LMFDB - Embedded newform 798.2.b.d.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(113,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("798.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.b (of order $2$, degree $1$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			113.2
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	798.113
Dual form			798.2.b.d.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.41421i q^{5} +(1.00000 + 1.41421i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.41421i q^{5} +(1.00000 + 1.41421i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.41421i q^{10} +2.82843i q^{11} +(1.00000 + 1.41421i) q^{12} +4.24264i q^{13} +1.00000 q^{14} +(2.00000 - 1.41421i) q^{15} +1.00000 q^{16} -5.65685i q^{17} +(-1.00000 + 2.82843i) q^{18} +(1.00000 + 4.24264i) q^{19} -1.41421i q^{20} +(1.00000 + 1.41421i) q^{21} +2.82843i q^{22} -1.41421i q^{23} +(1.00000 + 1.41421i) q^{24} +3.00000 q^{25} +4.24264i q^{26} +(-5.00000 + 1.41421i) q^{27} +1.00000 q^{28} +6.00000 q^{29} +(2.00000 - 1.41421i) q^{30} -4.24264i q^{31} +1.00000 q^{32} +(-4.00000 + 2.82843i) q^{33} -5.65685i q^{34} -1.41421i q^{35} +(-1.00000 + 2.82843i) q^{36} -4.24264i q^{37} +(1.00000 + 4.24264i) q^{38} +(-6.00000 + 4.24264i) q^{39} -1.41421i q^{40} +12.0000 q^{41} +(1.00000 + 1.41421i) q^{42} -10.0000 q^{43} +2.82843i q^{44} +(4.00000 + 1.41421i) q^{45} -1.41421i q^{46} -9.89949i q^{47} +(1.00000 + 1.41421i) q^{48} +1.00000 q^{49} +3.00000 q^{50} +(8.00000 - 5.65685i) q^{51} +4.24264i q^{52} -6.00000 q^{53} +(-5.00000 + 1.41421i) q^{54} +4.00000 q^{55} +1.00000 q^{56} +(-5.00000 + 5.65685i) q^{57} +6.00000 q^{58} -12.0000 q^{59} +(2.00000 - 1.41421i) q^{60} -10.0000 q^{61} -4.24264i q^{62} +(-1.00000 + 2.82843i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(-4.00000 + 2.82843i) q^{66} +8.48528i q^{67} -5.65685i q^{68} +(2.00000 - 1.41421i) q^{69} -1.41421i q^{70} +(-1.00000 + 2.82843i) q^{72} -16.0000 q^{73} -4.24264i q^{74} +(3.00000 + 4.24264i) q^{75} +(1.00000 + 4.24264i) q^{76} +2.82843i q^{77} +(-6.00000 + 4.24264i) q^{78} +4.24264i q^{79} -1.41421i q^{80} +(-7.00000 - 5.65685i) q^{81} +12.0000 q^{82} +2.82843i q^{83} +(1.00000 + 1.41421i) q^{84} -8.00000 q^{85} -10.0000 q^{86} +(6.00000 + 8.48528i) q^{87} +2.82843i q^{88} +6.00000 q^{89} +(4.00000 + 1.41421i) q^{90} +4.24264i q^{91} -1.41421i q^{92} +(6.00000 - 4.24264i) q^{93} -9.89949i q^{94} +(6.00000 - 1.41421i) q^{95} +(1.00000 + 1.41421i) q^{96} -16.9706i q^{97} +1.00000 q^{98} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{12} + 2 q^{14} + 4 q^{15} + 2 q^{16} - 2 q^{18} + 2 q^{19} + 2 q^{21} + 2 q^{24} + 6 q^{25} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 4 q^{30} + 2 q^{32} - 8 q^{33} - 2 q^{36} + 2 q^{38} - 12 q^{39} + 24 q^{41} + 2 q^{42} - 20 q^{43} + 8 q^{45} + 2 q^{48} + 2 q^{49} + 6 q^{50} + 16 q^{51} - 12 q^{53} - 10 q^{54} + 8 q^{55} + 2 q^{56} - 10 q^{57} + 12 q^{58} - 24 q^{59} + 4 q^{60} - 20 q^{61} - 2 q^{63} + 2 q^{64} + 12 q^{65} - 8 q^{66} + 4 q^{69} - 2 q^{72} - 32 q^{73} + 6 q^{75} + 2 q^{76} - 12 q^{78} - 14 q^{81} + 24 q^{82} + 2 q^{84} - 16 q^{85} - 20 q^{86} + 12 q^{87} + 12 q^{89} + 8 q^{90} + 12 q^{93} + 12 q^{95} + 2 q^{96} + 2 q^{98} - 16 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^12 + 2 * q^14 + 4 * q^15 + 2 * q^16 - 2 * q^18 + 2 * q^19 + 2 * q^21 + 2 * q^24 + 6 * q^25 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 4 * q^30 + 2 * q^32 - 8 * q^33 - 2 * q^36 + 2 * q^38 - 12 * q^39 + 24 * q^41 + 2 * q^42 - 20 * q^43 + 8 * q^45 + 2 * q^48 + 2 * q^49 + 6 * q^50 + 16 * q^51 - 12 * q^53 - 10 * q^54 + 8 * q^55 + 2 * q^56 - 10 * q^57 + 12 * q^58 - 24 * q^59 + 4 * q^60 - 20 * q^61 - 2 * q^63 + 2 * q^64 + 12 * q^65 - 8 * q^66 + 4 * q^69 - 2 * q^72 - 32 * q^73 + 6 * q^75 + 2 * q^76 - 12 * q^78 - 14 * q^81 + 24 * q^82 + 2 * q^84 - 16 * q^85 - 20 * q^86 + 12 * q^87 + 12 * q^89 + 8 * q^90 + 12 * q^93 + 12 * q^95 + 2 * q^96 + 2 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$-1$	$-1$

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			0.707107
$2$	1.00000			0.707107
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$	1.00000			0.500000
$5$		−	1.41421i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$		−	1.41421i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.00000			0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		−	1.41421i		−	0.447214i
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	1.00000	+	1.41421i	0.288675	+	0.408248i
$13$			4.24264i			1.17670i	0.808608	+	0.588348i	$0.200222\pi$
$13$			4.24264i			1.17670i	−0.808608	+	0.588348i	$0.799778\pi$
$14$	1.00000			0.267261
$15$	2.00000	−	1.41421i	0.516398	−	0.365148i
$16$	1.00000			0.250000
$17$		−	5.65685i		−	1.37199i	−0.727607	−	0.685994i	$-0.759367\pi$
$17$		−	5.65685i		−	1.37199i	0.727607	−	0.685994i	$-0.240633\pi$
$18$	−1.00000	+	2.82843i	−0.235702	+	0.666667i
$19$	1.00000	+	4.24264i	0.229416	+	0.973329i
$19$	1.00000	+	4.24264i	0.229416	+	0.973329i
$20$		−	1.41421i		−	0.316228i
$21$	1.00000	+	1.41421i	0.218218	+	0.308607i
$22$			2.82843i			0.603023i
$23$		−	1.41421i		−	0.294884i	−0.989071	−	0.147442i	$-0.952896\pi$
$23$		−	1.41421i		−	0.294884i	0.989071	−	0.147442i	$-0.0471040\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$	3.00000			0.600000
$26$			4.24264i			0.832050i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	1.00000			0.188982
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	2.00000	−	1.41421i	0.365148	−	0.258199i
$31$		−	4.24264i		−	0.762001i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$		−	4.24264i		−	0.762001i	0.924575	−	0.381000i	$-0.124420\pi$
$32$	1.00000			0.176777
$33$	−4.00000	+	2.82843i	−0.696311	+	0.492366i
$34$		−	5.65685i		−	0.970143i
$35$		−	1.41421i		−	0.239046i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		−	4.24264i		−	0.697486i	−0.937218	−	0.348743i	$-0.886609\pi$
$37$		−	4.24264i		−	0.697486i	0.937218	−	0.348743i	$-0.113391\pi$
$38$	1.00000	+	4.24264i	0.162221	+	0.688247i
$39$	−6.00000	+	4.24264i	−0.960769	+	0.679366i
$40$		−	1.41421i		−	0.223607i
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$	1.00000	+	1.41421i	0.154303	+	0.218218i
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$			2.82843i			0.426401i
$45$	4.00000	+	1.41421i	0.596285	+	0.210819i
$46$		−	1.41421i		−	0.208514i
$47$		−	9.89949i		−	1.44399i	−0.691898	−	0.721995i	$-0.743225\pi$
$47$		−	9.89949i		−	1.44399i	0.691898	−	0.721995i	$-0.256775\pi$
$48$	1.00000	+	1.41421i	0.144338	+	0.204124i
$49$	1.00000			0.142857
$50$	3.00000			0.424264
$51$	8.00000	−	5.65685i	1.12022	−	0.792118i
$52$			4.24264i			0.588348i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$	4.00000			0.539360
$56$	1.00000			0.133631
$57$	−5.00000	+	5.65685i	−0.662266	+	0.749269i
$58$	6.00000			0.787839
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$	2.00000	−	1.41421i	0.258199	−	0.182574i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$		−	4.24264i		−	0.538816i
$63$	−1.00000	+	2.82843i	−0.125988	+	0.356348i
$64$	1.00000			0.125000
$65$	6.00000			0.744208
$66$	−4.00000	+	2.82843i	−0.492366	+	0.348155i
$67$			8.48528i			1.03664i	0.855186	+	0.518321i	$0.173443\pi$
$67$			8.48528i			1.03664i	−0.855186	+	0.518321i	$0.826557\pi$
$68$		−	5.65685i		−	0.685994i
$69$	2.00000	−	1.41421i	0.240772	−	0.170251i
$70$		−	1.41421i		−	0.169031i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	−16.0000			−1.87266			−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000			−1.87266			−0.936329	+	0.351123i	$0.885800\pi$
$74$		−	4.24264i		−	0.493197i
$75$	3.00000	+	4.24264i	0.346410	+	0.489898i
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$			2.82843i			0.322329i
$78$	−6.00000	+	4.24264i	−0.679366	+	0.480384i
$79$			4.24264i			0.477334i	0.971101	+	0.238667i	$0.0767105\pi$
$79$			4.24264i			0.477334i	−0.971101	+	0.238667i	$0.923290\pi$
$80$		−	1.41421i		−	0.158114i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	12.0000			1.32518
$83$			2.82843i			0.310460i	0.987878	+	0.155230i	$0.0496119\pi$
$83$			2.82843i			0.310460i	−0.987878	+	0.155230i	$0.950388\pi$
$84$	1.00000	+	1.41421i	0.109109	+	0.154303i
$85$	−8.00000			−0.867722
$86$	−10.0000			−1.07833
$87$	6.00000	+	8.48528i	0.643268	+	0.909718i
$88$			2.82843i			0.301511i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	4.00000	+	1.41421i	0.421637	+	0.149071i
$91$			4.24264i			0.444750i
$92$		−	1.41421i		−	0.147442i
$93$	6.00000	−	4.24264i	0.622171	−	0.439941i
$94$		−	9.89949i		−	1.02105i
$95$	6.00000	−	1.41421i	0.615587	−	0.145095i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$		−	16.9706i		−	1.72310i	−0.507673	−	0.861550i	$-0.669494\pi$
$97$		−	16.9706i		−	1.72310i	0.507673	−	0.861550i	$-0.330506\pi$
$98$	1.00000			0.101015
$99$	−8.00000	−	2.82843i	−0.804030	−	0.284268i
$100$	3.00000			0.300000
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$	8.00000	−	5.65685i	0.792118	−	0.560112i
$103$		−	12.7279i		−	1.25412i	−0.778971	−	0.627060i	$-0.784258\pi$
$103$		−	12.7279i		−	1.25412i	0.778971	−	0.627060i	$-0.215742\pi$
$104$			4.24264i			0.416025i
$105$	2.00000	−	1.41421i	0.195180	−	0.138013i
$106$	−6.00000			−0.582772
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−5.00000	+	1.41421i	−0.481125	+	0.136083i
$109$			4.24264i			0.406371i	0.979140	+	0.203186i	$0.0651295\pi$
$109$			4.24264i			0.406371i	−0.979140	+	0.203186i	$0.934871\pi$
$110$	4.00000			0.381385
$111$	6.00000	−	4.24264i	0.569495	−	0.402694i
$112$	1.00000			0.0944911
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	−5.00000	+	5.65685i	−0.468293	+	0.529813i
$115$	−2.00000			−0.186501
$116$	6.00000			0.557086
$117$	−12.0000	−	4.24264i	−1.10940	−	0.392232i
$118$	−12.0000			−1.10469
$119$		−	5.65685i		−	0.518563i
$120$	2.00000	−	1.41421i	0.182574	−	0.129099i
$121$	3.00000			0.272727
$122$	−10.0000			−0.905357
$123$	12.0000	+	16.9706i	1.08200	+	1.53018i
$124$		−	4.24264i		−	0.381000i
$125$		−	11.3137i		−	1.01193i
$126$	−1.00000	+	2.82843i	−0.0890871	+	0.251976i
$127$			12.7279i			1.12942i	0.825289	+	0.564710i	$0.191012\pi$
$127$			12.7279i			1.12942i	−0.825289	+	0.564710i	$0.808988\pi$
$128$	1.00000			0.0883883
$129$	−10.0000	−	14.1421i	−0.880451	−	1.24515i
$130$	6.00000			0.526235
$131$		−	14.1421i		−	1.23560i	−0.786334	−	0.617802i	$-0.788023\pi$
$131$		−	14.1421i		−	1.23560i	0.786334	−	0.617802i	$-0.211977\pi$
$132$	−4.00000	+	2.82843i	−0.348155	+	0.246183i
$133$	1.00000	+	4.24264i	0.0867110	+	0.367884i
$134$			8.48528i			0.733017i
$135$	2.00000	+	7.07107i	0.172133	+	0.608581i
$136$		−	5.65685i		−	0.485071i
$137$			2.82843i			0.241649i	0.992674	+	0.120824i	$0.0385538\pi$
$137$			2.82843i			0.241649i	−0.992674	+	0.120824i	$0.961446\pi$
$138$	2.00000	−	1.41421i	0.170251	−	0.120386i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		−	1.41421i		−	0.119523i
$141$	14.0000	−	9.89949i	1.17901	−	0.833688i
$142$		0			0
$143$	−12.0000			−1.00349
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$		−	8.48528i		−	0.704664i
$146$	−16.0000			−1.32417
$147$	1.00000	+	1.41421i	0.0824786	+	0.116642i
$148$		−	4.24264i		−	0.348743i
$149$		−	1.41421i		−	0.115857i	−0.998321	−	0.0579284i	$-0.981550\pi$
$149$		−	1.41421i		−	0.115857i	0.998321	−	0.0579284i	$-0.0184495\pi$
$150$	3.00000	+	4.24264i	0.244949	+	0.346410i
$151$		−	12.7279i		−	1.03578i	−0.855446	−	0.517892i	$-0.826717\pi$
$151$		−	12.7279i		−	1.03578i	0.855446	−	0.517892i	$-0.173283\pi$
$152$	1.00000	+	4.24264i	0.0811107	+	0.344124i
$153$	16.0000	+	5.65685i	1.29352	+	0.457330i
$154$			2.82843i			0.227921i
$155$	−6.00000			−0.481932
$156$	−6.00000	+	4.24264i	−0.480384	+	0.339683i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$			4.24264i			0.337526i
$159$	−6.00000	−	8.48528i	−0.475831	−	0.672927i
$160$		−	1.41421i		−	0.111803i
$161$		−	1.41421i		−	0.111456i
$162$	−7.00000	−	5.65685i	−0.549972	−	0.444444i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	12.0000			0.937043
$165$	4.00000	+	5.65685i	0.311400	+	0.440386i
$166$			2.82843i			0.219529i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	1.00000	+	1.41421i	0.0771517	+	0.109109i
$169$	−5.00000			−0.384615
$170$	−8.00000			−0.613572
$171$	−13.0000	−	1.41421i	−0.994135	−	0.108148i
$172$	−10.0000			−0.762493
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	6.00000	+	8.48528i	0.454859	+	0.643268i
$175$	3.00000			0.226779
$176$			2.82843i			0.213201i
$177$	−12.0000	−	16.9706i	−0.901975	−	1.27559i
$178$	6.00000			0.449719
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$	4.00000	+	1.41421i	0.298142	+	0.105409i
$181$			12.7279i			0.946059i	0.881047	+	0.473029i	$0.156840\pi$
$181$			12.7279i			0.946059i	−0.881047	+	0.473029i	$0.843160\pi$
$182$			4.24264i			0.314485i
$183$	−10.0000	−	14.1421i	−0.739221	−	1.04542i
$184$		−	1.41421i		−	0.104257i
$185$	−6.00000			−0.441129
$186$	6.00000	−	4.24264i	0.439941	−	0.311086i
$187$	16.0000			1.17004
$188$		−	9.89949i		−	0.721995i
$189$	−5.00000	+	1.41421i	−0.363696	+	0.102869i
$190$	6.00000	−	1.41421i	0.435286	−	0.102598i
$191$			15.5563i			1.12562i	0.826587	+	0.562809i	$0.190279\pi$
$191$			15.5563i			1.12562i	−0.826587	+	0.562809i	$0.809721\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$			8.48528i			0.610784i	0.952227	+	0.305392i	$0.0987875\pi$
$193$			8.48528i			0.610784i	−0.952227	+	0.305392i	$0.901213\pi$
$194$		−	16.9706i		−	1.21842i
$195$	6.00000	+	8.48528i	0.429669	+	0.607644i
$196$	1.00000			0.0714286
$197$		−	18.3848i		−	1.30986i	−0.755689	−	0.654931i	$-0.772698\pi$
$197$		−	18.3848i		−	1.30986i	0.755689	−	0.654931i	$-0.227302\pi$
$198$	−8.00000	−	2.82843i	−0.568535	−	0.201008i
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	3.00000			0.212132
$201$	−12.0000	+	8.48528i	−0.846415	+	0.598506i
$202$		−	9.89949i		−	0.696526i
$203$	6.00000			0.421117
$204$	8.00000	−	5.65685i	0.560112	−	0.396059i
$205$		−	16.9706i		−	1.18528i
$206$		−	12.7279i		−	0.886796i
$207$	4.00000	+	1.41421i	0.278019	+	0.0982946i
$208$			4.24264i			0.294174i
$209$	−12.0000	+	2.82843i	−0.830057	+	0.195646i
$210$	2.00000	−	1.41421i	0.138013	−	0.0975900i
$211$			16.9706i			1.16830i	0.811645	+	0.584151i	$0.198572\pi$
$211$			16.9706i			1.16830i	−0.811645	+	0.584151i	$0.801428\pi$
$212$	−6.00000			−0.412082
$213$		0			0
$214$	−12.0000			−0.820303
$215$			14.1421i			0.964486i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$		−	4.24264i		−	0.288009i
$218$			4.24264i			0.287348i
$219$	−16.0000	−	22.6274i	−1.08118	−	1.52902i
$220$	4.00000			0.269680
$221$	24.0000			1.61441
$222$	6.00000	−	4.24264i	0.402694	−	0.284747i
$223$			21.2132i			1.42054i	0.703929	+	0.710271i	$0.251427\pi$
$223$			21.2132i			1.42054i	−0.703929	+	0.710271i	$0.748573\pi$
$224$	1.00000			0.0668153
$225$	−3.00000	+	8.48528i	−0.200000	+	0.565685i
$226$	12.0000			0.798228
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	−5.00000	+	5.65685i	−0.331133	+	0.374634i
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$	−2.00000			−0.131876
$231$	−4.00000	+	2.82843i	−0.263181	+	0.186097i
$232$	6.00000			0.393919
$233$		−	5.65685i		−	0.370593i	−0.982683	−	0.185296i	$-0.940675\pi$
$233$		−	5.65685i		−	0.370593i	0.982683	−	0.185296i	$-0.0593245\pi$
$234$	−12.0000	−	4.24264i	−0.784465	−	0.277350i
$235$	−14.0000			−0.913259
$236$	−12.0000			−0.781133
$237$	−6.00000	+	4.24264i	−0.389742	+	0.275589i
$238$		−	5.65685i		−	0.366679i
$239$		−	1.41421i		−	0.0914779i	−0.998953	−	0.0457389i	$-0.985436\pi$
$239$		−	1.41421i		−	0.0914779i	0.998953	−	0.0457389i	$-0.0145642\pi$
$240$	2.00000	−	1.41421i	0.129099	−	0.0912871i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	3.00000			0.192847
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$	−10.0000			−0.640184
$245$		−	1.41421i		−	0.0903508i
$246$	12.0000	+	16.9706i	0.765092	+	1.08200i
$247$	−18.0000	+	4.24264i	−1.14531	+	0.269953i
$248$		−	4.24264i		−	0.269408i
$249$	−4.00000	+	2.82843i	−0.253490	+	0.179244i
$250$		−	11.3137i		−	0.715542i
$251$			19.7990i			1.24970i	0.780744	+	0.624851i	$0.214840\pi$
$251$			19.7990i			1.24970i	−0.780744	+	0.624851i	$0.785160\pi$
$252$	−1.00000	+	2.82843i	−0.0629941	+	0.178174i
$253$	4.00000			0.251478
$254$			12.7279i			0.798621i
$255$	−8.00000	−	11.3137i	−0.500979	−	0.708492i
$256$	1.00000			0.0625000
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$	−10.0000	−	14.1421i	−0.622573	−	0.880451i
$259$		−	4.24264i		−	0.263625i
$260$	6.00000			0.372104
$261$	−6.00000	+	16.9706i	−0.371391	+	1.05045i
$262$		−	14.1421i		−	0.873704i
$263$			15.5563i			0.959246i	0.877475	+	0.479623i	$0.159226\pi$
$263$			15.5563i			0.959246i	−0.877475	+	0.479623i	$0.840774\pi$
$264$	−4.00000	+	2.82843i	−0.246183	+	0.174078i
$265$			8.48528i			0.521247i
$266$	1.00000	+	4.24264i	0.0613139	+	0.260133i
$267$	6.00000	+	8.48528i	0.367194	+	0.519291i
$268$			8.48528i			0.518321i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$	2.00000	+	7.07107i	0.121716	+	0.430331i
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$		−	5.65685i		−	0.342997i
$273$	−6.00000	+	4.24264i	−0.363137	+	0.256776i
$274$			2.82843i			0.170872i
$275$			8.48528i			0.511682i
$276$	2.00000	−	1.41421i	0.120386	−	0.0851257i
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	−4.00000			−0.239904
$279$	12.0000	+	4.24264i	0.718421	+	0.254000i
$280$		−	1.41421i		−	0.0845154i
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	14.0000	−	9.89949i	0.833688	−	0.589506i
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$		0			0
$285$	8.00000	+	7.07107i	0.473879	+	0.418854i
$286$	−12.0000			−0.709575
$287$	12.0000			0.708338
$288$	−1.00000	+	2.82843i	−0.0589256	+	0.166667i
$289$	−15.0000			−0.882353
$290$		−	8.48528i		−	0.498273i
$291$	24.0000	−	16.9706i	1.40690	−	0.994832i
$292$	−16.0000			−0.936329
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	1.00000	+	1.41421i	0.0583212	+	0.0824786i
$295$			16.9706i			0.988064i
$296$		−	4.24264i		−	0.246598i
$297$	−4.00000	−	14.1421i	−0.232104	−	0.820610i
$298$		−	1.41421i		−	0.0819232i
$299$	6.00000			0.346989
$300$	3.00000	+	4.24264i	0.173205	+	0.244949i
$301$	−10.0000			−0.576390
$302$		−	12.7279i		−	0.732410i
$303$	14.0000	−	9.89949i	0.804279	−	0.568711i
$304$	1.00000	+	4.24264i	0.0573539	+	0.243332i
$305$			14.1421i			0.809776i
$306$	16.0000	+	5.65685i	0.914659	+	0.323381i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$			2.82843i			0.161165i
$309$	18.0000	−	12.7279i	1.02398	−	0.724066i
$310$	−6.00000			−0.340777
$311$		−	26.8701i		−	1.52366i	−0.647776	−	0.761831i	$-0.724301\pi$
$311$		−	26.8701i		−	1.52366i	0.647776	−	0.761831i	$-0.275699\pi$
$312$	−6.00000	+	4.24264i	−0.339683	+	0.240192i
$313$	−28.0000			−1.58265			−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000			−1.58265			−0.791327	+	0.611393i	$0.790609\pi$
$314$	14.0000			0.790066
$315$	4.00000	+	1.41421i	0.225374	+	0.0796819i
$316$			4.24264i			0.238667i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	−6.00000	−	8.48528i	−0.336463	−	0.475831i
$319$			16.9706i			0.950169i
$320$		−	1.41421i		−	0.0790569i
$321$	−12.0000	−	16.9706i	−0.669775	−	0.947204i
$322$		−	1.41421i		−	0.0788110i
$323$	24.0000	−	5.65685i	1.33540	−	0.314756i
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$			12.7279i			0.706018i
$326$	20.0000			1.10770
$327$	−6.00000	+	4.24264i	−0.331801	+	0.234619i
$328$	12.0000			0.662589
$329$		−	9.89949i		−	0.545777i
$330$	4.00000	+	5.65685i	0.220193	+	0.311400i
$331$		−	8.48528i		−	0.466393i	−0.972430	−	0.233197i	$-0.925081\pi$
$331$		−	8.48528i		−	0.466393i	0.972430	−	0.233197i	$-0.0749186\pi$
$332$			2.82843i			0.155230i
$333$	12.0000	+	4.24264i	0.657596	+	0.232495i
$334$	12.0000			0.656611
$335$	12.0000			0.655630
$336$	1.00000	+	1.41421i	0.0545545	+	0.0771517i
$337$			16.9706i			0.924445i	0.886764	+	0.462223i	$0.152948\pi$
$337$			16.9706i			0.924445i	−0.886764	+	0.462223i	$0.847052\pi$
$338$	−5.00000			−0.271964
$339$	12.0000	+	16.9706i	0.651751	+	0.921714i
$340$	−8.00000			−0.433861
$341$	12.0000			0.649836
$342$	−13.0000	−	1.41421i	−0.702959	−	0.0764719i
$343$	1.00000			0.0539949
$344$	−10.0000			−0.539164
$345$	−2.00000	−	2.82843i	−0.107676	−	0.152277i
$346$	−6.00000			−0.322562
$347$		−	14.1421i		−	0.759190i	−0.925153	−	0.379595i	$-0.876063\pi$
$347$		−	14.1421i		−	0.759190i	0.925153	−	0.379595i	$-0.123937\pi$
$348$	6.00000	+	8.48528i	0.321634	+	0.454859i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	3.00000			0.160357
$351$	−6.00000	−	21.2132i	−0.320256	−	1.13228i
$352$			2.82843i			0.150756i
$353$			2.82843i			0.150542i	0.997163	+	0.0752710i	$0.0239822\pi$
$353$			2.82843i			0.150542i	−0.997163	+	0.0752710i	$0.976018\pi$
$354$	−12.0000	−	16.9706i	−0.637793	−	0.901975i
$355$		0			0
$356$	6.00000			0.317999
$357$	8.00000	−	5.65685i	0.423405	−	0.299392i
$358$	−6.00000			−0.317110
$359$			32.5269i			1.71670i	0.513061	+	0.858352i	$0.328512\pi$
$359$			32.5269i			1.71670i	−0.513061	+	0.858352i	$0.671488\pi$
$360$	4.00000	+	1.41421i	0.210819	+	0.0745356i
$361$	−17.0000	+	8.48528i	−0.894737	+	0.446594i
$362$			12.7279i			0.668965i
$363$	3.00000	+	4.24264i	0.157459	+	0.222681i
$364$			4.24264i			0.222375i
$365$			22.6274i			1.18437i
$366$	−10.0000	−	14.1421i	−0.522708	−	0.739221i
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$		−	1.41421i		−	0.0737210i
$369$	−12.0000	+	33.9411i	−0.624695	+	1.76690i
$370$	−6.00000			−0.311925
$371$	−6.00000			−0.311504
$372$	6.00000	−	4.24264i	0.311086	−	0.219971i
$373$		−	12.7279i		−	0.659027i	−0.944151	−	0.329513i	$-0.893115\pi$
$373$		−	12.7279i		−	0.659027i	0.944151	−	0.329513i	$-0.106885\pi$
$374$	16.0000			0.827340
$375$	16.0000	−	11.3137i	0.826236	−	0.584237i
$376$		−	9.89949i		−	0.510527i
$377$			25.4558i			1.31104i
$378$	−5.00000	+	1.41421i	−0.257172	+	0.0727393i
$379$			25.4558i			1.30758i	0.756677	+	0.653789i	$0.226822\pi$
$379$			25.4558i			1.30758i	−0.756677	+	0.653789i	$0.773178\pi$
$380$	6.00000	−	1.41421i	0.307794	−	0.0725476i
$381$	−18.0000	+	12.7279i	−0.922168	+	0.652071i
$382$			15.5563i			0.795932i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$	4.00000			0.203859
$386$			8.48528i			0.431889i
$387$	10.0000	−	28.2843i	0.508329	−	1.43777i
$388$		−	16.9706i		−	0.861550i
$389$		−	9.89949i		−	0.501924i	−0.967997	−	0.250962i	$-0.919253\pi$
$389$		−	9.89949i		−	0.501924i	0.967997	−	0.250962i	$-0.0807470\pi$
$390$	6.00000	+	8.48528i	0.303822	+	0.429669i
$391$	−8.00000			−0.404577
$392$	1.00000			0.0505076
$393$	20.0000	−	14.1421i	1.00887	−	0.713376i
$394$		−	18.3848i		−	0.926212i
$395$	6.00000			0.301893
$396$	−8.00000	−	2.82843i	−0.402015	−	0.142134i
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	20.0000			1.00251
$399$	−5.00000	+	5.65685i	−0.250313	+	0.283197i
$400$	3.00000			0.150000
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$	−12.0000	+	8.48528i	−0.598506	+	0.423207i
$403$	18.0000			0.896644
$404$		−	9.89949i		−	0.492518i
$405$	−8.00000	+	9.89949i	−0.397523	+	0.491910i
$406$	6.00000			0.297775
$407$	12.0000			0.594818
$408$	8.00000	−	5.65685i	0.396059	−	0.280056i
$409$		−	16.9706i		−	0.839140i	−0.907723	−	0.419570i	$-0.862181\pi$
$409$		−	16.9706i		−	0.839140i	0.907723	−	0.419570i	$-0.137819\pi$
$410$		−	16.9706i		−	0.838116i
$411$	−4.00000	+	2.82843i	−0.197305	+	0.139516i
$412$		−	12.7279i		−	0.627060i
$413$	−12.0000			−0.590481
$414$	4.00000	+	1.41421i	0.196589	+	0.0695048i
$415$	4.00000			0.196352
$416$			4.24264i			0.208013i
$417$	−4.00000	−	5.65685i	−0.195881	−	0.277017i
$418$	−12.0000	+	2.82843i	−0.586939	+	0.138343i
$419$			11.3137i			0.552711i	0.961056	+	0.276355i	$0.0891267\pi$
$419$			11.3137i			0.552711i	−0.961056	+	0.276355i	$0.910873\pi$
$420$	2.00000	−	1.41421i	0.0975900	−	0.0690066i
$421$		−	4.24264i		−	0.206774i	−0.994641	−	0.103387i	$-0.967032\pi$
$421$		−	4.24264i		−	0.206774i	0.994641	−	0.103387i	$-0.0329680\pi$
$422$			16.9706i			0.826114i
$423$	28.0000	+	9.89949i	1.36141	+	0.481330i
$424$	−6.00000			−0.291386
$425$		−	16.9706i		−	0.823193i
$426$		0			0
$427$	−10.0000			−0.483934
$428$	−12.0000			−0.580042
$429$	−12.0000	−	16.9706i	−0.579365	−	0.819346i
$430$			14.1421i			0.681994i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	−5.00000	+	1.41421i	−0.240563	+	0.0680414i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		−	4.24264i		−	0.203653i
$435$	12.0000	−	8.48528i	0.575356	−	0.406838i
$436$			4.24264i			0.203186i
$437$	6.00000	−	1.41421i	0.287019	−	0.0676510i
$438$	−16.0000	−	22.6274i	−0.764510	−	1.08118i
$439$		−	21.2132i		−	1.01245i	−0.862401	−	0.506225i	$-0.831040\pi$
$439$		−	21.2132i		−	1.01245i	0.862401	−	0.506225i	$-0.168960\pi$
$440$	4.00000			0.190693
$441$	−1.00000	+	2.82843i	−0.0476190	+	0.134687i
$442$	24.0000			1.14156
$443$			2.82843i			0.134383i	0.997740	+	0.0671913i	$0.0214038\pi$
$443$			2.82843i			0.134383i	−0.997740	+	0.0671913i	$0.978596\pi$
$444$	6.00000	−	4.24264i	0.284747	−	0.201347i
$445$		−	8.48528i		−	0.402241i
$446$			21.2132i			1.00447i
$447$	2.00000	−	1.41421i	0.0945968	−	0.0668900i
$448$	1.00000			0.0472456
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	−3.00000	+	8.48528i	−0.141421	+	0.400000i
$451$			33.9411i			1.59823i
$452$	12.0000			0.564433
$453$	18.0000	−	12.7279i	0.845714	−	0.598010i
$454$	−18.0000			−0.844782
$455$	6.00000			0.281284
$456$	−5.00000	+	5.65685i	−0.234146	+	0.264906i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	−22.0000			−1.02799
$459$	8.00000	+	28.2843i	0.373408	+	1.32020i
$460$	−2.00000			−0.0932505
$461$			15.5563i			0.724531i	0.932075	+	0.362266i	$0.117997\pi$
$461$			15.5563i			0.724531i	−0.932075	+	0.362266i	$0.882003\pi$
$462$	−4.00000	+	2.82843i	−0.186097	+	0.131590i
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	6.00000			0.278543
$465$	−6.00000	−	8.48528i	−0.278243	−	0.393496i
$466$		−	5.65685i		−	0.262049i
$467$		−	31.1127i		−	1.43972i	−0.694117	−	0.719862i	$-0.744205\pi$
$467$		−	31.1127i		−	1.43972i	0.694117	−	0.719862i	$-0.255795\pi$
$468$	−12.0000	−	4.24264i	−0.554700	−	0.196116i
$469$			8.48528i			0.391814i
$470$	−14.0000			−0.645772
$471$	14.0000	+	19.7990i	0.645086	+	0.912289i
$472$	−12.0000			−0.552345
$473$		−	28.2843i		−	1.30051i
$474$	−6.00000	+	4.24264i	−0.275589	+	0.194871i
$475$	3.00000	+	12.7279i	0.137649	+	0.583997i
$476$		−	5.65685i		−	0.259281i
$477$	6.00000	−	16.9706i	0.274721	−	0.777029i
$478$		−	1.41421i		−	0.0646846i
$479$			15.5563i			0.710788i	0.934717	+	0.355394i	$0.115653\pi$
$479$			15.5563i			0.710788i	−0.934717	+	0.355394i	$0.884347\pi$
$480$	2.00000	−	1.41421i	0.0912871	−	0.0645497i
$481$	18.0000			0.820729
$482$		0			0
$483$	2.00000	−	1.41421i	0.0910032	−	0.0643489i
$484$	3.00000			0.136364
$485$	−24.0000			−1.08978
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$			4.24264i			0.192252i	0.995369	+	0.0961262i	$0.0306452\pi$
$487$			4.24264i			0.192252i	−0.995369	+	0.0961262i	$0.969355\pi$
$488$	−10.0000			−0.452679
$489$	20.0000	+	28.2843i	0.904431	+	1.27906i
$490$		−	1.41421i		−	0.0638877i
$491$			11.3137i			0.510581i	0.966864	+	0.255290i	$0.0821710\pi$
$491$			11.3137i			0.510581i	−0.966864	+	0.255290i	$0.917829\pi$
$492$	12.0000	+	16.9706i	0.541002	+	0.765092i
$493$		−	33.9411i		−	1.52863i
$494$	−18.0000	+	4.24264i	−0.809858	+	0.190885i
$495$	−4.00000	+	11.3137i	−0.179787	+	0.508513i
$496$		−	4.24264i		−	0.190500i
$497$		0			0
$498$	−4.00000	+	2.82843i	−0.179244	+	0.126745i
$499$	−22.0000			−0.984855			−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000			−0.984855			−0.492428	+	0.870353i	$0.663890\pi$
$500$		−	11.3137i		−	0.505964i
$501$	12.0000	+	16.9706i	0.536120	+	0.758189i
$502$			19.7990i			0.883672i
$503$			32.5269i			1.45030i	0.688589	+	0.725152i	$0.258230\pi$
$503$			32.5269i			1.45030i	−0.688589	+	0.725152i	$0.741770\pi$
$504$	−1.00000	+	2.82843i	−0.0445435	+	0.125988i
$505$	−14.0000			−0.622992
$506$	4.00000			0.177822
$507$	−5.00000	−	7.07107i	−0.222058	−	0.314037i
$508$			12.7279i			0.564710i
$509$	−18.0000			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$510$	−8.00000	−	11.3137i	−0.354246	−	0.500979i
$511$	−16.0000			−0.707798
$512$	1.00000			0.0441942
$513$	−11.0000	−	19.7990i	−0.485662	−	0.874147i
$514$	−18.0000			−0.793946
$515$	−18.0000			−0.793175
$516$	−10.0000	−	14.1421i	−0.440225	−	0.622573i
$517$	28.0000			1.23144
$518$		−	4.24264i		−	0.186411i
$519$	−6.00000	−	8.48528i	−0.263371	−	0.372463i
$520$	6.00000			0.263117
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$	−6.00000	+	16.9706i	−0.262613	+	0.742781i
$523$			33.9411i			1.48414i	0.670321	+	0.742071i	$0.266156\pi$
$523$			33.9411i			1.48414i	−0.670321	+	0.742071i	$0.733844\pi$
$524$		−	14.1421i		−	0.617802i
$525$	3.00000	+	4.24264i	0.130931	+	0.185164i
$526$			15.5563i			0.678289i
$527$	−24.0000			−1.04546
$528$	−4.00000	+	2.82843i	−0.174078	+	0.123091i
$529$	21.0000			0.913043
$530$			8.48528i			0.368577i
$531$	12.0000	−	33.9411i	0.520756	−	1.47292i
$532$	1.00000	+	4.24264i	0.0433555	+	0.183942i
$533$			50.9117i			2.20523i
$534$	6.00000	+	8.48528i	0.259645	+	0.367194i
$535$			16.9706i			0.733701i
$536$			8.48528i			0.366508i
$537$	−6.00000	−	8.48528i	−0.258919	−	0.366167i
$538$	−6.00000			−0.258678
$539$			2.82843i			0.121829i
$540$	2.00000	+	7.07107i	0.0860663	+	0.304290i
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	20.0000			0.859074
$543$	−18.0000	+	12.7279i	−0.772454	+	0.546207i
$544$		−	5.65685i		−	0.242536i
$545$	6.00000			0.257012
$546$	−6.00000	+	4.24264i	−0.256776	+	0.181568i
$547$		−	42.4264i		−	1.81402i	−0.421107	−	0.907011i	$-0.638358\pi$
$547$		−	42.4264i		−	1.81402i	0.421107	−	0.907011i	$-0.361642\pi$
$548$			2.82843i			0.120824i
$549$	10.0000	−	28.2843i	0.426790	−	1.20714i
$550$			8.48528i			0.361814i
$551$	6.00000	+	25.4558i	0.255609	+	1.08446i
$552$	2.00000	−	1.41421i	0.0851257	−	0.0601929i
$553$			4.24264i			0.180415i
$554$	26.0000			1.10463
$555$	−6.00000	−	8.48528i	−0.254686	−	0.360180i
$556$	−4.00000			−0.169638
$557$			32.5269i			1.37821i	0.724662	+	0.689105i	$0.241996\pi$
$557$			32.5269i			1.37821i	−0.724662	+	0.689105i	$0.758004\pi$
$558$	12.0000	+	4.24264i	0.508001	+	0.179605i
$559$		−	42.4264i		−	1.79445i
$560$		−	1.41421i		−	0.0597614i
$561$	16.0000	+	22.6274i	0.675521	+	0.955330i
$562$	−12.0000			−0.506189
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$	14.0000	−	9.89949i	0.589506	−	0.416844i
$565$		−	16.9706i		−	0.713957i
$566$	−4.00000			−0.168133
$567$	−7.00000	−	5.65685i	−0.293972	−	0.237566i
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	8.00000	+	7.07107i	0.335083	+	0.296174i
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	−12.0000			−0.501745
$573$	−22.0000	+	15.5563i	−0.919063	+	0.649876i
$574$	12.0000			0.500870
$575$		−	4.24264i		−	0.176930i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	−15.0000			−0.623918
$579$	−12.0000	+	8.48528i	−0.498703	+	0.352636i
$580$		−	8.48528i		−	0.352332i
$581$			2.82843i			0.117343i
$582$	24.0000	−	16.9706i	0.994832	−	0.703452i
$583$		−	16.9706i		−	0.702849i
$584$	−16.0000			−0.662085
$585$	−6.00000	+	16.9706i	−0.248069	+	0.701646i
$586$	−6.00000			−0.247858
$587$			28.2843i			1.16742i	0.811963	+	0.583708i	$0.198399\pi$
$587$			28.2843i			1.16742i	−0.811963	+	0.583708i	$0.801601\pi$
$588$	1.00000	+	1.41421i	0.0412393	+	0.0583212i
$589$	18.0000	−	4.24264i	0.741677	−	0.174815i
$590$			16.9706i			0.698667i
$591$	26.0000	−	18.3848i	1.06950	−	0.756249i
$592$		−	4.24264i		−	0.174371i
$593$			19.7990i			0.813047i	0.913640	+	0.406524i	$0.133259\pi$
$593$			19.7990i			0.813047i	−0.913640	+	0.406524i	$0.866741\pi$
$594$	−4.00000	−	14.1421i	−0.164122	−	0.580259i
$595$	−8.00000			−0.327968
$596$		−	1.41421i		−	0.0579284i
$597$	20.0000	+	28.2843i	0.818546	+	1.15760i
$598$	6.00000			0.245358
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	3.00000	+	4.24264i	0.122474	+	0.173205i
$601$			8.48528i			0.346122i	0.984911	+	0.173061i	$0.0553658\pi$
$601$			8.48528i			0.346122i	−0.984911	+	0.173061i	$0.944634\pi$
$602$	−10.0000			−0.407570
$603$	−24.0000	−	8.48528i	−0.977356	−	0.345547i
$604$		−	12.7279i		−	0.517892i
$605$		−	4.24264i		−	0.172488i
$606$	14.0000	−	9.89949i	0.568711	−	0.402139i
$607$			12.7279i			0.516610i	0.966063	+	0.258305i	$0.0831640\pi$
$607$			12.7279i			0.516610i	−0.966063	+	0.258305i	$0.916836\pi$
$608$	1.00000	+	4.24264i	0.0405554	+	0.172062i
$609$	6.00000	+	8.48528i	0.243132	+	0.343841i
$610$			14.1421i			0.572598i
$611$	42.0000			1.69914
$612$	16.0000	+	5.65685i	0.646762	+	0.228665i
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$		0			0
$615$	24.0000	−	16.9706i	0.967773	−	0.684319i
$616$			2.82843i			0.113961i
$617$		−	39.5980i		−	1.59415i	−0.603877	−	0.797077i	$-0.706378\pi$
$617$		−	39.5980i		−	1.59415i	0.603877	−	0.797077i	$-0.293622\pi$
$618$	18.0000	−	12.7279i	0.724066	−	0.511992i
$619$	26.0000			1.04503			0.522514	−	0.852631i	$-0.324994\pi$
$619$	26.0000			1.04503			0.522514	+	0.852631i	$0.324994\pi$
$620$	−6.00000			−0.240966
$621$	2.00000	+	7.07107i	0.0802572	+	0.283752i
$622$		−	26.8701i		−	1.07739i
$623$	6.00000			0.240385
$624$	−6.00000	+	4.24264i	−0.240192	+	0.169842i
$625$	−1.00000			−0.0400000
$626$	−28.0000			−1.11911
$627$	−16.0000	−	14.1421i	−0.638978	−	0.564782i
$628$	14.0000			0.558661
$629$	−24.0000			−0.956943
$630$	4.00000	+	1.41421i	0.159364	+	0.0563436i
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$			4.24264i			0.168763i
$633$	−24.0000	+	16.9706i	−0.953914	+	0.674519i
$634$	−6.00000			−0.238290
$635$	18.0000			0.714308
$636$	−6.00000	−	8.48528i	−0.237915	−	0.336463i
$637$			4.24264i			0.168100i
$638$			16.9706i			0.671871i
$639$		0			0
$640$		−	1.41421i		−	0.0559017i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−12.0000	−	16.9706i	−0.473602	−	0.669775i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		−	1.41421i		−	0.0557278i
$645$	−20.0000	+	14.1421i	−0.787499	+	0.556846i
$646$	24.0000	−	5.65685i	0.944267	−	0.222566i
$647$		−	18.3848i		−	0.722780i	−0.932415	−	0.361390i	$-0.882302\pi$
$647$		−	18.3848i		−	0.722780i	0.932415	−	0.361390i	$-0.117698\pi$
$648$	−7.00000	−	5.65685i	−0.274986	−	0.222222i
$649$		−	33.9411i		−	1.33231i
$650$			12.7279i			0.499230i
$651$	6.00000	−	4.24264i	0.235159	−	0.166282i
$652$	20.0000			0.783260
$653$		−	26.8701i		−	1.05151i	−0.850637	−	0.525753i	$-0.823784\pi$
$653$		−	26.8701i		−	1.05151i	0.850637	−	0.525753i	$-0.176216\pi$
$654$	−6.00000	+	4.24264i	−0.234619	+	0.165900i
$655$	−20.0000			−0.781465
$656$	12.0000			0.468521
$657$	16.0000	−	45.2548i	0.624219	−	1.76556i
$658$		−	9.89949i		−	0.385922i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	4.00000	+	5.65685i	0.155700	+	0.220193i
$661$			21.2132i			0.825098i	0.910935	+	0.412549i	$0.135361\pi$
$661$			21.2132i			0.825098i	−0.910935	+	0.412549i	$0.864639\pi$
$662$		−	8.48528i		−	0.329790i
$663$	24.0000	+	33.9411i	0.932083	+	1.31816i
$664$			2.82843i			0.109764i
$665$	6.00000	−	1.41421i	0.232670	−	0.0548408i
$666$	12.0000	+	4.24264i	0.464991	+	0.164399i
$667$		−	8.48528i		−	0.328551i
$668$	12.0000			0.464294
$669$	−30.0000	+	21.2132i	−1.15987	+	0.820150i
$670$	12.0000			0.463600
$671$		−	28.2843i		−	1.09190i
$672$	1.00000	+	1.41421i	0.0385758	+	0.0545545i
$673$			8.48528i			0.327084i	0.986536	+	0.163542i	$0.0522919\pi$
$673$			8.48528i			0.327084i	−0.986536	+	0.163542i	$0.947708\pi$
$674$			16.9706i			0.653682i
$675$	−15.0000	+	4.24264i	−0.577350	+	0.163299i
$676$	−5.00000			−0.192308
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$	12.0000	+	16.9706i	0.460857	+	0.651751i
$679$		−	16.9706i		−	0.651270i
$680$	−8.00000			−0.306786
$681$	−18.0000	−	25.4558i	−0.689761	−	0.975470i
$682$	12.0000			0.459504
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$	−13.0000	−	1.41421i	−0.497067	−	0.0540738i
$685$	4.00000			0.152832
$686$	1.00000			0.0381802
$687$	−22.0000	−	31.1127i	−0.839352	−	1.18702i
$688$	−10.0000			−0.381246
$689$		−	25.4558i		−	0.969790i
$690$	−2.00000	−	2.82843i	−0.0761387	−	0.107676i
$691$	−10.0000			−0.380418			−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000			−0.380418			−0.190209	+	0.981744i	$0.560917\pi$
$692$	−6.00000			−0.228086
$693$	−8.00000	−	2.82843i	−0.303895	−	0.107443i
$694$		−	14.1421i		−	0.536828i
$695$			5.65685i			0.214577i
$696$	6.00000	+	8.48528i	0.227429	+	0.321634i
$697$		−	67.8823i		−	2.57122i
$698$	26.0000			0.984115
$699$	8.00000	−	5.65685i	0.302588	−	0.213962i
$700$	3.00000			0.113389
$701$			32.5269i			1.22852i	0.789102	+	0.614262i	$0.210546\pi$
$701$			32.5269i			1.22852i	−0.789102	+	0.614262i	$0.789454\pi$
$702$	−6.00000	−	21.2132i	−0.226455	−	0.800641i
$703$	18.0000	−	4.24264i	0.678883	−	0.160014i
$704$			2.82843i			0.106600i
$705$	−14.0000	−	19.7990i	−0.527271	−	0.745673i
$706$			2.82843i			0.106449i
$707$		−	9.89949i		−	0.372309i
$708$	−12.0000	−	16.9706i	−0.450988	−	0.637793i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$	−12.0000	−	4.24264i	−0.450035	−	0.159111i
$712$	6.00000			0.224860
$713$	−6.00000			−0.224702
$714$	8.00000	−	5.65685i	0.299392	−	0.211702i
$715$			16.9706i			0.634663i
$716$	−6.00000			−0.224231
$717$	2.00000	−	1.41421i	0.0746914	−	0.0528148i
$718$			32.5269i			1.21389i
$719$			32.5269i			1.21305i	0.795065	+	0.606525i	$0.207437\pi$
$719$			32.5269i			1.21305i	−0.795065	+	0.606525i	$0.792563\pi$
$720$	4.00000	+	1.41421i	0.149071	+	0.0527046i
$721$		−	12.7279i		−	0.474013i
$722$	−17.0000	+	8.48528i	−0.632674	+	0.315789i
$723$		0			0
$724$			12.7279i			0.473029i
$725$	18.0000			0.668503
$726$	3.00000	+	4.24264i	0.111340	+	0.157459i
$727$	44.0000			1.63187			0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000			1.63187			0.815935	+	0.578144i	$0.196223\pi$
$728$			4.24264i			0.157243i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$			22.6274i			0.837478i
$731$			56.5685i			2.09226i
$732$	−10.0000	−	14.1421i	−0.369611	−	0.522708i
$733$	50.0000			1.84679			0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000			1.84679			0.923396	+	0.383849i	$0.125402\pi$
$734$	8.00000			0.295285
$735$	2.00000	−	1.41421i	0.0737711	−	0.0521641i
$736$		−	1.41421i		−	0.0521286i
$737$	−24.0000			−0.884051
$738$	−12.0000	+	33.9411i	−0.441726	+	1.24939i
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−6.00000			−0.220564
$741$	−24.0000	−	21.2132i	−0.881662	−	0.779287i
$742$	−6.00000			−0.220267
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$	6.00000	−	4.24264i	0.219971	−	0.155543i
$745$	−2.00000			−0.0732743
$746$		−	12.7279i		−	0.466002i
$747$	−8.00000	−	2.82843i	−0.292705	−	0.103487i
$748$	16.0000			0.585018
$749$	−12.0000			−0.438470
$750$	16.0000	−	11.3137i	0.584237	−	0.413118i
$751$			12.7279i			0.464448i	0.972662	+	0.232224i	$0.0746003\pi$
$751$			12.7279i			0.464448i	−0.972662	+	0.232224i	$0.925400\pi$
$752$		−	9.89949i		−	0.360997i
$753$	−28.0000	+	19.7990i	−1.02038	+	0.721515i
$754$			25.4558i			0.927047i
$755$	−18.0000			−0.655087
$756$	−5.00000	+	1.41421i	−0.181848	+	0.0514344i
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$			25.4558i			0.924598i
$759$	4.00000	+	5.65685i	0.145191	+	0.205331i
$760$	6.00000	−	1.41421i	0.217643	−	0.0512989i
$761$		−	39.5980i		−	1.43543i	−0.696339	−	0.717713i	$-0.745189\pi$
$761$		−	39.5980i		−	1.43543i	0.696339	−	0.717713i	$-0.254811\pi$
$762$	−18.0000	+	12.7279i	−0.652071	+	0.461084i
$763$			4.24264i			0.153594i
$764$			15.5563i			0.562809i
$765$	8.00000	−	22.6274i	0.289241	−	0.818096i
$766$		0			0
$767$		−	50.9117i		−	1.83831i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$	4.00000			0.144150
$771$	−18.0000	−	25.4558i	−0.648254	−	0.916770i
$772$			8.48528i			0.305392i
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$	10.0000	−	28.2843i	0.359443	−	1.01666i
$775$		−	12.7279i		−	0.457200i
$776$		−	16.9706i		−	0.609208i
$777$	6.00000	−	4.24264i	0.215249	−	0.152204i
$778$		−	9.89949i		−	0.354914i
$779$	12.0000	+	50.9117i	0.429945	+	1.82410i
$780$	6.00000	+	8.48528i	0.214834	+	0.303822i
$781$		0			0
$782$	−8.00000			−0.286079
$783$	−30.0000	+	8.48528i	−1.07211	+	0.303239i
$784$	1.00000			0.0357143
$785$		−	19.7990i		−	0.706656i
$786$	20.0000	−	14.1421i	0.713376	−	0.504433i
$787$			8.48528i			0.302468i	0.988498	+	0.151234i	$0.0483246\pi$
$787$			8.48528i			0.302468i	−0.988498	+	0.151234i	$0.951675\pi$
$788$		−	18.3848i		−	0.654931i
$789$	−22.0000	+	15.5563i	−0.783221	+	0.553821i
$790$	6.00000			0.213470
$791$	12.0000			0.426671
$792$	−8.00000	−	2.82843i	−0.284268	−	0.100504i
$793$		−	42.4264i		−	1.50661i
$794$	2.00000			0.0709773
$795$	−12.0000	+	8.48528i	−0.425596	+	0.300942i
$796$	20.0000			0.708881
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$	−5.00000	+	5.65685i	−0.176998	+	0.200250i
$799$	−56.0000			−1.98114
$800$	3.00000			0.106066
$801$	−6.00000	+	16.9706i	−0.212000	+	0.599625i
$802$		0			0
$803$		−	45.2548i		−	1.59701i
$804$	−12.0000	+	8.48528i	−0.423207	+	0.299253i
$805$	−2.00000			−0.0704907
$806$	18.0000			0.634023
$807$	−6.00000	−	8.48528i	−0.211210	−	0.298696i
$808$		−	9.89949i		−	0.348263i
$809$		−	31.1127i		−	1.09386i	−0.837177	−	0.546932i	$-0.815796\pi$
$809$		−	31.1127i		−	1.09386i	0.837177	−	0.546932i	$-0.184204\pi$
$810$	−8.00000	+	9.89949i	−0.281091	+	0.347833i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	6.00000			0.210559
$813$	20.0000	+	28.2843i	0.701431	+	0.991973i
$814$	12.0000			0.420600
$815$		−	28.2843i		−	0.990755i
$816$	8.00000	−	5.65685i	0.280056	−	0.198030i
$817$	−10.0000	−	42.4264i	−0.349856	−	1.48431i
$818$		−	16.9706i		−	0.593362i
$819$	−12.0000	−	4.24264i	−0.419314	−	0.148250i
$820$		−	16.9706i		−	0.592638i
$821$			15.5563i			0.542920i	0.962450	+	0.271460i	$0.0875065\pi$
$821$			15.5563i			0.542920i	−0.962450	+	0.271460i	$0.912493\pi$
$822$	−4.00000	+	2.82843i	−0.139516	+	0.0986527i
$823$	32.0000			1.11545			0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000			1.11545			0.557725	+	0.830026i	$0.311674\pi$
$824$		−	12.7279i		−	0.443398i
$825$	−12.0000	+	8.48528i	−0.417786	+	0.295420i
$826$	−12.0000			−0.417533
$827$	−18.0000			−0.625921			−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000			−0.625921			−0.312961	+	0.949766i	$0.601321\pi$
$828$	4.00000	+	1.41421i	0.139010	+	0.0491473i
$829$			4.24264i			0.147353i	0.997282	+	0.0736765i	$0.0234732\pi$
$829$			4.24264i			0.147353i	−0.997282	+	0.0736765i	$0.976527\pi$
$830$	4.00000			0.138842
$831$	26.0000	+	36.7696i	0.901930	+	1.27552i
$832$			4.24264i			0.147087i
$833$		−	5.65685i		−	0.195998i
$834$	−4.00000	−	5.65685i	−0.138509	−	0.195881i
$835$		−	16.9706i		−	0.587291i
$836$	−12.0000	+	2.82843i	−0.415029	+	0.0978232i
$837$	6.00000	+	21.2132i	0.207390	+	0.733236i
$838$			11.3137i			0.390826i
$839$	−48.0000			−1.65714			−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000			−1.65714			−0.828572	+	0.559883i	$0.810846\pi$
$840$	2.00000	−	1.41421i	0.0690066	−	0.0487950i
$841$	7.00000			0.241379
$842$		−	4.24264i		−	0.146211i
$843$	−12.0000	−	16.9706i	−0.413302	−	0.584497i
$844$			16.9706i			0.584151i
$845$			7.07107i			0.243252i
$846$	28.0000	+	9.89949i	0.962660	+	0.340352i
$847$	3.00000			0.103081
$848$	−6.00000			−0.206041
$849$	−4.00000	−	5.65685i	−0.137280	−	0.194143i
$850$		−	16.9706i		−	0.582086i
$851$	−6.00000			−0.205677
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	−10.0000			−0.342193
$855$	−2.00000	+	18.3848i	−0.0683986	+	0.628746i
$856$	−12.0000			−0.410152
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$	−12.0000	−	16.9706i	−0.409673	−	0.579365i
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$			14.1421i			0.482243i
$861$	12.0000	+	16.9706i	0.408959	+	0.578355i
$862$	12.0000			0.408722
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$	−5.00000	+	1.41421i	−0.170103	+	0.0481125i
$865$			8.48528i			0.288508i
$866$		0			0
$867$	−15.0000	−	21.2132i	−0.509427	−	0.720438i
$868$		−	4.24264i		−	0.144005i
$869$	−12.0000			−0.407072
$870$	12.0000	−	8.48528i	0.406838	−	0.287678i
$871$	−36.0000			−1.21981
$872$			4.24264i			0.143674i
$873$	48.0000	+	16.9706i	1.62455	+	0.574367i
$874$	6.00000	−	1.41421i	0.202953	−	0.0478365i
$875$		−	11.3137i		−	0.382473i
$876$	−16.0000	−	22.6274i	−0.540590	−	0.764510i
$877$			38.1838i			1.28937i	0.764447	+	0.644687i	$0.223012\pi$
$877$			38.1838i			1.28937i	−0.764447	+	0.644687i	$0.776988\pi$
$878$		−	21.2132i		−	0.715911i
$879$	−6.00000	−	8.48528i	−0.202375	−	0.286201i
$880$	4.00000			0.134840
$881$			19.7990i			0.667045i	0.942742	+	0.333522i	$0.108237\pi$
$881$			19.7990i			0.667045i	−0.942742	+	0.333522i	$0.891763\pi$
$882$	−1.00000	+	2.82843i	−0.0336718	+	0.0952381i
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	24.0000			0.807207
$885$	−24.0000	+	16.9706i	−0.806751	+	0.570459i
$886$			2.82843i			0.0950229i
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	6.00000	−	4.24264i	0.201347	−	0.142374i
$889$			12.7279i			0.426881i
$890$		−	8.48528i		−	0.284427i
$891$	16.0000	−	19.7990i	0.536020	−	0.663291i
$892$			21.2132i			0.710271i
$893$	42.0000	−	9.89949i	1.40548	−	0.331274i
$894$	2.00000	−	1.41421i	0.0668900	−	0.0472984i
$895$			8.48528i			0.283632i
$896$	1.00000			0.0334077
$897$	6.00000	+	8.48528i	0.200334	+	0.283315i
$898$	18.0000			0.600668
$899$		−	25.4558i		−	0.849000i
$900$	−3.00000	+	8.48528i	−0.100000	+	0.282843i
$901$			33.9411i			1.13074i
$902$			33.9411i			1.13012i
$903$	−10.0000	−	14.1421i	−0.332779	−	0.470621i
$904$	12.0000			0.399114
$905$	18.0000			0.598340
$906$	18.0000	−	12.7279i	0.598010	−	0.422857i
$907$		−	25.4558i		−	0.845247i	−0.906305	−	0.422624i	$-0.861109\pi$
$907$		−	25.4558i		−	0.845247i	0.906305	−	0.422624i	$-0.138891\pi$
$908$	−18.0000			−0.597351
$909$	28.0000	+	9.89949i	0.928701	+	0.328346i
$910$	6.00000			0.198898
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	−5.00000	+	5.65685i	−0.165567	+	0.187317i
$913$	−8.00000			−0.264761
$914$	−10.0000			−0.330771
$915$	−20.0000	+	14.1421i	−0.661180	+	0.467525i
$916$	−22.0000			−0.726900
$917$		−	14.1421i		−	0.467014i
$918$	8.00000	+	28.2843i	0.264039	+	0.933520i
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	−2.00000			−0.0659380
$921$		0			0
$922$			15.5563i			0.512321i
$923$		0			0
$924$	−4.00000	+	2.82843i	−0.131590	+	0.0930484i
$925$		−	12.7279i		−	0.418491i
$926$	32.0000			1.05159
$927$	36.0000	+	12.7279i	1.18240	+	0.418040i
$928$	6.00000			0.196960
$929$		−	22.6274i		−	0.742381i	−0.928557	−	0.371191i	$-0.878950\pi$
$929$		−	22.6274i		−	0.742381i	0.928557	−	0.371191i	$-0.121050\pi$
$930$	−6.00000	−	8.48528i	−0.196748	−	0.278243i
$931$	1.00000	+	4.24264i	0.0327737	+	0.139047i
$932$		−	5.65685i		−	0.185296i
$933$	38.0000	−	26.8701i	1.24406	−	0.879686i
$934$		−	31.1127i		−	1.01804i
$935$		−	22.6274i		−	0.739996i
$936$	−12.0000	−	4.24264i	−0.392232	−	0.138675i
$937$	−16.0000			−0.522697			−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000			−0.522697			−0.261349	+	0.965244i	$0.584167\pi$
$938$			8.48528i			0.277054i
$939$	−28.0000	−	39.5980i	−0.913745	−	1.29223i
$940$	−14.0000			−0.456630
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	14.0000	+	19.7990i	0.456145	+	0.645086i
$943$		−	16.9706i		−	0.552638i
$944$	−12.0000			−0.390567
$945$	2.00000	+	7.07107i	0.0650600	+	0.230022i
$946$		−	28.2843i		−	0.919601i
$947$		−	22.6274i		−	0.735292i	−0.929966	−	0.367646i	$-0.880164\pi$
$947$		−	22.6274i		−	0.735292i	0.929966	−	0.367646i	$-0.119836\pi$
$948$	−6.00000	+	4.24264i	−0.194871	+	0.137795i
$949$		−	67.8823i		−	2.20355i
$950$	3.00000	+	12.7279i	0.0973329	+	0.412948i
$951$	−6.00000	−	8.48528i	−0.194563	−	0.275154i
$952$		−	5.65685i		−	0.183340i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$	6.00000	−	16.9706i	0.194257	−	0.549442i
$955$	22.0000			0.711903
$956$		−	1.41421i		−	0.0457389i
$957$	−24.0000	+	16.9706i	−0.775810	+	0.548580i
$958$			15.5563i			0.502603i
$959$			2.82843i			0.0913347i
$960$	2.00000	−	1.41421i	0.0645497	−	0.0456435i
$961$	13.0000			0.419355
$962$	18.0000			0.580343
$963$	12.0000	−	33.9411i	0.386695	−	1.09374i
$964$		0			0
$965$	12.0000			0.386294
$966$	2.00000	−	1.41421i	0.0643489	−	0.0455016i
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	3.00000			0.0964237
$969$	32.0000	+	28.2843i	1.02799	+	0.908622i
$970$	−24.0000			−0.770594
$971$	6.00000			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$972$	1.00000	−	15.5563i	0.0320750	−	0.498970i
$973$	−4.00000			−0.128234
$974$			4.24264i			0.135943i
$975$	−18.0000	+	12.7279i	−0.576461	+	0.407620i
$976$	−10.0000			−0.320092
$977$	24.0000			0.767828			0.383914	−	0.923369i	$-0.374576\pi$
$977$	24.0000			0.767828			0.383914	+	0.923369i	$0.374576\pi$
$978$	20.0000	+	28.2843i	0.639529	+	0.904431i
$979$			16.9706i			0.542382i
$980$		−	1.41421i		−	0.0451754i
$981$	−12.0000	−	4.24264i	−0.383131	−	0.135457i
$982$			11.3137i			0.361035i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$	12.0000	+	16.9706i	0.382546	+	0.541002i
$985$	−26.0000			−0.828429
$986$		−	33.9411i		−	1.08091i
$987$	14.0000	−	9.89949i	0.445625	−	0.315104i
$988$	−18.0000	+	4.24264i	−0.572656	+	0.134976i
$989$			14.1421i			0.449694i
$990$	−4.00000	+	11.3137i	−0.127128	+	0.359573i
$991$		−	21.2132i		−	0.673860i	−0.941530	−	0.336930i	$-0.890611\pi$
$991$		−	21.2132i		−	0.673860i	0.941530	−	0.336930i	$-0.109389\pi$
$992$		−	4.24264i		−	0.134704i
$993$	12.0000	−	8.48528i	0.380808	−	0.269272i
$994$		0			0
$995$		−	28.2843i		−	0.896672i
$996$	−4.00000	+	2.82843i	−0.126745	+	0.0896221i
$997$	−10.0000			−0.316703			−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000			−0.316703			−0.158352	+	0.987383i	$0.550618\pi$
$998$	−22.0000			−0.696398
$999$	6.00000	+	21.2132i	0.189832	+	0.671156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.b.d.113.2	yes	2
3.2	odd	2		798.2.b.a.113.2	yes	2
19.18	odd	2		798.2.b.a.113.1	✓	2
57.56	even	2	inner	798.2.b.d.113.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.b.a.113.1	✓	2	19.18	odd	2
798.2.b.a.113.2	yes	2	3.2	odd	2
798.2.b.d.113.1	yes	2	57.56	even	2	inner
798.2.b.d.113.2	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.41421i q^{5} +(1.00000 + 1.41421i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.41421i q^{5} +(1.00000 + 1.41421i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.41421i q^{10} +2.82843i q^{11} +(1.00000 + 1.41421i) q^{12} +4.24264i q^{13} +1.00000 q^{14} +(2.00000 - 1.41421i) q^{15} +1.00000 q^{16} -5.65685i q^{17} +(-1.00000 + 2.82843i) q^{18} +(1.00000 + 4.24264i) q^{19} -1.41421i q^{20} +(1.00000 + 1.41421i) q^{21} +2.82843i q^{22} -1.41421i q^{23} +(1.00000 + 1.41421i) q^{24} +3.00000 q^{25} +4.24264i q^{26} +(-5.00000 + 1.41421i) q^{27} +1.00000 q^{28} +6.00000 q^{29} +(2.00000 - 1.41421i) q^{30} -4.24264i q^{31} +1.00000 q^{32} +(-4.00000 + 2.82843i) q^{33} -5.65685i q^{34} -1.41421i q^{35} +(-1.00000 + 2.82843i) q^{36} -4.24264i q^{37} +(1.00000 + 4.24264i) q^{38} +(-6.00000 + 4.24264i) q^{39} -1.41421i q^{40} +12.0000 q^{41} +(1.00000 + 1.41421i) q^{42} -10.0000 q^{43} +2.82843i q^{44} +(4.00000 + 1.41421i) q^{45} -1.41421i q^{46} -9.89949i q^{47} +(1.00000 + 1.41421i) q^{48} +1.00000 q^{49} +3.00000 q^{50} +(8.00000 - 5.65685i) q^{51} +4.24264i q^{52} -6.00000 q^{53} +(-5.00000 + 1.41421i) q^{54} +4.00000 q^{55} +1.00000 q^{56} +(-5.00000 + 5.65685i) q^{57} +6.00000 q^{58} -12.0000 q^{59} +(2.00000 - 1.41421i) q^{60} -10.0000 q^{61} -4.24264i q^{62} +(-1.00000 + 2.82843i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(-4.00000 + 2.82843i) q^{66} +8.48528i q^{67} -5.65685i q^{68} +(2.00000 - 1.41421i) q^{69} -1.41421i q^{70} +(-1.00000 + 2.82843i) q^{72} -16.0000 q^{73} -4.24264i q^{74} +(3.00000 + 4.24264i) q^{75} +(1.00000 + 4.24264i) q^{76} +2.82843i q^{77} +(-6.00000 + 4.24264i) q^{78} +4.24264i q^{79} -1.41421i q^{80} +(-7.00000 - 5.65685i) q^{81} +12.0000 q^{82} +2.82843i q^{83} +(1.00000 + 1.41421i) q^{84} -8.00000 q^{85} -10.0000 q^{86} +(6.00000 + 8.48528i) q^{87} +2.82843i q^{88} +6.00000 q^{89} +(4.00000 + 1.41421i) q^{90} +4.24264i q^{91} -1.41421i q^{92} +(6.00000 - 4.24264i) q^{93} -9.89949i q^{94} +(6.00000 - 1.41421i) q^{95} +(1.00000 + 1.41421i) q^{96} -16.9706i q^{97} +1.00000 q^{98} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{12} + 2 q^{14} + 4 q^{15} + 2 q^{16} - 2 q^{18} + 2 q^{19} + 2 q^{21} + 2 q^{24} + 6 q^{25} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 4 q^{30} + 2 q^{32} - 8 q^{33} - 2 q^{36} + 2 q^{38} - 12 q^{39} + 24 q^{41} + 2 q^{42} - 20 q^{43} + 8 q^{45} + 2 q^{48} + 2 q^{49} + 6 q^{50} + 16 q^{51} - 12 q^{53} - 10 q^{54} + 8 q^{55} + 2 q^{56} - 10 q^{57} + 12 q^{58} - 24 q^{59} + 4 q^{60} - 20 q^{61} - 2 q^{63} + 2 q^{64} + 12 q^{65} - 8 q^{66} + 4 q^{69} - 2 q^{72} - 32 q^{73} + 6 q^{75} + 2 q^{76} - 12 q^{78} - 14 q^{81} + 24 q^{82} + 2 q^{84} - 16 q^{85} - 20 q^{86} + 12 q^{87} + 12 q^{89} + 8 q^{90} + 12 q^{93} + 12 q^{95} + 2 q^{96} + 2 q^{98} - 16 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^12 + 2 * q^14 + 4 * q^15 + 2 * q^16 - 2 * q^18 + 2 * q^19 + 2 * q^21 + 2 * q^24 + 6 * q^25 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 4 * q^30 + 2 * q^32 - 8 * q^33 - 2 * q^36 + 2 * q^38 - 12 * q^39 + 24 * q^41 + 2 * q^42 - 20 * q^43 + 8 * q^45 + 2 * q^48 + 2 * q^49 + 6 * q^50 + 16 * q^51 - 12 * q^53 - 10 * q^54 + 8 * q^55 + 2 * q^56 - 10 * q^57 + 12 * q^58 - 24 * q^59 + 4 * q^60 - 20 * q^61 - 2 * q^63 + 2 * q^64 + 12 * q^65 - 8 * q^66 + 4 * q^69 - 2 * q^72 - 32 * q^73 + 6 * q^75 + 2 * q^76 - 12 * q^78 - 14 * q^81 + 24 * q^82 + 2 * q^84 - 16 * q^85 - 20 * q^86 + 12 * q^87 + 12 * q^89 + 8 * q^90 + 12 * q^93 + 12 * q^95 + 2 * q^96 + 2 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more