LMFDB - Embedded newform 400.2.l.c.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			101.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +2.00000i q^{4} +2.00000 q^{6} +2.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +2.00000i q^{4} +2.00000 q^{6} +2.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{12} +(1.00000 - 1.00000i) q^{13} +(-2.00000 + 2.00000i) q^{14} -4.00000 q^{16} +2.00000 q^{17} +(-1.00000 + 1.00000i) q^{18} +(3.00000 - 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +2.00000i q^{22} -6.00000i q^{23} +4.00000i q^{24} +2.00000 q^{26} +(4.00000 + 4.00000i) q^{27} -4.00000 q^{28} +(3.00000 - 3.00000i) q^{29} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +2.00000 q^{33} +(2.00000 + 2.00000i) q^{34} -2.00000 q^{36} +(-3.00000 - 3.00000i) q^{37} +6.00000 q^{38} -2.00000i q^{39} +4.00000i q^{42} +(-5.00000 - 5.00000i) q^{43} +(-2.00000 + 2.00000i) q^{44} +(6.00000 - 6.00000i) q^{46} -8.00000 q^{47} +(-4.00000 + 4.00000i) q^{48} +3.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(2.00000 + 2.00000i) q^{52} +(5.00000 + 5.00000i) q^{53} +8.00000i q^{54} +(-4.00000 - 4.00000i) q^{56} -6.00000i q^{57} +6.00000 q^{58} +(-3.00000 - 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} +(-8.00000 - 8.00000i) q^{62} -2.00000 q^{63} -8.00000i q^{64} +(2.00000 + 2.00000i) q^{66} +(5.00000 - 5.00000i) q^{67} +4.00000i q^{68} +(-6.00000 - 6.00000i) q^{69} -10.0000i q^{71} +(-2.00000 - 2.00000i) q^{72} +4.00000i q^{73} -6.00000i q^{74} +(6.00000 + 6.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +(2.00000 - 2.00000i) q^{78} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{83} +(-4.00000 + 4.00000i) q^{84} -10.0000i q^{86} -6.00000i q^{87} -4.00000 q^{88} +4.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +12.0000 q^{92} +(-8.00000 + 8.00000i) q^{93} +(-8.00000 - 8.00000i) q^{94} -8.00000 q^{96} +2.00000 q^{97} +(3.00000 + 3.00000i) q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^6 - 4 * q^8	$ 2 q + 2 q^{2} + 2 q^{3} + 4 q^{6} - 4 q^{8} + 2 q^{11} + 4 q^{12} + 2 q^{13} - 4 q^{14} - 8 q^{16} + 4 q^{17} - 2 q^{18} + 6 q^{19} + 4 q^{21} + 4 q^{26} + 8 q^{27} - 8 q^{28} + 6 q^{29} - 16 q^{31} - 8 q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{36} - 6 q^{37} + 12 q^{38} - 10 q^{43} - 4 q^{44} + 12 q^{46} - 16 q^{47} - 8 q^{48} + 6 q^{49} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 8 q^{56} + 12 q^{58} - 6 q^{59} - 18 q^{61} - 16 q^{62} - 4 q^{63} + 4 q^{66} + 10 q^{67} - 12 q^{69} - 4 q^{72} + 12 q^{76} - 4 q^{77} + 4 q^{78} + 10 q^{81} + 2 q^{83} - 8 q^{84} - 8 q^{88} + 4 q^{91} + 24 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{96} + 4 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^6 - 4 * q^8 + 2 * q^11 + 4 * q^12 + 2 * q^13 - 4 * q^14 - 8 * q^16 + 4 * q^17 - 2 * q^18 + 6 * q^19 + 4 * q^21 + 4 * q^26 + 8 * q^27 - 8 * q^28 + 6 * q^29 - 16 * q^31 - 8 * q^32 + 4 * q^33 + 4 * q^34 - 4 * q^36 - 6 * q^37 + 12 * q^38 - 10 * q^43 - 4 * q^44 + 12 * q^46 - 16 * q^47 - 8 * q^48 + 6 * q^49 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 8 * q^56 + 12 * q^58 - 6 * q^59 - 18 * q^61 - 16 * q^62 - 4 * q^63 + 4 * q^66 + 10 * q^67 - 12 * q^69 - 4 * q^72 + 12 * q^76 - 4 * q^77 + 4 * q^78 + 10 * q^81 + 2 * q^83 - 8 * q^84 - 8 * q^88 + 4 * q^91 + 24 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^96 + 4 * q^97 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$			2.00000i			1.00000i
$5$		0			0
$5$		0			0
$6$	2.00000			0.816497
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$	2.00000	+	2.00000i	0.577350	+	0.577350i
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	0.832050	+	0.554700i	$0.187167\pi$
$14$	−2.00000	+	2.00000i	−0.534522	+	0.534522i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	+	1.00000i	−0.235702	+	0.235702i
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$			2.00000i			0.426401i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$			4.00000i			0.816497i
$25$		0			0
$26$	2.00000			0.392232
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$	−4.00000			−0.755929
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	0.928477	+	0.371391i	$0.121119\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	2.00000			0.348155
$34$	2.00000	+	2.00000i	0.342997	+	0.342997i
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	6.00000			0.973329
$39$		−	2.00000i		−	0.320256i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$			4.00000i			0.617213i
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	0.214280	−	0.976772i	$-0.431260\pi$
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	−0.976772	+	0.214280i	$0.931260\pi$
$44$	−2.00000	+	2.00000i	−0.301511	+	0.301511i
$45$		0			0
$46$	6.00000	−	6.00000i	0.884652	−	0.884652i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	−4.00000	+	4.00000i	−0.577350	+	0.577350i
$49$	3.00000			0.428571
$50$		0			0
$51$	2.00000	−	2.00000i	0.280056	−	0.280056i
$52$	2.00000	+	2.00000i	0.277350	+	0.277350i
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$			8.00000i			1.08866i
$55$		0			0
$56$	−4.00000	−	4.00000i	−0.534522	−	0.534522i
$57$		−	6.00000i		−	0.794719i
$58$	6.00000			0.787839
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	0.484323	−	0.874889i	$-0.339066\pi$
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	−0.874889	+	0.484323i	$0.839066\pi$
$60$		0			0
$61$	−9.00000	+	9.00000i	−1.15233	+	1.15233i	−0.166248	+	0.986084i	$0.553165\pi$
$61$	−9.00000	+	9.00000i	−1.15233	+	1.15233i	−0.986084	+	0.166248i	$0.946835\pi$
$62$	−8.00000	−	8.00000i	−1.01600	−	1.01600i
$63$	−2.00000			−0.251976
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	2.00000	+	2.00000i	0.246183	+	0.246183i
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	−0.332320	−	0.943167i	$-0.607831\pi$
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	0.943167	+	0.332320i	$0.107831\pi$
$68$			4.00000i			0.485071i
$69$	−6.00000	−	6.00000i	−0.722315	−	0.722315i
$70$		0			0
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$	−2.00000	−	2.00000i	−0.235702	−	0.235702i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$		−	6.00000i		−	0.697486i
$75$		0			0
$76$	6.00000	+	6.00000i	0.688247	+	0.688247i
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$	2.00000	−	2.00000i	0.226455	−	0.226455i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	1.00000	−	1.00000i	0.109764	−	0.109764i	−0.650092	−	0.759856i	$-0.725269\pi$
$83$	1.00000	−	1.00000i	0.109764	−	0.109764i	0.759856	+	0.650092i	$0.225269\pi$
$84$	−4.00000	+	4.00000i	−0.436436	+	0.436436i
$85$		0			0
$86$		−	10.0000i		−	1.07833i
$87$		−	6.00000i		−	0.643268i
$88$	−4.00000			−0.426401
$89$			4.00000i			0.423999i	0.977270	+	0.212000i	$0.0679975\pi$
$89$			4.00000i			0.423999i	−0.977270	+	0.212000i	$0.932002\pi$
$90$		0			0
$91$	2.00000	+	2.00000i	0.209657	+	0.209657i
$92$	12.0000			1.25109
$93$	−8.00000	+	8.00000i	−0.829561	+	0.829561i
$94$	−8.00000	−	8.00000i	−0.825137	−	0.825137i
$95$		0			0
$96$	−8.00000			−0.816497
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	3.00000	+	3.00000i	0.303046	+	0.303046i
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$		0			0
$101$	11.0000	+	11.0000i	1.09454	+	1.09454i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$	11.0000	+	11.0000i	1.09454	+	1.09454i	0.0995037	+	0.995037i	$0.468274\pi$
$102$	4.00000			0.396059
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$			4.00000i			0.392232i
$105$		0			0
$106$			10.0000i			0.971286i
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	0.959256	−	0.282540i	$-0.0911770\pi$
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	−0.282540	+	0.959256i	$0.591177\pi$
$108$	−8.00000	+	8.00000i	−0.769800	+	0.769800i
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	−0.548683	−	0.836031i	$-0.684871\pi$
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	0.836031	+	0.548683i	$0.184871\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		−	8.00000i		−	0.755929i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	6.00000	−	6.00000i	0.561951	−	0.561951i
$115$		0			0
$116$	6.00000	+	6.00000i	0.557086	+	0.557086i
$117$	1.00000	+	1.00000i	0.0924500	+	0.0924500i
$118$		−	6.00000i		−	0.552345i
$119$			4.00000i			0.366679i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$	−18.0000			−1.62964
$123$		0			0
$124$		−	16.0000i		−	1.43684i
$125$		0			0
$126$	−2.00000	−	2.00000i	−0.178174	−	0.178174i
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	−10.0000			−0.880451
$130$		0			0
$131$	11.0000	−	11.0000i	0.961074	−	0.961074i	−0.0381958	−	0.999270i	$-0.512161\pi$
$131$	11.0000	−	11.0000i	0.961074	−	0.961074i	0.999270	+	0.0381958i	$0.0121611\pi$
$132$			4.00000i			0.348155i
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$	10.0000			0.863868
$135$		0			0
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$		−	8.00000i		−	0.683486i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$		−	8.00000i		−	0.683486i	0.939793	−	0.341743i	$-0.111017\pi$
$138$		−	12.0000i		−	1.02151i
$139$	−3.00000	−	3.00000i	−0.254457	−	0.254457i	0.568338	−	0.822795i	$-0.307586\pi$
$139$	−3.00000	−	3.00000i	−0.254457	−	0.254457i	−0.822795	+	0.568338i	$0.807586\pi$
$140$		0			0
$141$	−8.00000	+	8.00000i	−0.673722	+	0.673722i
$142$	10.0000	−	10.0000i	0.839181	−	0.839181i
$143$	2.00000			0.167248
$144$		−	4.00000i		−	0.333333i
$145$		0			0
$146$	−4.00000	+	4.00000i	−0.331042	+	0.331042i
$147$	3.00000	−	3.00000i	0.247436	−	0.247436i
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	7.00000	+	7.00000i	0.573462	+	0.573462i	0.933094	−	0.359632i	$-0.117098\pi$
$149$	7.00000	+	7.00000i	0.573462	+	0.573462i	−0.359632	+	0.933094i	$0.617098\pi$
$150$		0			0
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$			12.0000i			0.973329i
$153$			2.00000i			0.161690i
$154$	−4.00000			−0.322329
$155$		0			0
$156$	4.00000			0.320256
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$		0			0
$159$	10.0000			0.793052
$160$		0			0
$161$	12.0000			0.945732
$162$	5.00000	+	5.00000i	0.392837	+	0.392837i
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	−0.666858	−	0.745184i	$-0.732361\pi$
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	0.745184	+	0.666858i	$0.232361\pi$
$164$		0			0
$165$		0			0
$166$	2.00000			0.155230
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$	−8.00000			−0.617213
$169$			11.0000i			0.846154i
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$	10.0000	−	10.0000i	0.762493	−	0.762493i
$173$	1.00000	−	1.00000i	0.0760286	−	0.0760286i	−0.668070	−	0.744099i	$-0.732879\pi$
$173$	1.00000	−	1.00000i	0.0760286	−	0.0760286i	0.744099	+	0.668070i	$0.232879\pi$
$174$	6.00000	−	6.00000i	0.454859	−	0.454859i
$175$		0			0
$176$	−4.00000	−	4.00000i	−0.301511	−	0.301511i
$177$	−6.00000			−0.450988
$178$	−4.00000	+	4.00000i	−0.299813	+	0.299813i
$179$	−17.0000	+	17.0000i	−1.27064	+	1.27064i	−0.324887	+	0.945753i	$0.605326\pi$
$179$	−17.0000	+	17.0000i	−1.27064	+	1.27064i	−0.945753	+	0.324887i	$0.894674\pi$
$180$		0			0
$181$	−9.00000	−	9.00000i	−0.668965	−	0.668965i	0.288512	−	0.957476i	$-0.406840\pi$
$181$	−9.00000	−	9.00000i	−0.668965	−	0.668965i	−0.957476	+	0.288512i	$0.906840\pi$
$182$			4.00000i			0.296500i
$183$			18.0000i			1.33060i
$184$	12.0000	+	12.0000i	0.884652	+	0.884652i
$185$		0			0
$186$	−16.0000			−1.17318
$187$	2.00000	+	2.00000i	0.146254	+	0.146254i
$188$		−	16.0000i		−	1.16692i
$189$	−8.00000	+	8.00000i	−0.581914	+	0.581914i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−8.00000	−	8.00000i	−0.577350	−	0.577350i
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$	2.00000	+	2.00000i	0.143592	+	0.143592i
$195$		0			0
$196$			6.00000i			0.428571i
$197$	17.0000	+	17.0000i	1.21120	+	1.21120i	0.970632	+	0.240567i	$0.0773335\pi$
$197$	17.0000	+	17.0000i	1.21120	+	1.21120i	0.240567	+	0.970632i	$0.422666\pi$
$198$	−2.00000			−0.142134
$199$			14.0000i			0.992434i	0.868199	+	0.496217i	$0.165278\pi$
$199$			14.0000i			0.992434i	−0.868199	+	0.496217i	$0.834722\pi$
$200$		0			0
$201$		−	10.0000i		−	0.705346i
$202$			22.0000i			1.54791i
$203$	6.00000	+	6.00000i	0.421117	+	0.421117i
$204$	4.00000	+	4.00000i	0.280056	+	0.280056i
$205$		0			0
$206$	6.00000	−	6.00000i	0.418040	−	0.418040i
$207$	6.00000			0.417029
$208$	−4.00000	+	4.00000i	−0.277350	+	0.277350i
$209$	6.00000			0.415029
$210$		0			0
$211$	−9.00000	+	9.00000i	−0.619586	+	0.619586i	−0.945425	−	0.325840i	$-0.894353\pi$
$211$	−9.00000	+	9.00000i	−0.619586	+	0.619586i	0.325840	+	0.945425i	$0.394353\pi$
$212$	−10.0000	+	10.0000i	−0.686803	+	0.686803i
$213$	−10.0000	−	10.0000i	−0.685189	−	0.685189i
$214$			14.0000i			0.957020i
$215$		0			0
$216$	−16.0000			−1.08866
$217$		−	16.0000i		−	1.08615i
$218$	6.00000			0.406371
$219$	4.00000	+	4.00000i	0.270295	+	0.270295i
$220$		0			0
$221$	2.00000	−	2.00000i	0.134535	−	0.134535i
$222$	−6.00000	−	6.00000i	−0.402694	−	0.402694i
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$	8.00000	−	8.00000i	0.534522	−	0.534522i
$225$		0			0
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$	−15.0000	+	15.0000i	−0.995585	+	0.995585i	−0.999990	−	0.00440533i	$-0.998598\pi$
$227$	−15.0000	+	15.0000i	−0.995585	+	0.995585i	0.00440533	+	0.999990i	$0.498598\pi$
$228$	12.0000			0.794719
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	0.899498	−	0.436925i	$-0.143932\pi$
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	−0.436925	+	0.899498i	$0.643932\pi$
$230$		0			0
$231$			4.00000i			0.263181i
$232$			12.0000i			0.787839i
$233$			4.00000i			0.262049i	0.991379	+	0.131024i	$0.0418266\pi$
$233$			4.00000i			0.262049i	−0.991379	+	0.131024i	$0.958173\pi$
$234$			2.00000i			0.130744i
$235$		0			0
$236$	6.00000	−	6.00000i	0.390567	−	0.390567i
$237$		0			0
$238$	−4.00000	+	4.00000i	−0.259281	+	0.259281i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	9.00000	−	9.00000i	0.578542	−	0.578542i
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$	−18.0000	−	18.0000i	−1.15233	−	1.15233i
$245$		0			0
$246$		0			0
$247$		−	6.00000i		−	0.381771i
$248$	16.0000	−	16.0000i	1.01600	−	1.01600i
$249$		−	2.00000i		−	0.126745i
$250$		0			0
$251$	21.0000	+	21.0000i	1.32551	+	1.32551i	0.909243	+	0.416265i	$0.136661\pi$
$251$	21.0000	+	21.0000i	1.32551	+	1.32551i	0.416265	+	0.909243i	$0.363339\pi$
$252$		−	4.00000i		−	0.251976i
$253$	6.00000	−	6.00000i	0.377217	−	0.377217i
$254$	−8.00000	−	8.00000i	−0.501965	−	0.501965i
$255$		0			0
$256$	16.0000			1.00000
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$	−10.0000	−	10.0000i	−0.622573	−	0.622573i
$259$	6.00000	−	6.00000i	0.372822	−	0.372822i
$260$		0			0
$261$	3.00000	+	3.00000i	0.185695	+	0.185695i
$262$	22.0000			1.35916
$263$		−	6.00000i		−	0.369976i	−0.982741	−	0.184988i	$-0.940775\pi$
$263$		−	6.00000i		−	0.369976i	0.982741	−	0.184988i	$-0.0592246\pi$
$264$	−4.00000	+	4.00000i	−0.246183	+	0.246183i
$265$		0			0
$266$			12.0000i			0.735767i
$267$	4.00000	+	4.00000i	0.244796	+	0.244796i
$268$	10.0000	+	10.0000i	0.610847	+	0.610847i
$269$	3.00000	−	3.00000i	0.182913	−	0.182913i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	3.00000	−	3.00000i	0.182913	−	0.182913i	0.792624	+	0.609711i	$0.208714\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−8.00000			−0.485071
$273$	4.00000			0.242091
$274$	8.00000	−	8.00000i	0.483298	−	0.483298i
$275$		0			0
$276$	12.0000	−	12.0000i	0.722315	−	0.722315i
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	0.611213	−	0.791466i	$-0.290682\pi$
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	−0.791466	+	0.611213i	$0.790682\pi$
$278$		−	6.00000i		−	0.359856i
$279$		−	8.00000i		−	0.478947i
$280$		0			0
$281$		−	20.0000i		−	1.19310i	−0.802576	−	0.596550i	$-0.796538\pi$
$281$		−	20.0000i		−	1.19310i	0.802576	−	0.596550i	$-0.203462\pi$
$282$	−16.0000			−0.952786
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	0.994679	−	0.103022i	$-0.0328511\pi$
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	−0.103022	+	0.994679i	$0.532851\pi$
$284$	20.0000			1.18678
$285$		0			0
$286$	2.00000	+	2.00000i	0.118262	+	0.118262i
$287$		0			0
$288$	4.00000	−	4.00000i	0.235702	−	0.235702i
$289$	−13.0000			−0.764706
$290$		0			0
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$	−8.00000			−0.468165
$293$	−15.0000	−	15.0000i	−0.876309	−	0.876309i	0.116841	−	0.993151i	$-0.462723\pi$
$293$	−15.0000	−	15.0000i	−0.876309	−	0.876309i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	6.00000			0.349927
$295$		0			0
$296$	12.0000			0.697486
$297$			8.00000i			0.464207i
$298$			14.0000i			0.810998i
$299$	−6.00000	−	6.00000i	−0.346989	−	0.346989i
$300$		0			0
$301$	10.0000	−	10.0000i	0.576390	−	0.576390i
$302$	10.0000	−	10.0000i	0.575435	−	0.575435i
$303$	22.0000			1.26387
$304$	−12.0000	+	12.0000i	−0.688247	+	0.688247i
$305$		0			0
$306$	−2.00000	+	2.00000i	−0.114332	+	0.114332i
$307$	5.00000	−	5.00000i	0.285365	−	0.285365i	−0.549879	−	0.835244i	$-0.685326\pi$
$307$	5.00000	−	5.00000i	0.285365	−	0.285365i	0.835244	+	0.549879i	$0.185326\pi$
$308$	−4.00000	−	4.00000i	−0.227921	−	0.227921i
$309$	−6.00000	−	6.00000i	−0.341328	−	0.341328i
$310$		0			0
$311$			30.0000i			1.70114i	0.525859	+	0.850572i	$0.323744\pi$
$311$			30.0000i			1.70114i	−0.525859	+	0.850572i	$0.676256\pi$
$312$	4.00000	+	4.00000i	0.226455	+	0.226455i
$313$		−	16.0000i		−	0.904373i	−0.891923	−	0.452187i	$-0.850644\pi$
$313$		−	16.0000i		−	0.904373i	0.891923	−	0.452187i	$-0.149356\pi$
$314$	−30.0000			−1.69300
$315$		0			0
$316$		0			0
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	−0.552611	−	0.833439i	$-0.686369\pi$
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	0.833439	+	0.552611i	$0.186369\pi$
$318$	10.0000	+	10.0000i	0.560772	+	0.560772i
$319$	6.00000			0.335936
$320$		0			0
$321$	14.0000			0.781404
$322$	12.0000	+	12.0000i	0.668734	+	0.668734i
$323$	6.00000	−	6.00000i	0.333849	−	0.333849i
$324$			10.0000i			0.555556i
$325$		0			0
$326$	2.00000			0.110770
$327$		−	6.00000i		−	0.331801i
$328$		0			0
$329$		−	16.0000i		−	0.882109i
$330$		0			0
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	0.734055	−	0.679090i	$-0.237625\pi$
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	−0.679090	+	0.734055i	$0.737625\pi$
$332$	2.00000	+	2.00000i	0.109764	+	0.109764i
$333$	3.00000	−	3.00000i	0.164399	−	0.164399i
$334$	−2.00000	+	2.00000i	−0.109435	+	0.109435i
$335$		0			0
$336$	−8.00000	−	8.00000i	−0.436436	−	0.436436i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	−11.0000	+	11.0000i	−0.598321	+	0.598321i
$339$	6.00000	−	6.00000i	0.325875	−	0.325875i
$340$		0			0
$341$	−8.00000	−	8.00000i	−0.433224	−	0.433224i
$342$			6.00000i			0.324443i
$343$			20.0000i			1.07990i
$344$	20.0000			1.07833
$345$		0			0
$346$	2.00000			0.107521
$347$	−13.0000	−	13.0000i	−0.697877	−	0.697877i	0.266076	−	0.963952i	$-0.414273\pi$
$347$	−13.0000	−	13.0000i	−0.697877	−	0.697877i	−0.963952	+	0.266076i	$0.914273\pi$
$348$	12.0000			0.643268
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		−	8.00000i		−	0.426401i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	−6.00000	−	6.00000i	−0.318896	−	0.318896i
$355$		0			0
$356$	−8.00000			−0.423999
$357$	4.00000	+	4.00000i	0.211702	+	0.211702i
$358$	−34.0000			−1.79696
$359$		−	26.0000i		−	1.37223i	−0.727494	−	0.686114i	$-0.759315\pi$
$359$		−	26.0000i		−	1.37223i	0.727494	−	0.686114i	$-0.240685\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		−	18.0000i		−	0.946059i
$363$	−9.00000	−	9.00000i	−0.472377	−	0.472377i
$364$	−4.00000	+	4.00000i	−0.209657	+	0.209657i
$365$		0			0
$366$	−18.0000	+	18.0000i	−0.940875	+	0.940875i
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$			24.0000i			1.25109i
$369$		0			0
$370$		0			0
$371$	−10.0000	+	10.0000i	−0.519174	+	0.519174i
$372$	−16.0000	−	16.0000i	−0.829561	−	0.829561i
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	0.824603	−	0.565712i	$-0.191399\pi$
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	−0.565712	+	0.824603i	$0.691399\pi$
$374$			4.00000i			0.206835i
$375$		0			0
$376$	16.0000	−	16.0000i	0.825137	−	0.825137i
$377$		−	6.00000i		−	0.309016i
$378$	−16.0000			−0.822951
$379$	−3.00000	−	3.00000i	−0.154100	−	0.154100i	0.625847	−	0.779946i	$-0.284754\pi$
$379$	−3.00000	−	3.00000i	−0.154100	−	0.154100i	−0.779946	+	0.625847i	$0.784754\pi$
$380$		0			0
$381$	−8.00000	+	8.00000i	−0.409852	+	0.409852i
$382$	−8.00000	−	8.00000i	−0.409316	−	0.409316i
$383$	16.0000			0.817562			0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000			0.817562			0.408781	+	0.912633i	$0.365954\pi$
$384$		−	16.0000i		−	0.816497i
$385$		0			0
$386$	−14.0000	−	14.0000i	−0.712581	−	0.712581i
$387$	5.00000	−	5.00000i	0.254164	−	0.254164i
$388$			4.00000i			0.203069i
$389$	−13.0000	−	13.0000i	−0.659126	−	0.659126i	0.296047	−	0.955173i	$-0.404331\pi$
$389$	−13.0000	−	13.0000i	−0.659126	−	0.659126i	−0.955173	+	0.296047i	$0.904331\pi$
$390$		0			0
$391$		−	12.0000i		−	0.606866i
$392$	−6.00000	+	6.00000i	−0.303046	+	0.303046i
$393$		−	22.0000i		−	1.10975i
$394$			34.0000i			1.71290i
$395$		0			0
$396$	−2.00000	−	2.00000i	−0.100504	−	0.100504i
$397$	5.00000	−	5.00000i	0.250943	−	0.250943i	−0.570414	−	0.821357i	$-0.693217\pi$
$397$	5.00000	−	5.00000i	0.250943	−	0.250943i	0.821357	+	0.570414i	$0.193217\pi$
$398$	−14.0000	+	14.0000i	−0.701757	+	0.701757i
$399$	12.0000			0.600751
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	10.0000	−	10.0000i	0.498755	−	0.498755i
$403$	−8.00000	+	8.00000i	−0.398508	+	0.398508i
$404$	−22.0000	+	22.0000i	−1.09454	+	1.09454i
$405$		0			0
$406$			12.0000i			0.595550i
$407$		−	6.00000i		−	0.297409i
$408$			8.00000i			0.396059i
$409$		−	16.0000i		−	0.791149i	−0.918434	−	0.395575i	$-0.870545\pi$
$409$		−	16.0000i		−	0.791149i	0.918434	−	0.395575i	$-0.129455\pi$
$410$		0			0
$411$	−8.00000	−	8.00000i	−0.394611	−	0.394611i
$412$	12.0000			0.591198
$413$	6.00000	−	6.00000i	0.295241	−	0.295241i
$414$	6.00000	+	6.00000i	0.294884	+	0.294884i
$415$		0			0
$416$	−8.00000			−0.392232
$417$	−6.00000			−0.293821
$418$	6.00000	+	6.00000i	0.293470	+	0.293470i
$419$	3.00000	−	3.00000i	0.146560	−	0.146560i	−0.630020	−	0.776579i	$-0.716953\pi$
$419$	3.00000	−	3.00000i	0.146560	−	0.146560i	0.776579	+	0.630020i	$0.216953\pi$
$420$		0			0
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	0.452919	−	0.891552i	$-0.350383\pi$
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	−0.891552	+	0.452919i	$0.850383\pi$
$422$	−18.0000			−0.876226
$423$		−	8.00000i		−	0.388973i
$424$	−20.0000			−0.971286
$425$		0			0
$426$		−	20.0000i		−	0.969003i
$427$	−18.0000	−	18.0000i	−0.871081	−	0.871081i
$428$	−14.0000	+	14.0000i	−0.676716	+	0.676716i
$429$	2.00000	−	2.00000i	0.0965609	−	0.0965609i
$430$		0			0
$431$	32.0000			1.54139			0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000			1.54139			0.770693	+	0.637207i	$0.219910\pi$
$432$	−16.0000	−	16.0000i	−0.769800	−	0.769800i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	16.0000	−	16.0000i	0.768025	−	0.768025i
$435$		0			0
$436$	6.00000	+	6.00000i	0.287348	+	0.287348i
$437$	−18.0000	−	18.0000i	−0.861057	−	0.861057i
$438$			8.00000i			0.382255i
$439$			14.0000i			0.668184i	0.942541	+	0.334092i	$0.108430\pi$
$439$			14.0000i			0.668184i	−0.942541	+	0.334092i	$0.891570\pi$
$440$		0			0
$441$			3.00000i			0.142857i
$442$	4.00000			0.190261
$443$	15.0000	+	15.0000i	0.712672	+	0.712672i	0.967093	−	0.254422i	$-0.0818852\pi$
$443$	15.0000	+	15.0000i	0.712672	+	0.712672i	−0.254422	+	0.967093i	$0.581885\pi$
$444$		−	12.0000i		−	0.569495i
$445$		0			0
$446$	−24.0000	−	24.0000i	−1.13643	−	1.13643i
$447$	14.0000			0.662177
$448$	16.0000			0.755929
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$		0			0
$452$			12.0000i			0.564433i
$453$	−10.0000	−	10.0000i	−0.469841	−	0.469841i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	12.0000	+	12.0000i	0.561951	+	0.561951i
$457$			32.0000i			1.49690i	0.663193	+	0.748448i	$0.269201\pi$
$457$			32.0000i			1.49690i	−0.663193	+	0.748448i	$0.730799\pi$
$458$			14.0000i			0.654177i
$459$	8.00000	+	8.00000i	0.373408	+	0.373408i
$460$		0			0
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	−0.402916	−	0.915237i	$-0.632003\pi$
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	0.915237	+	0.402916i	$0.132003\pi$
$462$	−4.00000	+	4.00000i	−0.186097	+	0.186097i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−12.0000	+	12.0000i	−0.557086	+	0.557086i
$465$		0			0
$466$	−4.00000	+	4.00000i	−0.185296	+	0.185296i
$467$	5.00000	−	5.00000i	0.231372	−	0.231372i	−0.581893	−	0.813265i	$-0.697688\pi$
$467$	5.00000	−	5.00000i	0.231372	−	0.231372i	0.813265	+	0.581893i	$0.197688\pi$
$468$	−2.00000	+	2.00000i	−0.0924500	+	0.0924500i
$469$	10.0000	+	10.0000i	0.461757	+	0.461757i
$470$		0			0
$471$			30.0000i			1.38233i
$472$	12.0000			0.552345
$473$		−	10.0000i		−	0.459800i
$474$		0			0
$475$		0			0
$476$	−8.00000			−0.366679
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$		0			0
$479$	−40.0000			−1.82765			−0.913823	−	0.406112i	$-0.866884\pi$
$479$	−40.0000			−1.82765			−0.913823	+	0.406112i	$0.866884\pi$
$480$		0			0
$481$	−6.00000			−0.273576
$482$	−18.0000	−	18.0000i	−0.819878	−	0.819878i
$483$	12.0000	−	12.0000i	0.546019	−	0.546019i
$484$	18.0000			0.818182
$485$		0			0
$486$	−14.0000			−0.635053
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$		−	36.0000i		−	1.62964i
$489$		−	2.00000i		−	0.0904431i
$490$		0			0
$491$	−19.0000	−	19.0000i	−0.857458	−	0.857458i	0.133580	−	0.991038i	$-0.457353\pi$
$491$	−19.0000	−	19.0000i	−0.857458	−	0.857458i	−0.991038	+	0.133580i	$0.957353\pi$
$492$		0			0
$493$	6.00000	−	6.00000i	0.270226	−	0.270226i
$494$	6.00000	−	6.00000i	0.269953	−	0.269953i
$495$		0			0
$496$	32.0000			1.43684
$497$	20.0000			0.897123
$498$	2.00000	−	2.00000i	0.0896221	−	0.0896221i
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	2.00000	+	2.00000i	0.0893534	+	0.0893534i
$502$			42.0000i			1.87455i
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$	4.00000	−	4.00000i	0.178174	−	0.178174i
$505$		0			0
$506$	12.0000			0.533465
$507$	11.0000	+	11.0000i	0.488527	+	0.488527i
$508$		−	16.0000i		−	0.709885i
$509$	23.0000	−	23.0000i	1.01946	−	1.01946i	0.0196502	−	0.999807i	$-0.493745\pi$
$509$	23.0000	−	23.0000i	1.01946	−	1.01946i	0.999807	−	0.0196502i	$-0.00625524\pi$
$510$		0			0
$511$	−8.00000			−0.353899
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	24.0000			1.05963
$514$	22.0000	+	22.0000i	0.970378	+	0.970378i
$515$		0			0
$516$		−	20.0000i		−	0.880451i
$517$	−8.00000	−	8.00000i	−0.351840	−	0.351840i
$518$	12.0000			0.527250
$519$		−	2.00000i		−	0.0877903i
$520$		0			0
$521$			40.0000i			1.75243i	0.481919	+	0.876216i	$0.339940\pi$
$521$			40.0000i			1.75243i	−0.481919	+	0.876216i	$0.660060\pi$
$522$			6.00000i			0.262613i
$523$	−25.0000	−	25.0000i	−1.09317	−	1.09317i	−0.995188	−	0.0979859i	$-0.968760\pi$
$523$	−25.0000	−	25.0000i	−1.09317	−	1.09317i	−0.0979859	−	0.995188i	$-0.531240\pi$
$524$	22.0000	+	22.0000i	0.961074	+	0.961074i
$525$		0			0
$526$	6.00000	−	6.00000i	0.261612	−	0.261612i
$527$	−16.0000			−0.696971
$528$	−8.00000			−0.348155
$529$	−13.0000			−0.565217
$530$		0			0
$531$	3.00000	−	3.00000i	0.130189	−	0.130189i
$532$	−12.0000	+	12.0000i	−0.520266	+	0.520266i
$533$		0			0
$534$			8.00000i			0.346194i
$535$		0			0
$536$			20.0000i			0.863868i
$537$			34.0000i			1.46721i
$538$	6.00000			0.258678
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	−8.00000	−	8.00000i	−0.343629	−	0.343629i
$543$	−18.0000			−0.772454
$544$	−8.00000	−	8.00000i	−0.342997	−	0.342997i
$545$		0			0
$546$	4.00000	+	4.00000i	0.171184	+	0.171184i
$547$	5.00000	−	5.00000i	0.213785	−	0.213785i	−0.592088	−	0.805873i	$-0.701696\pi$
$547$	5.00000	−	5.00000i	0.213785	−	0.213785i	0.805873	+	0.592088i	$0.201696\pi$
$548$	16.0000			0.683486
$549$	−9.00000	−	9.00000i	−0.384111	−	0.384111i
$550$		0			0
$551$		−	18.0000i		−	0.766826i
$552$	24.0000			1.02151
$553$		0			0
$554$		−	6.00000i		−	0.254916i
$555$		0			0
$556$	6.00000	−	6.00000i	0.254457	−	0.254457i
$557$	25.0000	−	25.0000i	1.05928	−	1.05928i	0.0611558	−	0.998128i	$-0.480521\pi$
$557$	25.0000	−	25.0000i	1.05928	−	1.05928i	0.998128	−	0.0611558i	$-0.0194786\pi$
$558$	8.00000	−	8.00000i	0.338667	−	0.338667i
$559$	−10.0000			−0.422955
$560$		0			0
$561$	4.00000			0.168880
$562$	20.0000	−	20.0000i	0.843649	−	0.843649i
$563$	−19.0000	+	19.0000i	−0.800755	+	0.800755i	−0.983213	−	0.182459i	$-0.941594\pi$
$563$	−19.0000	+	19.0000i	−0.800755	+	0.800755i	0.182459	+	0.983213i	$0.441594\pi$
$564$	−16.0000	−	16.0000i	−0.673722	−	0.673722i
$565$		0			0
$566$			30.0000i			1.26099i
$567$			10.0000i			0.419961i
$568$	20.0000	+	20.0000i	0.839181	+	0.839181i
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	1.00000	+	1.00000i	0.0418487	+	0.0418487i	0.727721	−	0.685873i	$-0.240579\pi$
$571$	1.00000	+	1.00000i	0.0418487	+	0.0418487i	−0.685873	+	0.727721i	$0.740579\pi$
$572$			4.00000i			0.167248i
$573$	−8.00000	+	8.00000i	−0.334205	+	0.334205i
$574$		0			0
$575$		0			0
$576$	8.00000			0.333333
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	−13.0000	−	13.0000i	−0.540729	−	0.540729i
$579$	−14.0000	+	14.0000i	−0.581820	+	0.581820i
$580$		0			0
$581$	2.00000	+	2.00000i	0.0829740	+	0.0829740i
$582$	4.00000			0.165805
$583$			10.0000i			0.414158i
$584$	−8.00000	−	8.00000i	−0.331042	−	0.331042i
$585$		0			0
$586$		−	30.0000i		−	1.23929i
$587$	7.00000	+	7.00000i	0.288921	+	0.288921i	0.836653	−	0.547733i	$-0.184509\pi$
$587$	7.00000	+	7.00000i	0.288921	+	0.288921i	−0.547733	+	0.836653i	$0.684509\pi$
$588$	6.00000	+	6.00000i	0.247436	+	0.247436i
$589$	−24.0000	+	24.0000i	−0.988903	+	0.988903i
$590$		0			0
$591$	34.0000			1.39857
$592$	12.0000	+	12.0000i	0.493197	+	0.493197i
$593$	−34.0000			−1.39621			−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$	−8.00000	+	8.00000i	−0.328244	+	0.328244i
$595$		0			0
$596$	−14.0000	+	14.0000i	−0.573462	+	0.573462i
$597$	14.0000	+	14.0000i	0.572982	+	0.572982i
$598$		−	12.0000i		−	0.490716i
$599$			14.0000i			0.572024i	0.958226	+	0.286012i	$0.0923298\pi$
$599$			14.0000i			0.572024i	−0.958226	+	0.286012i	$0.907670\pi$
$600$		0			0
$601$			20.0000i			0.815817i	0.913023	+	0.407909i	$0.133742\pi$
$601$			20.0000i			0.815817i	−0.913023	+	0.407909i	$0.866258\pi$
$602$	20.0000			0.815139
$603$	5.00000	+	5.00000i	0.203616	+	0.203616i
$604$	20.0000			0.813788
$605$		0			0
$606$	22.0000	+	22.0000i	0.893689	+	0.893689i
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$	−24.0000			−0.973329
$609$	12.0000			0.486265
$610$		0			0
$611$	−8.00000	+	8.00000i	−0.323645	+	0.323645i
$612$	−4.00000			−0.161690
$613$	25.0000	+	25.0000i	1.00974	+	1.00974i	0.999952	+	0.00978840i	$0.00311579\pi$
$613$	25.0000	+	25.0000i	1.00974	+	1.00974i	0.00978840	+	0.999952i	$0.496884\pi$
$614$	10.0000			0.403567
$615$		0			0
$616$		−	8.00000i		−	0.322329i
$617$			12.0000i			0.483102i	0.970388	+	0.241551i	$0.0776561\pi$
$617$			12.0000i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$618$		−	12.0000i		−	0.482711i
$619$	17.0000	+	17.0000i	0.683288	+	0.683288i	0.960740	−	0.277452i	$-0.0894899\pi$
$619$	17.0000	+	17.0000i	0.683288	+	0.683288i	−0.277452	+	0.960740i	$0.589490\pi$
$620$		0			0
$621$	24.0000	−	24.0000i	0.963087	−	0.963087i
$622$	−30.0000	+	30.0000i	−1.20289	+	1.20289i
$623$	−8.00000			−0.320513
$624$			8.00000i			0.320256i
$625$		0			0
$626$	16.0000	−	16.0000i	0.639489	−	0.639489i
$627$	6.00000	−	6.00000i	0.239617	−	0.239617i
$628$	−30.0000	−	30.0000i	−1.19713	−	1.19713i
$629$	−6.00000	−	6.00000i	−0.239236	−	0.239236i
$630$		0			0
$631$		−	10.0000i		−	0.398094i	−0.979990	−	0.199047i	$-0.936215\pi$
$631$		−	10.0000i		−	0.398094i	0.979990	−	0.199047i	$-0.0637846\pi$
$632$		0			0
$633$			18.0000i			0.715436i
$634$	10.0000			0.397151
$635$		0			0
$636$			20.0000i			0.793052i
$637$	3.00000	−	3.00000i	0.118864	−	0.118864i
$638$	6.00000	+	6.00000i	0.237542	+	0.237542i
$639$	10.0000			0.395594
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	14.0000	+	14.0000i	0.552536	+	0.552536i
$643$	21.0000	−	21.0000i	0.828159	−	0.828159i	−0.159103	−	0.987262i	$-0.550860\pi$
$643$	21.0000	−	21.0000i	0.828159	−	0.828159i	0.987262	+	0.159103i	$0.0508601\pi$
$644$			24.0000i			0.945732i
$645$		0			0
$646$	12.0000			0.472134
$647$			42.0000i			1.65119i	0.564263	+	0.825595i	$0.309160\pi$
$647$			42.0000i			1.65119i	−0.564263	+	0.825595i	$0.690840\pi$
$648$	−10.0000	+	10.0000i	−0.392837	+	0.392837i
$649$		−	6.00000i		−	0.235521i
$650$		0			0
$651$	−16.0000	−	16.0000i	−0.627089	−	0.627089i
$652$	2.00000	+	2.00000i	0.0783260	+	0.0783260i
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	−0.973255	−	0.229728i	$-0.926216\pi$
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	0.229728	+	0.973255i	$0.426216\pi$
$654$	6.00000	−	6.00000i	0.234619	−	0.234619i
$655$		0			0
$656$		0			0
$657$	−4.00000			−0.156055
$658$	16.0000	−	16.0000i	0.623745	−	0.623745i
$659$	−17.0000	+	17.0000i	−0.662226	+	0.662226i	−0.955904	−	0.293678i	$-0.905121\pi$
$659$	−17.0000	+	17.0000i	−0.662226	+	0.662226i	0.293678	+	0.955904i	$0.405121\pi$
$660$		0			0
$661$	−9.00000	−	9.00000i	−0.350059	−	0.350059i	0.510072	−	0.860132i	$-0.329619\pi$
$661$	−9.00000	−	9.00000i	−0.350059	−	0.350059i	−0.860132	+	0.510072i	$0.829619\pi$
$662$			2.00000i			0.0777322i
$663$		−	4.00000i		−	0.155347i
$664$			4.00000i			0.155230i
$665$		0			0
$666$	6.00000			0.232495
$667$	−18.0000	−	18.0000i	−0.696963	−	0.696963i
$668$	−4.00000			−0.154765
$669$	−24.0000	+	24.0000i	−0.927894	+	0.927894i
$670$		0			0
$671$	−18.0000			−0.694882
$672$		−	16.0000i		−	0.617213i
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−18.0000	−	18.0000i	−0.693334	−	0.693334i
$675$		0			0
$676$	−22.0000			−0.846154
$677$	−3.00000	−	3.00000i	−0.115299	−	0.115299i	0.647103	−	0.762402i	$-0.275980\pi$
$677$	−3.00000	−	3.00000i	−0.115299	−	0.115299i	−0.762402	+	0.647103i	$0.775980\pi$
$678$	12.0000			0.460857
$679$			4.00000i			0.153506i
$680$		0			0
$681$			30.0000i			1.14960i
$682$		−	16.0000i		−	0.612672i
$683$	−5.00000	−	5.00000i	−0.191320	−	0.191320i	0.604946	−	0.796266i	$-0.293195\pi$
$683$	−5.00000	−	5.00000i	−0.191320	−	0.191320i	−0.796266	+	0.604946i	$0.793195\pi$
$684$	−6.00000	+	6.00000i	−0.229416	+	0.229416i
$685$		0			0
$686$	−20.0000	+	20.0000i	−0.763604	+	0.763604i
$687$	14.0000			0.534133
$688$	20.0000	+	20.0000i	0.762493	+	0.762493i
$689$	10.0000			0.380970
$690$		0			0
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	−0.857260	−	0.514884i	$-0.827835\pi$
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	0.514884	+	0.857260i	$0.327835\pi$
$692$	2.00000	+	2.00000i	0.0760286	+	0.0760286i
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$		−	26.0000i		−	0.986947i
$695$		0			0
$696$	12.0000	+	12.0000i	0.454859	+	0.454859i
$697$		0			0
$698$	6.00000			0.227103
$699$	4.00000	+	4.00000i	0.151294	+	0.151294i
$700$		0			0
$701$	31.0000	−	31.0000i	1.17085	−	1.17085i	0.188847	−	0.982006i	$-0.439525\pi$
$701$	31.0000	−	31.0000i	1.17085	−	1.17085i	0.982006	−	0.188847i	$-0.0604752\pi$
$702$	8.00000	+	8.00000i	0.301941	+	0.301941i
$703$	−18.0000			−0.678883
$704$	8.00000	−	8.00000i	0.301511	−	0.301511i
$705$		0			0
$706$	6.00000	+	6.00000i	0.225813	+	0.225813i
$707$	−22.0000	+	22.0000i	−0.827395	+	0.827395i
$708$		−	12.0000i		−	0.450988i
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.999901	+	0.0141058i	$0.00449016\pi$
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.0141058	+	0.999901i	$0.495510\pi$
$710$		0			0
$711$		0			0
$712$	−8.00000	−	8.00000i	−0.299813	−	0.299813i
$713$			48.0000i			1.79761i
$714$			8.00000i			0.299392i
$715$		0			0
$716$	−34.0000	−	34.0000i	−1.27064	−	1.27064i
$717$		0			0
$718$	26.0000	−	26.0000i	0.970311	−	0.970311i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−1.00000	+	1.00000i	−0.0372161	+	0.0372161i
$723$	−18.0000	+	18.0000i	−0.669427	+	0.669427i
$724$	18.0000	−	18.0000i	0.668965	−	0.668965i
$725$		0			0
$726$		−	18.0000i		−	0.668043i
$727$			2.00000i			0.0741759i	0.999312	+	0.0370879i	$0.0118082\pi$
$727$			2.00000i			0.0741759i	−0.999312	+	0.0370879i	$0.988192\pi$
$728$	−8.00000			−0.296500
$729$			29.0000i			1.07407i
$730$		0			0
$731$	−10.0000	−	10.0000i	−0.369863	−	0.369863i
$732$	−36.0000			−1.33060
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	−0.203436	−	0.979088i	$-0.565211\pi$
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	0.979088	+	0.203436i	$0.0652108\pi$
$734$	−8.00000	−	8.00000i	−0.295285	−	0.295285i
$735$		0			0
$736$	−24.0000	+	24.0000i	−0.884652	+	0.884652i
$737$	10.0000			0.368355
$738$		0			0
$739$	23.0000	−	23.0000i	0.846069	−	0.846069i	−0.143571	−	0.989640i	$-0.545859\pi$
$739$	23.0000	−	23.0000i	0.846069	−	0.846069i	0.989640	+	0.143571i	$0.0458586\pi$
$740$		0			0
$741$	−6.00000	−	6.00000i	−0.220416	−	0.220416i
$742$	−20.0000			−0.734223
$743$		−	46.0000i		−	1.68758i	−0.536676	−	0.843788i	$-0.680320\pi$
$743$		−	46.0000i		−	1.68758i	0.536676	−	0.843788i	$-0.319680\pi$
$744$		−	32.0000i		−	1.17318i
$745$		0			0
$746$			10.0000i			0.366126i
$747$	1.00000	+	1.00000i	0.0365881	+	0.0365881i
$748$	−4.00000	+	4.00000i	−0.146254	+	0.146254i
$749$	−14.0000	+	14.0000i	−0.511549	+	0.511549i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	32.0000			1.16692
$753$	42.0000			1.53057
$754$	6.00000	−	6.00000i	0.218507	−	0.218507i
$755$		0			0
$756$	−16.0000	−	16.0000i	−0.581914	−	0.581914i
$757$	−23.0000	−	23.0000i	−0.835949	−	0.835949i	0.152374	−	0.988323i	$-0.451308\pi$
$757$	−23.0000	−	23.0000i	−0.835949	−	0.835949i	−0.988323	+	0.152374i	$0.951308\pi$
$758$		−	6.00000i		−	0.217930i
$759$		−	12.0000i		−	0.435572i
$760$		0			0
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	−16.0000			−0.579619
$763$	6.00000	+	6.00000i	0.217215	+	0.217215i
$764$		−	16.0000i		−	0.578860i
$765$		0			0
$766$	16.0000	+	16.0000i	0.578103	+	0.578103i
$767$	−6.00000			−0.216647
$768$	16.0000	−	16.0000i	0.577350	−	0.577350i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	22.0000	−	22.0000i	0.792311	−	0.792311i
$772$		−	28.0000i		−	1.00774i
$773$	5.00000	+	5.00000i	0.179838	+	0.179838i	0.791285	−	0.611448i	$-0.209412\pi$
$773$	5.00000	+	5.00000i	0.179838	+	0.179838i	−0.611448	+	0.791285i	$0.709412\pi$
$774$	10.0000			0.359443
$775$		0			0
$776$	−4.00000	+	4.00000i	−0.143592	+	0.143592i
$777$		−	12.0000i		−	0.430498i
$778$		−	26.0000i		−	0.932145i
$779$		0			0
$780$		0			0
$781$	10.0000	−	10.0000i	0.357828	−	0.357828i
$782$	12.0000	−	12.0000i	0.429119	−	0.429119i
$783$	24.0000			0.857690
$784$	−12.0000			−0.428571
$785$		0			0
$786$	22.0000	−	22.0000i	0.784714	−	0.784714i
$787$	−15.0000	+	15.0000i	−0.534692	+	0.534692i	−0.921965	−	0.387273i	$-0.873417\pi$
$787$	−15.0000	+	15.0000i	−0.534692	+	0.534692i	0.387273	+	0.921965i	$0.373417\pi$
$788$	−34.0000	+	34.0000i	−1.21120	+	1.21120i
$789$	−6.00000	−	6.00000i	−0.213606	−	0.213606i
$790$		0			0
$791$			12.0000i			0.426671i
$792$		−	4.00000i		−	0.142134i
$793$			18.0000i			0.639199i
$794$	10.0000			0.354887
$795$		0			0
$796$	−28.0000			−0.992434
$797$	25.0000	−	25.0000i	0.885545	−	0.885545i	−0.108546	−	0.994091i	$-0.534619\pi$
$797$	25.0000	−	25.0000i	0.885545	−	0.885545i	0.994091	+	0.108546i	$0.0346195\pi$
$798$	12.0000	+	12.0000i	0.424795	+	0.424795i
$799$	−16.0000			−0.566039
$800$		0			0
$801$	−4.00000			−0.141333
$802$	−18.0000	−	18.0000i	−0.635602	−	0.635602i
$803$	−4.00000	+	4.00000i	−0.141157	+	0.141157i
$804$	20.0000			0.705346
$805$		0			0
$806$	−16.0000			−0.563576
$807$		−	6.00000i		−	0.211210i
$808$	−44.0000			−1.54791
$809$		−	16.0000i		−	0.562530i	−0.959630	−	0.281265i	$-0.909246\pi$
$809$		−	16.0000i		−	0.562530i	0.959630	−	0.281265i	$-0.0907540\pi$
$810$		0			0
$811$	−39.0000	−	39.0000i	−1.36948	−	1.36948i	−0.861187	−	0.508288i	$-0.830278\pi$
$811$	−39.0000	−	39.0000i	−1.36948	−	1.36948i	−0.508288	−	0.861187i	$-0.669722\pi$
$812$	−12.0000	+	12.0000i	−0.421117	+	0.421117i
$813$	−8.00000	+	8.00000i	−0.280572	+	0.280572i
$814$	6.00000	−	6.00000i	0.210300	−	0.210300i
$815$		0			0
$816$	−8.00000	+	8.00000i	−0.280056	+	0.280056i
$817$	−30.0000			−1.04957
$818$	16.0000	−	16.0000i	0.559427	−	0.559427i
$819$	−2.00000	+	2.00000i	−0.0698857	+	0.0698857i
$820$		0			0
$821$	11.0000	+	11.0000i	0.383903	+	0.383903i	0.872506	−	0.488603i	$-0.162493\pi$
$821$	11.0000	+	11.0000i	0.383903	+	0.383903i	−0.488603	+	0.872506i	$0.662493\pi$
$822$		−	16.0000i		−	0.558064i
$823$			34.0000i			1.18517i	0.805510	+	0.592583i	$0.201892\pi$
$823$			34.0000i			1.18517i	−0.805510	+	0.592583i	$0.798108\pi$
$824$	12.0000	+	12.0000i	0.418040	+	0.418040i
$825$		0			0
$826$	12.0000			0.417533
$827$	−33.0000	−	33.0000i	−1.14752	−	1.14752i	−0.987038	−	0.160484i	$-0.948695\pi$
$827$	−33.0000	−	33.0000i	−1.14752	−	1.14752i	−0.160484	−	0.987038i	$-0.551305\pi$
$828$			12.0000i			0.417029i
$829$	23.0000	−	23.0000i	0.798823	−	0.798823i	−0.184087	−	0.982910i	$-0.558933\pi$
$829$	23.0000	−	23.0000i	0.798823	−	0.798823i	0.982910	+	0.184087i	$0.0589328\pi$
$830$		0			0
$831$	−6.00000			−0.208138
$832$	−8.00000	−	8.00000i	−0.277350	−	0.277350i
$833$	6.00000			0.207888
$834$	−6.00000	−	6.00000i	−0.207763	−	0.207763i
$835$		0			0
$836$			12.0000i			0.415029i
$837$	−32.0000	−	32.0000i	−1.10608	−	1.10608i
$838$	6.00000			0.207267
$839$			14.0000i			0.483334i	0.970359	+	0.241667i	$0.0776941\pi$
$839$			14.0000i			0.483334i	−0.970359	+	0.241667i	$0.922306\pi$
$840$		0			0
$841$			11.0000i			0.379310i
$842$		−	18.0000i		−	0.620321i
$843$	−20.0000	−	20.0000i	−0.688837	−	0.688837i
$844$	−18.0000	−	18.0000i	−0.619586	−	0.619586i
$845$		0			0
$846$	8.00000	−	8.00000i	0.275046	−	0.275046i
$847$	18.0000			0.618487
$848$	−20.0000	−	20.0000i	−0.686803	−	0.686803i
$849$	30.0000			1.02960
$850$		0			0
$851$	−18.0000	+	18.0000i	−0.617032	+	0.617032i
$852$	20.0000	−	20.0000i	0.685189	−	0.685189i
$853$	5.00000	+	5.00000i	0.171197	+	0.171197i	0.787505	−	0.616308i	$-0.211372\pi$
$853$	5.00000	+	5.00000i	0.171197	+	0.171197i	−0.616308	+	0.787505i	$0.711372\pi$
$854$		−	36.0000i		−	1.23189i
$855$		0			0
$856$	−28.0000			−0.957020
$857$		−	8.00000i		−	0.273275i	−0.990621	−	0.136637i	$-0.956370\pi$
$857$		−	8.00000i		−	0.273275i	0.990621	−	0.136637i	$-0.0436295\pi$
$858$	4.00000			0.136558
$859$	−3.00000	−	3.00000i	−0.102359	−	0.102359i	0.654073	−	0.756432i	$-0.273059\pi$
$859$	−3.00000	−	3.00000i	−0.102359	−	0.102359i	−0.756432	+	0.654073i	$0.773059\pi$
$860$		0			0
$861$		0			0
$862$	32.0000	+	32.0000i	1.08992	+	1.08992i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		−	32.0000i		−	1.08866i
$865$		0			0
$866$	−14.0000	−	14.0000i	−0.475739	−	0.475739i
$867$	−13.0000	+	13.0000i	−0.441503	+	0.441503i
$868$	32.0000			1.08615
$869$		0			0
$870$		0			0
$871$		−	10.0000i		−	0.338837i
$872$			12.0000i			0.406371i
$873$			2.00000i			0.0676897i
$874$		−	36.0000i		−	1.21772i
$875$		0			0
$876$	−8.00000	+	8.00000i	−0.270295	+	0.270295i
$877$	5.00000	−	5.00000i	0.168838	−	0.168838i	−0.617630	−	0.786468i	$-0.711907\pi$
$877$	5.00000	−	5.00000i	0.168838	−	0.168838i	0.786468	+	0.617630i	$0.211907\pi$
$878$	−14.0000	+	14.0000i	−0.472477	+	0.472477i
$879$	−30.0000			−1.01187
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	−3.00000	+	3.00000i	−0.101015	+	0.101015i
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	−0.259135	−	0.965841i	$-0.583437\pi$
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	0.965841	+	0.259135i	$0.0834374\pi$
$884$	4.00000	+	4.00000i	0.134535	+	0.134535i
$885$		0			0
$886$			30.0000i			1.00787i
$887$			2.00000i			0.0671534i	0.999436	+	0.0335767i	$0.0106898\pi$
$887$			2.00000i			0.0671534i	−0.999436	+	0.0335767i	$0.989310\pi$
$888$	12.0000	−	12.0000i	0.402694	−	0.402694i
$889$		−	16.0000i		−	0.536623i
$890$		0			0
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$		−	48.0000i		−	1.60716i
$893$	−24.0000	+	24.0000i	−0.803129	+	0.803129i
$894$	14.0000	+	14.0000i	0.468230	+	0.468230i
$895$		0			0
$896$	16.0000	+	16.0000i	0.534522	+	0.534522i
$897$	−12.0000			−0.400668
$898$	30.0000	+	30.0000i	1.00111	+	1.00111i
$899$	−24.0000	+	24.0000i	−0.800445	+	0.800445i
$900$		0			0
$901$	10.0000	+	10.0000i	0.333148	+	0.333148i
$902$		0			0
$903$		−	20.0000i		−	0.665558i
$904$	−12.0000	+	12.0000i	−0.399114	+	0.399114i
$905$		0			0
$906$		−	20.0000i		−	0.664455i
$907$	27.0000	+	27.0000i	0.896520	+	0.896520i	0.995127	−	0.0986062i	$-0.0314384\pi$
$907$	27.0000	+	27.0000i	0.896520	+	0.896520i	−0.0986062	+	0.995127i	$0.531438\pi$
$908$	−30.0000	−	30.0000i	−0.995585	−	0.995585i
$909$	−11.0000	+	11.0000i	−0.364847	+	0.364847i
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$			24.0000i			0.794719i
$913$	2.00000			0.0661903
$914$	−32.0000	+	32.0000i	−1.05847	+	1.05847i
$915$		0			0
$916$	−14.0000	+	14.0000i	−0.462573	+	0.462573i
$917$	22.0000	+	22.0000i	0.726504	+	0.726504i
$918$			16.0000i			0.528079i
$919$		−	26.0000i		−	0.857661i	−0.903385	−	0.428830i	$-0.858926\pi$
$919$		−	26.0000i		−	0.857661i	0.903385	−	0.428830i	$-0.141074\pi$
$920$		0			0
$921$		−	10.0000i		−	0.329511i
$922$	22.0000			0.724531
$923$	−10.0000	−	10.0000i	−0.329154	−	0.329154i
$924$	−8.00000			−0.263181
$925$		0			0
$926$	16.0000	+	16.0000i	0.525793	+	0.525793i
$927$	6.00000			0.197066
$928$	−24.0000			−0.787839
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$		0			0
$931$	9.00000	−	9.00000i	0.294963	−	0.294963i
$932$	−8.00000			−0.262049
$933$	30.0000	+	30.0000i	0.982156	+	0.982156i
$934$	10.0000			0.327210
$935$		0			0
$936$	−4.00000			−0.130744
$937$		−	28.0000i		−	0.914720i	−0.889282	−	0.457360i	$-0.848795\pi$
$937$		−	28.0000i		−	0.914720i	0.889282	−	0.457360i	$-0.151205\pi$
$938$			20.0000i			0.653023i
$939$	−16.0000	−	16.0000i	−0.522140	−	0.522140i
$940$		0			0
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	−0.998583	−	0.0532103i	$-0.983055\pi$
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	0.0532103	+	0.998583i	$0.483055\pi$
$942$	−30.0000	+	30.0000i	−0.977453	+	0.977453i
$943$		0			0
$944$	12.0000	+	12.0000i	0.390567	+	0.390567i
$945$		0			0
$946$	10.0000	−	10.0000i	0.325128	−	0.325128i
$947$	5.00000	−	5.00000i	0.162478	−	0.162478i	−0.621185	−	0.783664i	$-0.713349\pi$
$947$	5.00000	−	5.00000i	0.162478	−	0.162478i	0.783664	+	0.621185i	$0.213349\pi$
$948$		0			0
$949$	4.00000	+	4.00000i	0.129845	+	0.129845i
$950$		0			0
$951$		−	10.0000i		−	0.324272i
$952$	−8.00000	−	8.00000i	−0.259281	−	0.259281i
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$	−10.0000			−0.323762
$955$		0			0
$956$		0			0
$957$	6.00000	−	6.00000i	0.193952	−	0.193952i
$958$	−40.0000	−	40.0000i	−1.29234	−	1.29234i
$959$	16.0000			0.516667
$960$		0			0
$961$	33.0000			1.06452
$962$	−6.00000	−	6.00000i	−0.193448	−	0.193448i
$963$	−7.00000	+	7.00000i	−0.225572	+	0.225572i
$964$		−	36.0000i		−	1.15948i
$965$		0			0
$966$	24.0000			0.772187
$967$			2.00000i			0.0643157i	0.999483	+	0.0321578i	$0.0102379\pi$
$967$			2.00000i			0.0643157i	−0.999483	+	0.0321578i	$0.989762\pi$
$968$	18.0000	+	18.0000i	0.578542	+	0.578542i
$969$		−	12.0000i		−	0.385496i
$970$		0			0
$971$	−19.0000	−	19.0000i	−0.609739	−	0.609739i	0.333139	−	0.942878i	$-0.391892\pi$
$971$	−19.0000	−	19.0000i	−0.609739	−	0.609739i	−0.942878	+	0.333139i	$0.891892\pi$
$972$	−14.0000	−	14.0000i	−0.449050	−	0.449050i
$973$	6.00000	−	6.00000i	0.192351	−	0.192351i
$974$	−2.00000	+	2.00000i	−0.0640841	+	0.0640841i
$975$		0			0
$976$	36.0000	−	36.0000i	1.15233	−	1.15233i
$977$	2.00000			0.0639857			0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000			0.0639857			0.0319928	+	0.999488i	$0.489815\pi$
$978$	2.00000	−	2.00000i	0.0639529	−	0.0639529i
$979$	−4.00000	+	4.00000i	−0.127841	+	0.127841i
$980$		0			0
$981$	3.00000	+	3.00000i	0.0957826	+	0.0957826i
$982$		−	38.0000i		−	1.21263i
$983$			34.0000i			1.08443i	0.840239	+	0.542216i	$0.182414\pi$
$983$			34.0000i			1.08443i	−0.840239	+	0.542216i	$0.817586\pi$
$984$		0			0
$985$		0			0
$986$	12.0000			0.382158
$987$	−16.0000	−	16.0000i	−0.509286	−	0.509286i
$988$	12.0000			0.381771
$989$	−30.0000	+	30.0000i	−0.953945	+	0.953945i
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$	32.0000	+	32.0000i	1.01600	+	1.01600i
$993$	2.00000			0.0634681
$994$	20.0000	+	20.0000i	0.634361	+	0.634361i
$995$		0			0
$996$	4.00000			0.126745
$997$	37.0000	+	37.0000i	1.17180	+	1.17180i	0.981780	+	0.190022i	$0.0608559\pi$
$997$	37.0000	+	37.0000i	1.17180	+	1.17180i	0.190022	+	0.981780i	$0.439144\pi$
$998$	46.0000			1.45610
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.c.101.1		2
4.3	odd	2		1600.2.l.a.1201.1		2
5.2	odd	4		400.2.q.a.149.1		2
5.3	odd	4		400.2.q.b.149.1		2
5.4	even	2		16.2.e.a.5.1	✓	2
15.14	odd	2		144.2.k.a.37.1		2
16.3	odd	4		1600.2.l.a.401.1		2
16.13	even	4	inner	400.2.l.c.301.1		2
20.3	even	4		1600.2.q.a.49.1		2
20.7	even	4		1600.2.q.b.49.1		2
20.19	odd	2		64.2.e.a.49.1		2
35.4	even	6		784.2.x.f.373.1		4
35.9	even	6		784.2.x.f.165.1		4
35.19	odd	6		784.2.x.c.165.1		4
35.24	odd	6		784.2.x.c.373.1		4
35.34	odd	2		784.2.m.b.197.1		2
40.19	odd	2		128.2.e.a.97.1		2
40.29	even	2		128.2.e.b.97.1		2
60.59	even	2		576.2.k.a.433.1		2
80.3	even	4		1600.2.q.b.849.1		2
80.13	odd	4		400.2.q.a.349.1		2
80.19	odd	4		64.2.e.a.17.1		2
80.29	even	4		16.2.e.a.13.1	yes	2
80.59	odd	4		128.2.e.a.33.1		2
80.67	even	4		1600.2.q.a.849.1		2
80.69	even	4		128.2.e.b.33.1		2
80.77	odd	4		400.2.q.b.349.1		2
120.29	odd	2		1152.2.k.b.865.1		2
120.59	even	2		1152.2.k.a.865.1		2
160.19	odd	8		1024.2.a.e.1.1		2
160.29	even	8		1024.2.a.b.1.1		2
160.59	odd	8		1024.2.b.b.513.2		2
160.69	even	8		1024.2.b.e.513.1		2
160.99	odd	8		1024.2.a.e.1.2		2
160.109	even	8		1024.2.a.b.1.2		2
160.139	odd	8		1024.2.b.b.513.1		2
160.149	even	8		1024.2.b.e.513.2		2
240.29	odd	4		144.2.k.a.109.1		2
240.59	even	4		1152.2.k.a.289.1		2
240.149	odd	4		1152.2.k.b.289.1		2
240.179	even	4		576.2.k.a.145.1		2
480.29	odd	8		9216.2.a.d.1.1		2
480.179	even	8		9216.2.a.s.1.2		2
480.269	odd	8		9216.2.a.d.1.2		2
480.419	even	8		9216.2.a.s.1.1		2
560.109	even	12		784.2.x.f.765.1		4
560.269	odd	12		784.2.x.c.765.1		4
560.349	odd	4		784.2.m.b.589.1		2
560.429	even	12		784.2.x.f.557.1		4
560.509	odd	12		784.2.x.c.557.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.2.e.a.5.1	✓	2	5.4	even	2
16.2.e.a.13.1	yes	2	80.29	even	4
64.2.e.a.17.1		2	80.19	odd	4
64.2.e.a.49.1		2	20.19	odd	2
128.2.e.a.33.1		2	80.59	odd	4
128.2.e.a.97.1		2	40.19	odd	2
128.2.e.b.33.1		2	80.69	even	4
128.2.e.b.97.1		2	40.29	even	2
144.2.k.a.37.1		2	15.14	odd	2
144.2.k.a.109.1		2	240.29	odd	4
400.2.l.c.101.1		2	1.1	even	1	trivial
400.2.l.c.301.1		2	16.13	even	4	inner
400.2.q.a.149.1		2	5.2	odd	4
400.2.q.a.349.1		2	80.13	odd	4
400.2.q.b.149.1		2	5.3	odd	4
400.2.q.b.349.1		2	80.77	odd	4
576.2.k.a.145.1		2	240.179	even	4
576.2.k.a.433.1		2	60.59	even	2
784.2.m.b.197.1		2	35.34	odd	2
784.2.m.b.589.1		2	560.349	odd	4
784.2.x.c.165.1		4	35.19	odd	6
784.2.x.c.373.1		4	35.24	odd	6
784.2.x.c.557.1		4	560.509	odd	12
784.2.x.c.765.1		4	560.269	odd	12
784.2.x.f.165.1		4	35.9	even	6
784.2.x.f.373.1		4	35.4	even	6
784.2.x.f.557.1		4	560.429	even	12
784.2.x.f.765.1		4	560.109	even	12
1024.2.a.b.1.1		2	160.29	even	8
1024.2.a.b.1.2		2	160.109	even	8
1024.2.a.e.1.1		2	160.19	odd	8
1024.2.a.e.1.2		2	160.99	odd	8
1024.2.b.b.513.1		2	160.139	odd	8
1024.2.b.b.513.2		2	160.59	odd	8
1024.2.b.e.513.1		2	160.69	even	8
1024.2.b.e.513.2		2	160.149	even	8
1152.2.k.a.289.1		2	240.59	even	4
1152.2.k.a.865.1		2	120.59	even	2
1152.2.k.b.289.1		2	240.149	odd	4
1152.2.k.b.865.1		2	120.29	odd	2
1600.2.l.a.401.1		2	16.3	odd	4
1600.2.l.a.1201.1		2	4.3	odd	2
1600.2.q.a.49.1		2	20.3	even	4
1600.2.q.a.849.1		2	80.67	even	4
1600.2.q.b.49.1		2	20.7	even	4
1600.2.q.b.849.1		2	80.3	even	4
9216.2.a.d.1.1		2	480.29	odd	8
9216.2.a.d.1.2		2	480.269	odd	8
9216.2.a.s.1.1		2	480.419	even	8
9216.2.a.s.1.2		2	480.179	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +2.00000i q^{4} +2.00000 q^{6} +2.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +2.00000i q^{4} +2.00000 q^{6} +2.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{12} +(1.00000 - 1.00000i) q^{13} +(-2.00000 + 2.00000i) q^{14} -4.00000 q^{16} +2.00000 q^{17} +(-1.00000 + 1.00000i) q^{18} +(3.00000 - 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +2.00000i q^{22} -6.00000i q^{23} +4.00000i q^{24} +2.00000 q^{26} +(4.00000 + 4.00000i) q^{27} -4.00000 q^{28} +(3.00000 - 3.00000i) q^{29} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +2.00000 q^{33} +(2.00000 + 2.00000i) q^{34} -2.00000 q^{36} +(-3.00000 - 3.00000i) q^{37} +6.00000 q^{38} -2.00000i q^{39} +4.00000i q^{42} +(-5.00000 - 5.00000i) q^{43} +(-2.00000 + 2.00000i) q^{44} +(6.00000 - 6.00000i) q^{46} -8.00000 q^{47} +(-4.00000 + 4.00000i) q^{48} +3.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(2.00000 + 2.00000i) q^{52} +(5.00000 + 5.00000i) q^{53} +8.00000i q^{54} +(-4.00000 - 4.00000i) q^{56} -6.00000i q^{57} +6.00000 q^{58} +(-3.00000 - 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} +(-8.00000 - 8.00000i) q^{62} -2.00000 q^{63} -8.00000i q^{64} +(2.00000 + 2.00000i) q^{66} +(5.00000 - 5.00000i) q^{67} +4.00000i q^{68} +(-6.00000 - 6.00000i) q^{69} -10.0000i q^{71} +(-2.00000 - 2.00000i) q^{72} +4.00000i q^{73} -6.00000i q^{74} +(6.00000 + 6.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +(2.00000 - 2.00000i) q^{78} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{83} +(-4.00000 + 4.00000i) q^{84} -10.0000i q^{86} -6.00000i q^{87} -4.00000 q^{88} +4.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +12.0000 q^{92} +(-8.00000 + 8.00000i) q^{93} +(-8.00000 - 8.00000i) q^{94} -8.00000 q^{96} +2.00000 q^{97} +(3.00000 + 3.00000i) q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^6 - 4 * q^8	\( 2 q + 2 q^{2} + 2 q^{3} + 4 q^{6} - 4 q^{8} + 2 q^{11} + 4 q^{12} + 2 q^{13} - 4 q^{14} - 8 q^{16} + 4 q^{17} - 2 q^{18} + 6 q^{19} + 4 q^{21} + 4 q^{26} + 8 q^{27} - 8 q^{28} + 6 q^{29} - 16 q^{31} - 8 q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{36} - 6 q^{37} + 12 q^{38} - 10 q^{43} - 4 q^{44} + 12 q^{46} - 16 q^{47} - 8 q^{48} + 6 q^{49} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 8 q^{56} + 12 q^{58} - 6 q^{59} - 18 q^{61} - 16 q^{62} - 4 q^{63} + 4 q^{66} + 10 q^{67} - 12 q^{69} - 4 q^{72} + 12 q^{76} - 4 q^{77} + 4 q^{78} + 10 q^{81} + 2 q^{83} - 8 q^{84} - 8 q^{88} + 4 q^{91} + 24 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{96} + 4 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^6 - 4 * q^8 + 2 * q^11 + 4 * q^12 + 2 * q^13 - 4 * q^14 - 8 * q^16 + 4 * q^17 - 2 * q^18 + 6 * q^19 + 4 * q^21 + 4 * q^26 + 8 * q^27 - 8 * q^28 + 6 * q^29 - 16 * q^31 - 8 * q^32 + 4 * q^33 + 4 * q^34 - 4 * q^36 - 6 * q^37 + 12 * q^38 - 10 * q^43 - 4 * q^44 + 12 * q^46 - 16 * q^47 - 8 * q^48 + 6 * q^49 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 8 * q^56 + 12 * q^58 - 6 * q^59 - 18 * q^61 - 16 * q^62 - 4 * q^63 + 4 * q^66 + 10 * q^67 - 12 * q^69 - 4 * q^72 + 12 * q^76 - 4 * q^77 + 4 * q^78 + 10 * q^81 + 2 * q^83 - 8 * q^84 - 8 * q^88 + 4 * q^91 + 24 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^96 + 4 * q^97 + 6 * q^98 - 2 * q^99

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