−0.0160299	+	0.0160299i	−0.715076	−	0.699046i	$-0.753608\pi$
$37$	−0.0975060	+	0.0975060i	−0.0160299	+	0.0160299i	0.699046	+	0.715076i	$0.253608\pi$
$38$	−6.85881	−	0.726013i	−1.11265	−	0.117775i
$39$		−	0.705826i		−	0.113023i
$40$	2.68805	+	0.879991i	0.425018	+	0.139139i
$41$		−	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	−0.282432	−	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
$45$	2.10095	+	2.10095i	0.313192	+	0.313192i
$46$	−0.628908	−	0.777810i	−0.0927274	−	0.114682i
$47$	−1.89428			−0.276310			−0.138155	−	0.990411i	$-0.544117\pi$
$47$	−1.89428			−0.276310			−0.138155	+	0.990411i	$0.544117\pi$
$48$	0.241413	+	0.634498i	0.0348449	+	0.0915820i
$49$	−0.122561			−0.0175087
$50$	−0.889181	−	1.09971i	−0.125749	−	0.155522i
$51$	−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	$0.507024\pi$
$53$	−7.43897	+	7.43897i	−1.02182	+	1.02182i	−0.999757	+	0.0220650i	$0.992976\pi$
$54$	−0.150862	+	1.42523i	−0.0205298	+	0.193949i
$55$		−	4.94571i		−	0.666879i
$56$	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	$0.221845\pi$
$60$	0.0710632	−	0.331914i	0.00917422	−	0.0428500i
$61$	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
$65$	−4.15881			−0.515837
$66$	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	$0.652317\pi$
$68$	0.775103	−	3.62027i	0.0939951	−	0.439022i
$69$	−0.0848809	+	0.0848809i	−0.0102185	+	0.0102185i
$70$	−3.75330	−	0.397291i	−0.448605	−	0.0474854i
$71$			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	$0.368776\pi$
$73$			15.6564i			1.83244i	−0.400675	+	0.916220i	$0.631224\pi$
$74$	−0.0205276	+	0.193929i	−0.00238628	+	0.0225437i
$75$	−0.120009	+	0.120009i	−0.0138574	+	0.0138574i
$76$	−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	$0.623052\pi$
$80$	3.73854	−	1.42243i	0.417982	−	0.159033i
$81$	−8.74159			−0.971288
$82$	−9.07431	−	11.2228i	−1.00209	−	1.23935i
$83$	−3.87327	−	3.87327i	−0.425147	−	0.425147i	0.461825	−	0.886971i	$-0.347195\pi$
$83$	−3.87327	−	3.87327i	−0.425147	−	0.425147i	−0.886971	+	0.461825i	$0.847195\pi$
$84$	−0.492261	−	0.760473i	−0.0537101	−	0.0829744i
$85$	−1.30896	+	1.30896i	−0.141977	+	0.141977i
$86$	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	$0.812033\pi$
$90$	4.17856	+	0.442305i	0.440459	+	0.0466231i
$91$	−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
$95$	4.87701			0.500370
$96$	0.829667	+	0.483103i	0.0846776	+	0.0493065i
$97$	4.79937			0.487303			0.243651	−	0.969863i	$-0.421655\pi$
$97$	4.79937			0.487303			0.243651	+	0.969863i	$0.421655\pi$
$98$	−0.134781	+	0.108979i	−0.0136150	+	0.0110085i
$99$	10.3907	+	10.3907i	1.04430	+	1.04430i
$100$	−1.95568	−	0.418713i	−0.195568	−	0.0418713i
$101$	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	$-0.830567\pi$
$103$		−	10.3013i		−	1.01502i	0.861647	−	0.507508i	$-0.169433\pi$
$104$	3.65972	−	11.1791i	0.358865	−	1.09620i
$105$			0.452946i			0.0442030i
$106$	−1.56610	+	14.7953i	−0.152113	+	1.43705i
$107$	14.5069	−	14.5069i	1.40244	−	1.40244i	0.610165	−	0.792274i	$-0.291103\pi$
$107$	14.5069	−	14.5069i	1.40244	−	1.40244i	0.792274	−	0.610165i	$-0.208897\pi$
$108$	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	$0.732825\pi$
$110$	−4.39763	−	5.43883i	−0.419298	−	0.518572i
$111$	0.0234032			0.00222133
$112$	4.37081	−	9.73945i	0.413003	−	0.920292i
$113$	0.842524			0.0792580			0.0396290	−	0.999214i	$-0.487382\pi$
$113$	0.842524			0.0792580			0.0396290	+	0.999214i	$0.487382\pi$
$114$	0.735990	+	0.910246i	0.0689318	+	0.0852524i
$115$	0.500128	+	0.500128i	0.0466372	+	0.0466372i
$116$	−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
$120$	−0.216983	−	0.428197i	−0.0198078	−	0.0390888i
$121$		−	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
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	8.72020	−	7.05082i	0.776857	−	0.628137i
$127$	−21.1693			−1.87847			−0.939234	−	0.343277i	$-0.888463\pi$
$127$	−21.1693			−1.87847			−0.939234	+	0.343277i	$0.888463\pi$
$128$	0.533685	+	11.3011i	0.0471715	+	0.998887i
$129$	−1.06530			−0.0937947
$130$	−4.57348	+	3.69794i	−0.401120	+	0.324331i
$131$	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
$135$		−	1.01342i		−	0.0872214i
$136$	−2.36669	−	4.67044i	−0.202942	−	0.400487i
$137$			10.2840i			0.878623i	0.898335	+	0.439312i	$0.144778\pi$
$137$			10.2840i			0.878623i	−0.898335	+	0.439312i	$0.855222\pi$
$138$	−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	$0.153336\pi$
$140$	−4.48080	+	2.90046i	−0.378697	+	0.245134i
$141$	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
$145$	4.94847			0.410948
$146$	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	$0.0798390\pi$
$150$	−0.0252650	+	0.238684i	−0.00206288	+	0.0194885i
$151$		−	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
$155$	−4.83853	+	4.83853i	−0.388640	+	0.388640i
$156$	−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	$0.817359\pi$
$158$	−7.37037	+	5.95940i	−0.586355	+	0.474104i
$159$	1.78549			0.141598
$160$	2.84650	−	4.88850i	0.225036	−	0.386470i
$161$	1.88762			0.148765
$162$	−9.61319	+	7.77286i	−0.755284	+	0.610694i
$163$	2.11630	+	2.11630i	0.165761	+	0.165761i	0.785113	−	0.619352i	$-0.212605\pi$
$163$	2.11630	+	2.11630i	0.165761	+	0.165761i	−0.619352	+	0.785113i	$0.712605\pi$
$164$	−19.9582	−	4.27307i	−1.55847	−	0.333671i
$165$	−0.593529	+	0.593529i	−0.0462062	+	0.0462062i
$166$	−7.70350	−	0.815425i	−0.597908	−	0.0632892i
$167$			18.1604i			1.40530i	0.711538	+	0.702648i	$0.247999\pi$
$167$			18.1604i			1.40530i	−0.711538	+	0.702648i	$0.752001\pi$
$168$	−1.21754	−	0.398589i	−0.0939354	−	0.0307518i
$169$			4.29572i			0.330440i
$170$	−0.275571	+	2.60339i	−0.0211354	+	0.199671i
$171$	−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	0.303800	−	0.952736i	$-0.401745\pi$
$173$	−8.53542	−	8.53542i	−0.648936	−	0.648936i	−0.952736	+	0.303800i	$0.901745\pi$
$174$	0.746774	+	0.923584i	0.0566128	+	0.0700167i
$175$	2.66881			0.201743
$176$	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	$0.790909\pi$
$180$	4.98848	−	3.22909i	0.371820	−	0.240682i
$181$	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
$185$		−	0.137894i		−	0.0101382i
$186$	−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
$190$	5.36328	−	4.33654i	0.389093	−	0.314606i
$191$	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	$-0.633805\pi$
$193$	−11.3388			−0.816181			−0.408091	+	0.912941i	$0.633805\pi$
$194$	5.27791	−	4.26751i	0.378932	−	0.306390i
$195$	0.499094	+	0.499094i	0.0357409	+	0.0357409i
$196$	−0.0513179	+	0.239690i	−0.00366557	+	0.0171207i
$197$	1.10001	−	1.10001i	0.0783725	−	0.0783725i	−0.666834	−	0.745206i	$-0.732351\pi$
$197$	1.10001	−	1.10001i	0.0783725	−	0.0783725i	0.745206	+	0.666834i	$0.232351\pi$
$198$	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	$0.831174\pi$
$200$	−2.52299	+	1.27849i	−0.178402	+	0.0904030i
$201$		−	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
$205$	7.21620	+	7.21620i	0.504001	+	0.504001i
$206$	−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
$210$	0.402751	+	0.498108i	0.0277925	+	0.0343727i
$211$	−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
$215$			6.27690i			0.428081i
$216$	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
$220$	−9.67222	−	2.07083i	−0.652101	−	0.139616i
$221$	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	$-0.467043\pi$
$223$	3.08673			0.206703			0.103351	+	0.994645i	$0.467043\pi$
$224$	−3.85353	−	14.5970i	−0.257475	−	0.975303i
$225$	−2.97120			−0.198080
$226$	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	$0.622362\pi$
$228$	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	$0.404579\pi$
$230$	0.994700	+	0.105290i	0.0655886	+	0.00694262i
$231$			2.24014i			0.147390i
$232$	−4.35461	+	13.3017i	−0.285894	+	0.873301i
$233$		−	13.9015i		−	0.910718i	−0.890308	−	0.455359i	$-0.849511\pi$
$233$		−	13.9015i		−	0.910718i	0.890308	−	0.455359i	$-0.150489\pi$
$234$	1.83947	−	17.3779i	0.120250	−	1.13603i
$235$	1.33946	−	1.33946i	0.0873768	−	0.0873768i
$236$	−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	$0.613236\pi$
$240$	−0.619363	−	0.277954i	−0.0399797	−	0.0179418i
$241$	−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
$245$	0.0866638	−	0.0866638i	0.00553675	−	0.00553675i
$246$	−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
$250$	1.40636	+	0.148864i	0.0889458	+	0.00941502i
$251$	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
$255$	0.314175			0.0196744
$256$	10.6356	+	11.9534i	0.664727	+	0.747086i
$257$	3.11011			0.194003			0.0970016	−	0.995284i	$-0.469075\pi$
$257$	3.11011			0.194003			0.0970016	+	0.995284i	$0.469075\pi$
$258$	−1.17152	+	0.947248i	−0.0729358	+	0.0589731i
$259$	−0.260225	−	0.260225i	−0.0161696	−	0.0161696i
$260$	−1.74135	+	8.13330i	−0.107994	+	0.504406i
$261$	−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	$0.186692\pi$
$263$			17.9512i			1.10692i	−0.832877	+	0.553458i	$0.813308\pi$
$264$	−1.07314	−	2.11774i	−0.0660469	−	0.130338i
$265$		−	10.5203i		−	0.646257i
$266$	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	$0.727690\pi$
$270$	−0.901115	−	1.11447i	−0.0548401	−	0.0678243i
$271$	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
$275$	3.49714	+	3.49714i	0.210886	+	0.210886i
$276$	0.130459	+	0.201541i	0.00785271	+	0.0121313i
$277$	−13.8675	+	13.8675i	−0.833218	+	0.833218i	−0.987956	−	0.154737i	$-0.950547\pi$
$277$	−13.8675	+	13.8675i	−0.833218	+	0.833218i	0.154737	+	0.987956i	$0.450547\pi$
$278$	1.04966	−	9.91636i	0.0629543	−	0.594744i
$279$		−	20.3310i		−	1.21719i
$280$	−2.34853	+	7.17390i	−0.140352	+	0.428723i
$281$			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	−0.999644	−	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
$285$	−0.585284	−	0.585284i	−0.0346692	−	0.0346692i
$286$	−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
$290$	5.44187	−	4.40008i	0.319557	−	0.258382i
$291$	−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	−0.819560	−	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
$295$			1.35704i			0.0790101i
$296$	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
$300$	0.184450	+	0.284948i	0.0106492	+	0.0164515i
$301$	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
$305$	−9.18991			−0.526213
$306$	−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	$0.920339\pi$
$308$	−22.1607	+	14.3448i	−1.26272	+	0.817373i
$309$	−1.23625	+	1.23625i	−0.0703276	+	0.0703276i
$310$	−1.01864	+	9.62330i	−0.0578547	+	0.546567i
$311$		−	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	$-0.817618\pi$
$313$		−	19.1825i		−	1.08426i	0.840295	−	0.542129i	$-0.182382\pi$
$314$	−7.40239	−	0.783551i	−0.417741	−	0.0442183i
$315$	−5.60705	+	5.60705i	−0.315921	+	0.315921i
$316$	−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	$0.872022\pi$
$318$	1.96351	−	1.58762i	0.110108	−	0.0890293i
$319$	24.4737			1.37026
$320$	−1.21644	−	7.90698i	−0.0680012	−	0.442013i
$321$	−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
$325$	2.94072	−	2.94072i	0.163122	−	0.163122i
$326$	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
$330$	−0.124953	+	1.18046i	−0.00687846	+	0.0649824i
$331$	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
$335$	−4.94538			−0.270195
$336$	−1.69336	+	0.644285i	−0.0923802	+	0.0351486i
$337$	3.31961			0.180831			0.0904153	−	0.995904i	$-0.471181\pi$
$337$	3.31961			0.180831			0.0904153	+	0.995904i	$0.471181\pi$
$338$	3.81967	+	4.72403i	0.207763	+	0.256954i
$339$	−0.101110	−	0.101110i	−0.00549156	−	0.00549156i
$340$	2.01183	+	3.10800i	0.109107	+	0.168555i
$341$	−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
$345$		−	0.120040i		−	0.00646272i
$346$	−16.9760	−	1.79693i	−0.912635	−	0.0966035i
$347$	17.8860	−	17.8860i	0.960171	−	0.960171i	−0.0390656	−	0.999237i	$-0.512438\pi$
$347$	17.8860	−	17.8860i	0.960171	−	0.960171i	0.999237	+	0.0390656i	$0.0124381\pi$
$348$	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	$0.794579\pi$
$350$	2.93491	−	2.37306i	0.156878	−	0.126845i
$351$	−4.21463			−0.224960
$352$	14.0780	−	24.1771i	0.750358	−	1.28864i
$353$	33.0951			1.76148			0.880738	−	0.473604i	$-0.157047\pi$
$353$	33.0951			1.76148			0.880738	+	0.473604i	$0.157047\pi$
$354$	−0.253279	+	0.204792i	−0.0134616	+	0.0108846i
$355$	−5.56335	−	5.56335i	−0.295272	−	0.295272i
$356$	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	$-0.0550856\pi$
$360$	2.61463	−	7.98672i	0.137803	−	0.420937i
$361$			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
$365$	−11.0707	−	11.0707i	−0.579469	−	0.579469i
$366$	−1.38685	−	1.71521i	−0.0724919	−	0.0896554i
$367$	−11.0338			−0.575959			−0.287980	−	0.957636i	$-0.592984\pi$
$367$	−11.0338			−0.575959			−0.287980	+	0.957636i	$0.592984\pi$
$368$	−1.15835	+	2.58115i	−0.0603833	+	0.134552i
$369$	−30.3218			−1.57849
$370$	−0.122613	−	0.151643i	−0.00637435	−	0.00788357i
$371$	−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	−0.507341	−	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
$375$		−	0.169718i		−	0.00876421i
$376$	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	$0.369653\pi$
$380$	2.04207	−	9.53786i	0.104756	−	0.489282i
$381$	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	$-0.227922\pi$
$383$	29.5283			1.50883			0.754413	+	0.656400i	$0.227922\pi$
$384$	1.29219	−	1.42028i	0.0659417	−	0.0724784i
$385$	13.1992			0.672692
$386$	−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	$0.238689\pi$
$390$	0.992643	+	0.105072i	0.0502645	+	0.00532055i
$391$		−	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
$395$	4.73911	−	4.73911i	0.238451	−	0.238451i
$396$	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	$0.543815\pi$
$398$	12.6905	+	15.6952i	0.636119	+	0.786730i
$399$	−2.20902			−0.110589
$400$	−1.63774	+	3.64936i	−0.0818868	+	0.182468i
$401$	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
$405$	6.18124	−	6.18124i	0.307148	−	0.307148i
$406$	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	$-0.105794\pi$
$410$	14.3522	+	1.51920i	0.708805	+	0.0750279i
$411$	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
$415$	5.47763			0.268886
$416$	−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	$0.861390\pi$
$420$	0.885817	+	0.189654i	0.0432234	+	0.00925419i
$421$	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
$425$		−	1.85116i		−	0.0897943i
$426$	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
$430$	5.58130	+	6.90275i	0.269154	+	0.332880i
$431$	−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	$-0.643308\pi$
$433$	−18.1101			−0.870318			−0.435159	+	0.900354i	$0.643308\pi$
$434$	16.2382	+	20.0828i	0.779457	+	0.964004i
$435$	−0.593860	−	0.593860i	−0.0284734	−	0.0284734i
$436$	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	$0.910774\pi$
$440$	−12.4780	+	6.32304i	−0.594863	+	0.301439i
$441$			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	$0.525848\pi$
$443$	−22.6855	+	22.6855i	−1.07782	+	1.07782i	−0.996705	+	0.0811145i	$0.974152\pi$
$444$	0.00979922	−	0.0457691i	0.000465050	−	0.00217211i
$445$	−7.42850	−	7.42850i	−0.352145	−	0.352145i
$446$	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	$0.407052\pi$
$450$	−3.26745	+	2.64193i	−0.154029	+	0.124542i
$451$	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
$455$		−	11.0991i		−	0.520333i
$456$	2.08832	−	1.05823i	0.0977945	−	0.0495561i
$457$		−	1.70660i		−	0.0798314i	−0.999203	−	0.0399157i	$-0.987291\pi$
$457$		−	1.70660i		−	0.0798314i	0.999203	−	0.0399157i	$-0.0127089\pi$
$458$	−2.10297	+	19.8672i	−0.0982652	+	0.928334i
$459$	−1.32653	+	1.32653i	−0.0619172	+	0.0619172i
$460$	1.18750	−	0.768680i	0.0553675	−	0.0358399i
$461$	−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	$-0.583623\pi$
$463$	−11.1761			−0.519398			−0.259699	+	0.965690i	$0.583623\pi$
$464$	7.03886	+	18.5000i	0.326771	+	0.858843i
$465$	1.16133			0.0538556
$466$	−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	$0.728479\pi$
$468$	−13.4292	−	20.7462i	−0.620764	−	0.958992i
$469$	−9.33260	+	9.33260i	−0.430940	+	0.430940i
$470$	0.281992	−	2.66404i	0.0130073	−	0.122883i
$471$			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
$475$	−3.44856	+	3.44856i	−0.158231	+	0.158231i
$476$	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	$0.899802\pi$
$480$	−0.928269	+	0.245058i	−0.0423695	+	0.0111853i
$481$	−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
$485$	−3.39367	+	3.39367i	−0.154099	+	0.154099i
$486$	6.36217	+	0.673443i	0.288594	+	0.0305480i
$487$			8.25627i			0.374127i	0.982348	+	0.187064i	$0.0598970\pi$
$487$			8.25627i			0.374127i	−0.982348	+	0.187064i	$0.940103\pi$
$488$	8.08704	−	24.7029i	0.366083	−	1.11825i
$489$		−	0.507950i		−	0.0229703i
$490$	0.0182450	−	0.172365i	0.000824225	−	0.00778664i
$491$	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
$495$	−14.6947			−0.660476
$496$	−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	$0.908961\pi$
$500$	1.67895	−	1.08680i	0.0750849	−	0.0486031i
$501$	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	$0.136444\pi$
$503$			18.6439i			0.831291i	−0.909527	+	0.415646i	$0.863556\pi$
$504$	−10.1379	−	20.0062i	−0.451577	−	0.891146i
$505$			0.527472i			0.0234722i
$506$	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	$0.631298\pi$
$510$	0.345500	−	0.279358i	0.0152990	−	0.0123702i
$511$	−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
$515$	7.28411	+	7.28411i	0.320976	+	0.320976i
$516$	−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
$520$	5.31700	+	10.4926i	0.233166	+	0.460132i
$521$			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	−0.562570	−	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
$525$	−0.320281	−	0.320281i	−0.0139782	−	0.0139782i
$526$	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
$530$	−9.35445	−	11.5692i	−0.406331	−	0.502536i
$531$	−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
$535$			20.5159i			0.886981i
$536$	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
$540$	−1.98193	−	0.424333i	−0.0852885	−	0.0182604i
$541$	−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
$545$	−1.12612			−0.0482375
$546$	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	$0.500433\pi$
$548$	20.1122	+	4.30605i	0.859152	+	0.183945i
$549$	19.3076	−	19.3076i	0.824027	−	0.824027i
$550$	6.95543	+	0.736240i	0.296581	+	0.0313934i
$551$			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
$555$	−0.0165485	+	0.0165485i	−0.000702447	+	0.000702447i
$556$	−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	$0.796854\pi$
$558$	−18.0780	−	22.3582i	−0.765302	−	0.946498i
$559$	26.1044			1.10410
$560$	3.79620	+	9.97747i	0.160419	+	0.421625i
$561$	1.55382			0.0656022
$562$	9.54774	+	11.8083i	0.402747	+	0.498103i
$563$	1.28613	+	1.28613i	0.0542040	+	0.0542040i	0.733689	−	0.679485i	$-0.237797\pi$
$563$	1.28613	+	1.28613i	0.0542040	+	0.0542040i	−0.679485	+	0.733689i	$0.737797\pi$
$564$	0.539773	−	0.349400i	0.0227285	−	0.0147124i
$565$	−0.595755	+	0.595755i	−0.0250636	+	0.0250636i
$566$	−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	$-0.0773543\pi$
$570$	−1.16407	−	0.123218i	−0.0487573	−	0.00516102i
$571$	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
$575$	−0.707288			−0.0294960
$576$	19.1679	+	14.0565i	0.798661	+	0.585687i
$577$	−20.3419			−0.846842			−0.423421	−	0.905933i	$-0.639171\pi$
$577$	−20.3419			−0.846842			−0.423421	+	0.905933i	$0.639171\pi$
$578$	−14.9266	+	12.0691i	−0.620864	+	0.502007i
$579$	1.36075	+	1.36075i	0.0565509	+	0.0565509i
$580$	2.07199	−	9.67761i	0.0860346	−	0.401841i
$581$	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
$585$			12.3566i			0.510884i
$586$	−0.888530	+	8.39415i	−0.0367048	+	0.346759i
$587$	−25.8136	+	25.8136i	−1.06544	+	1.06544i	−0.0677360	+	0.997703i	$0.521578\pi$
$587$	−25.8136	+	25.8136i	−1.06544	+	1.06544i	−0.997703	+	0.0677360i	$0.978422\pi$
$588$	0.0349236	−	0.0226063i	0.00144022	−	0.000932270i
$589$	−23.5975	−	23.5975i	−0.972320	−	0.972320i
$590$	1.20666	+	1.49235i	0.0496773	+	0.0614391i
$591$	−0.264022			−0.0108604
$592$	0.515524	−	0.196145i	0.0211879	−	0.00806152i
$593$	4.02945			0.165470			0.0827349	−	0.996572i	$-0.473635\pi$
$593$	4.02945			0.165470			0.0827349	+	0.996572i	$0.473635\pi$
$594$	−4.45665	−	5.51183i	−0.182859	−	0.226153i
$595$	−3.49338	−	3.49338i	−0.143215	−	0.143215i
$596$	−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	$-0.223977\pi$
$600$	0.456211	+	0.149351i	0.0186247	+	0.00609721i
$601$			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
$605$	9.51768	+	9.51768i	0.386949	+	0.386949i
$606$	−0.0984477	+	0.0796010i	−0.00399916	+	0.00323357i
$607$	13.6128			0.552528			0.276264	−	0.961082i	$-0.410904\pi$
$607$	13.6128			0.552528			0.276264	+	0.961082i	$0.410904\pi$
$608$	23.8412	+	13.8824i	0.966890	+	0.563006i
$609$	−2.24139			−0.0908257
$610$	−10.1062	+	8.17150i	−0.409189	+	0.330854i
$611$	−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	−0.895442	−	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
$615$		−	1.73202i		−	0.0698416i
$616$	−11.6152	+	35.4800i	−0.467988	+	1.42953i
$617$			1.96695i			0.0791863i	0.999216	+	0.0395932i	$0.0126062\pi$
$617$			1.96695i			0.0791863i	−0.999216	+	0.0395932i	$0.987394\pi$
$618$	−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	$0.178460\pi$
$620$	7.43666	+	11.4886i	0.298663	+	0.461392i
$621$	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
$625$	−1.00000			−0.0400000
$626$	−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
$630$	−1.18043	+	11.1518i	−0.0470295	+	0.444298i
$631$			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
$635$	14.9689	−	14.9689i	0.594024	−	0.594024i
$636$	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
$640$	−8.36847	−	7.61372i	−0.330793	−	0.300959i
$641$	−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	0.551424	−	0.834225i	$-0.314085\pi$
$643$	−7.17110	−	7.17110i	−0.282801	−	0.282801i	−0.834225	+	0.551424i	$0.814085\pi$
$644$	0.790371	−	3.69158i	0.0311450	−	0.145469i
$645$	0.753283	−	0.753283i	0.0296605	−	0.0296605i
$646$	−12.6967	−	1.34396i	−0.499546	−	0.0528775i
$647$		−	26.4735i		−	1.04078i	−0.853928	−	0.520391i	$-0.825786\pi$
$647$		−	26.4735i		−	1.04078i	0.853928	−	0.520391i	$-0.174214\pi$
$648$	11.1760	+	22.0549i	0.439037	+	0.866399i
$649$			6.71153i			0.263451i
$650$	0.619099	−	5.84877i	0.0242831	−	0.229408i
$651$	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	0.883065	−	0.469250i	$-0.155476\pi$
$653$	10.5746	+	10.5746i	0.413815	+	0.413815i	−0.469250	+	0.883065i	$0.655476\pi$
$654$	−0.169942	−	0.210179i	−0.00664527	−	0.00821863i
$655$	−6.60789			−0.258192
$656$	−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	$0.518587\pi$
$660$	0.912234	+	1.40927i	0.0355086	+	0.0548558i
$661$	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
$665$			13.0158i			0.504732i
$666$	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
$670$	−5.43847	+	4.39734i	−0.210107	+	0.169884i
$671$	−45.4506			−1.75460
$672$	−1.28931	+	2.21423i	−0.0497363	+	0.0854157i
$673$	−41.8069			−1.61154			−0.805769	−	0.592230i	$-0.798248\pi$
$673$	−41.8069			−1.61154			−0.805769	+	0.592230i	$0.798248\pi$
$674$	3.65060	−	2.95173i	0.140616	−	0.113697i
$675$	0.716597	+	0.716597i	0.0275818	+	0.0275818i
$676$	8.40105	+	1.79867i	0.323117	+	0.0691798i
$677$	−22.7350	+	22.7350i	−0.873776	+	0.873776i	−0.992882	−	0.119106i	$-0.961997\pi$
$677$	−22.7350	+	22.7350i	−0.873776	+	0.873776i	0.119106	+	0.992882i	$0.461997\pi$
$678$	−0.201097	−	0.0212864i	−0.00772310	−	0.000817499i
$679$			12.8086i			0.491550i
$680$	4.97600	+	1.62900i	0.190821	+	0.0624693i
$681$		−	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	$-0.368206\pi$
$683$	34.4402	−	34.4402i	1.31782	−	1.31782i	0.915501	−	0.402315i	$-0.131794\pi$
$684$	15.7483	+	24.3289i	0.602151	+	0.930238i
$685$	−7.27190	−	7.27190i	−0.277845	−	0.277845i
$686$	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
$690$	−0.106737	−	0.132009i	−0.00406341	−	0.00502548i
$691$	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
$695$			7.05110i			0.267463i
$696$	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
$700$	1.11747	−	5.21934i	0.0422363	−	0.197273i
$701$	−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
$705$	−0.321495			−0.0121082
$706$	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	$0.361467\pi$
$710$	−11.0649	−	1.17123i	−0.415258	−	0.0439555i
$711$			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
$715$	14.5440	−	14.5440i	0.543913	−	0.543913i
$716$	−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	$0.397103\pi$
$720$	−4.22632	−	11.1079i	−0.157506	−	0.413968i
$721$	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
$725$	−3.49909	+	3.49909i	−0.129953	+	0.129953i
$726$	−0.340068	+	3.21270i	−0.0126211	+	0.119234i
$727$			31.7051i			1.17588i	0.808905	+	0.587939i	$0.200061\pi$
$727$			31.7051i			1.17588i	−0.808905	+	0.587939i	$0.799939\pi$
$728$	29.8349	+	9.76710i	1.10576	+	0.361993i
$729$			25.4570i			0.942852i
$730$	−22.0185	−	2.33068i	−0.814940	−	0.0862623i
$731$	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	0.775065	−	0.631881i	$-0.217717\pi$
$733$	3.87657	+	3.87657i	0.143184	+	0.143184i	−0.631881	+	0.775065i	$0.717717\pi$
$734$	−12.1339	+	9.81105i	−0.447872	+	0.362132i
$735$	−0.0208008			−0.000767251
$736$	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	$0.655016\pi$
$740$	−0.269677	−	0.0577382i	−0.00991352	−	0.00212250i
$741$	−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	$-0.809446\pi$
$743$		−	30.7210i		−	1.12704i	0.826102	−	0.563521i	$-0.190554\pi$
$744$	−1.02196	+	3.12172i	−0.0374670	+	0.114448i
$745$			12.4379i			0.455690i
$746$	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
$750$	−0.150910	−	0.186640i	−0.00551046	−	0.00681514i
$751$	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
$755$	15.6863	+	15.6863i	0.570883	+	0.570883i
$756$	−4.54093	+	2.93939i	−0.165152	+	0.106905i
$757$	21.9737	−	21.9737i	0.798649	−	0.798649i	−0.184233	−	0.982883i	$-0.558980\pi$
$757$	21.9737	−	21.9737i	0.798649	−	0.798649i	0.982883	+	0.184233i	$0.0589802\pi$
$758$	−2.12783	+	20.1021i	−0.0772861	+	0.730140i
$759$		−	0.593681i		−	0.0215493i
$760$	−6.23521	−	12.3046i	−0.226175	−	0.446336i
$761$		−	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
$765$	3.88919	+	3.88919i	0.140614	+	0.140614i
$766$	32.4725	−	26.2560i	1.17328	−	0.948668i
$767$	5.64368			0.203782
$768$	0.158140	−	2.71088i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09971 - 0.889181i) q^{2} +(-0.120009 - 0.120009i) q^{3} +(0.418713 - 1.95568i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.238684 - 0.0252650i) q^{6} +2.66881i q^{7} +(-1.27849 - 2.52299i) q^{8} -2.97120i q^{9} +O(q^{10})\)	\(q+(1.09971 - 0.889181i) q^{2} +(-0.120009 - 0.120009i) q^{3} +(0.418713 - 1.95568i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.238684 - 0.0252650i) q^{6} +2.66881i q^{7} +(-1.27849 - 2.52299i) q^{8} -2.97120i q^{9} +(-0.148864 + 1.40636i) q^{10} +(-3.49714 + 3.49714i) q^{11} +(-0.284948 + 0.184450i) q^{12} +(2.94072 + 2.94072i) q^{13} +(2.37306 + 2.93491i) q^{14} +0.169718 q^{15} +(-3.64936 - 1.63774i) q^{16} +1.85116 q^{17} +(-2.64193 - 3.26745i) q^{18} +(-3.44856 - 3.44856i) q^{19} +(1.08680 + 1.67895i) q^{20} +(0.320281 - 0.320281i) q^{21} +(-0.736240 + 6.95543i) q^{22} -0.707288i q^{23} +(-0.149351 + 0.456211i) q^{24} -1.00000i q^{25} +(5.84877 + 0.619099i) q^{26} +(-0.716597 + 0.716597i) q^{27} +(5.21934 + 1.11747i) q^{28} +(-3.49909 - 3.49909i) q^{29} +(0.186640 - 0.150910i) q^{30} +6.84272 q^{31} +(-5.46947 + 1.44391i) q^{32} +0.839377 q^{33} +(2.03573 - 1.64601i) q^{34} +(-1.88714 - 1.88714i) q^{35} +(-5.81070 - 1.24408i) q^{36} +(-0.0975060 + 0.0975060i) q^{37} +(-6.85881 - 0.726013i) q^{38} -0.705826i q^{39} +(2.68805 + 0.879991i) q^{40} -10.2052i q^{41} +(0.0674276 - 0.637004i) q^{42} +(4.43844 - 4.43844i) q^{43} +(5.37499 + 8.30359i) q^{44} +(2.10095 + 2.10095i) q^{45} +(-0.628908 - 0.777810i) q^{46} -1.89428 q^{47} +(0.241413 + 0.634498i) q^{48} -0.122561 q^{49} +(-0.889181 - 1.09971i) q^{50} +(-0.222155 - 0.222155i) q^{51} +(6.98243 - 4.51979i) q^{52} +(-7.43897 + 7.43897i) q^{53} +(-0.150862 + 1.42523i) q^{54} -4.94571i q^{55} +(6.73338 - 3.41205i) q^{56} +0.827717i q^{57} +(-6.95931 - 0.736651i) q^{58} +(0.959574 - 0.959574i) q^{59} +(0.0710632 - 0.331914i) q^{60} +(6.49825 + 6.49825i) q^{61} +(7.52499 - 6.08442i) q^{62} +7.92956 q^{63} +(-4.73092 + 6.45123i) q^{64} -4.15881 q^{65} +(0.923069 - 0.746358i) q^{66} +(3.49691 + 3.49691i) q^{67} +(0.775103 - 3.62027i) q^{68} +(-0.0848809 + 0.0848809i) q^{69} +(-3.75330 - 0.397291i) q^{70} +7.86777i q^{71} +(-7.49629 + 3.79865i) q^{72} +15.6564i q^{73} +(-0.0205276 + 0.193929i) q^{74} +(-0.120009 + 0.120009i) q^{75} +(-8.18824 + 5.30033i) q^{76} +(-9.33322 - 9.33322i) q^{77} +(-0.627607 - 0.776202i) q^{78} -6.70212 q^{79} +(3.73854 - 1.42243i) q^{80} -8.74159 q^{81} +(-9.07431 - 11.2228i) q^{82} +(-3.87327 - 3.87327i) q^{83} +(-0.492261 - 0.760473i) q^{84} +(-1.30896 + 1.30896i) q^{85} +(0.934407 - 8.82755i) q^{86} +0.839845i q^{87} +(13.2943 + 4.35218i) q^{88} +10.5055i q^{89} +(4.17856 + 0.442305i) q^{90} +(-7.84824 + 7.84824i) q^{91} +(-1.38323 - 0.296151i) q^{92} +(-0.821187 - 0.821187i) q^{93} +(-2.08316 + 1.68436i) q^{94} +4.87701 q^{95} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 12 * q^6	\( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 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 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Introduction

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