LMFDB - Embedded newform 322.2.c.c.321.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [322,2,Mod(321,322)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("322.321"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(322, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,4,-8,0,-2,4,-8,-8,0,0,0,-2,0,4,12,-8,16,-8,-8,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2312.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			321.4
Root			$-0.780776 - 1.17915i$ of defining polynomial
Character	$\chi$	$=$	322.321
Dual form			322.2.c.c.321.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +3.02045i q^{3} +1.00000 q^{4} -2.00000 q^{5} +3.02045i q^{6} +(-2.56155 + 0.662153i) q^{7} +1.00000 q^{8} -6.12311 q^{9} -2.00000 q^{10} +3.02045i q^{11} +3.02045i q^{12} -1.69614i q^{13} +(-2.56155 + 0.662153i) q^{14} -6.04090i q^{15} +1.00000 q^{16} +7.12311 q^{17} -6.12311 q^{18} +4.00000 q^{19} -2.00000 q^{20} +(-2.00000 - 7.73704i) q^{21} +3.02045i q^{22} +(2.56155 + 4.05444i) q^{23} +3.02045i q^{24} -1.00000 q^{25} -1.69614i q^{26} -9.43318i q^{27} +(-2.56155 + 0.662153i) q^{28} -2.00000 q^{29} -6.04090i q^{30} +8.10887i q^{31} +1.00000 q^{32} -9.12311 q^{33} +7.12311 q^{34} +(5.12311 - 1.32431i) q^{35} -6.12311 q^{36} +1.69614i q^{37} +4.00000 q^{38} +5.12311 q^{39} -2.00000 q^{40} +3.39228i q^{41} +(-2.00000 - 7.73704i) q^{42} +3.02045i q^{43} +3.02045i q^{44} +12.2462 q^{45} +(2.56155 + 4.05444i) q^{46} -7.36520i q^{47} +3.02045i q^{48} +(6.12311 - 3.39228i) q^{49} -1.00000 q^{50} +21.5150i q^{51} -1.69614i q^{52} -13.7779i q^{53} -9.43318i q^{54} -6.04090i q^{55} +(-2.56155 + 0.662153i) q^{56} +12.0818i q^{57} -2.00000 q^{58} -9.06134i q^{59} -6.04090i q^{60} -4.24621 q^{61} +8.10887i q^{62} +(15.6847 - 4.05444i) q^{63} +1.00000 q^{64} +3.39228i q^{65} -9.12311 q^{66} -0.371834i q^{67} +7.12311 q^{68} +(-12.2462 + 7.73704i) q^{69} +(5.12311 - 1.32431i) q^{70} +15.3693 q^{71} -6.12311 q^{72} +12.0818i q^{73} +1.69614i q^{74} -3.02045i q^{75} +4.00000 q^{76} +(-2.00000 - 7.73704i) q^{77} +5.12311 q^{78} -3.97292i q^{79} -2.00000 q^{80} +10.1231 q^{81} +3.39228i q^{82} +4.00000 q^{83} +(-2.00000 - 7.73704i) q^{84} -14.2462 q^{85} +3.02045i q^{86} -6.04090i q^{87} +3.02045i q^{88} +2.00000 q^{89} +12.2462 q^{90} +(1.12311 + 4.34475i) q^{91} +(2.56155 + 4.05444i) q^{92} -24.4924 q^{93} -7.36520i q^{94} -8.00000 q^{95} +3.02045i q^{96} +4.24621 q^{97} +(6.12311 - 3.39228i) q^{98} -18.4945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} - 8 q^{5} - 2 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{10} - 2 q^{14} + 4 q^{16} + 12 q^{17} - 8 q^{18} + 16 q^{19} - 8 q^{20} - 8 q^{21} + 2 q^{23} - 4 q^{25} - 2 q^{28} - 8 q^{29} + 4 q^{32}+ \cdots + 8 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 - 8 * q^5 - 2 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^10 - 2 * q^14 + 4 * q^16 + 12 * q^17 - 8 * q^18 + 16 * q^19 - 8 * q^20 - 8 * q^21 + 2 * q^23 - 4 * q^25 - 2 * q^28 - 8 * q^29 + 4 * q^32 - 20 * q^33 + 12 * q^34 + 4 * q^35 - 8 * q^36 + 16 * q^38 + 4 * q^39 - 8 * q^40 - 8 * q^42 + 16 * q^45 + 2 * q^46 + 8 * q^49 - 4 * q^50 - 2 * q^56 - 8 * q^58 + 16 * q^61 + 38 * q^63 + 4 * q^64 - 20 * q^66 + 12 * q^68 - 16 * q^69 + 4 * q^70 + 12 * q^71 - 8 * q^72 + 16 * q^76 - 8 * q^77 + 4 * q^78 - 8 * q^80 + 24 * q^81 + 16 * q^83 - 8 * q^84 - 24 * q^85 + 8 * q^89 + 16 * q^90 - 12 * q^91 + 2 * q^92 - 32 * q^93 - 32 * q^95 - 16 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$-1$	$-1$

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
$3$			3.02045i			1.74386i	0.489634	+	0.871928i	$0.337130\pi$
$3$			3.02045i			1.74386i	−0.489634	+	0.871928i	$0.662870\pi$
$4$	1.00000			0.500000
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$			3.02045i			1.23309i
$7$	−2.56155	+	0.662153i	−0.968176	+	0.250270i
$7$	−2.56155	+	0.662153i	−0.968176	+	0.250270i
$8$	1.00000			0.353553
$9$	−6.12311			−2.04104
$10$	−2.00000			−0.632456
$11$			3.02045i			0.910699i	0.890313	+	0.455350i	$0.150486\pi$
$11$			3.02045i			0.910699i	−0.890313	+	0.455350i	$0.849514\pi$
$12$			3.02045i			0.871928i
$13$		−	1.69614i		−	0.470425i	−0.971944	−	0.235212i	$-0.924421\pi$
$13$		−	1.69614i		−	0.470425i	0.971944	−	0.235212i	$-0.0755786\pi$
$14$	−2.56155	+	0.662153i	−0.684604	+	0.176968i
$15$		−	6.04090i		−	1.55975i
$16$	1.00000			0.250000
$17$	7.12311			1.72761			0.863803	−	0.503829i	$-0.168076\pi$
$17$	7.12311			1.72761			0.863803	+	0.503829i	$0.168076\pi$
$18$	−6.12311			−1.44323
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000			−0.447214
$21$	−2.00000	−	7.73704i	−0.436436	−	1.68836i
$22$			3.02045i			0.643962i
$23$	2.56155	+	4.05444i	0.534121	+	0.845408i
$23$	2.56155	+	4.05444i	0.534121	+	0.845408i
$24$			3.02045i			0.616546i
$25$	−1.00000			−0.200000
$26$		−	1.69614i		−	0.332641i
$27$		−	9.43318i		−	1.81542i
$28$	−2.56155	+	0.662153i	−0.484088	+	0.125135i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		−	6.04090i		−	1.10291i
$31$			8.10887i			1.45640i	0.685367	+	0.728198i	$0.259642\pi$
$31$			8.10887i			1.45640i	−0.685367	+	0.728198i	$0.740358\pi$
$32$	1.00000			0.176777
$33$	−9.12311			−1.58813
$34$	7.12311			1.22160
$35$	5.12311	−	1.32431i	0.865963	−	0.223849i
$36$	−6.12311			−1.02052
$37$			1.69614i			0.278844i	0.990233	+	0.139422i	$0.0445244\pi$
$37$			1.69614i			0.278844i	−0.990233	+	0.139422i	$0.955476\pi$
$38$	4.00000			0.648886
$39$	5.12311			0.820353
$40$	−2.00000			−0.316228
$41$			3.39228i			0.529785i	0.964278	+	0.264893i	$0.0853365\pi$
$41$			3.39228i			0.529785i	−0.964278	+	0.264893i	$0.914663\pi$
$42$	−2.00000	−	7.73704i	−0.308607	−	1.19385i
$43$			3.02045i			0.460614i	0.973118	+	0.230307i	$0.0739730\pi$
$43$			3.02045i			0.460614i	−0.973118	+	0.230307i	$0.926027\pi$
$44$			3.02045i			0.455350i
$45$	12.2462			1.82556
$46$	2.56155	+	4.05444i	0.377680	+	0.597794i
$47$		−	7.36520i		−	1.07433i	−0.843479	−	0.537163i	$-0.819496\pi$
$47$		−	7.36520i		−	1.07433i	0.843479	−	0.537163i	$-0.180504\pi$
$48$			3.02045i			0.435964i
$49$	6.12311	−	3.39228i	0.874729	−	0.484612i
$50$	−1.00000			−0.141421
$51$			21.5150i			3.01270i
$52$		−	1.69614i		−	0.235212i
$53$		−	13.7779i		−	1.89254i	−0.323371	−	0.946272i	$-0.604816\pi$
$53$		−	13.7779i		−	1.89254i	0.323371	−	0.946272i	$-0.395184\pi$
$54$		−	9.43318i		−	1.28369i
$55$		−	6.04090i		−	0.814554i
$56$	−2.56155	+	0.662153i	−0.342302	+	0.0884840i
$57$			12.0818i			1.60027i
$58$	−2.00000			−0.262613
$59$		−	9.06134i		−	1.17969i	−0.807518	−	0.589843i	$-0.799190\pi$
$59$		−	9.06134i		−	1.17969i	0.807518	−	0.589843i	$-0.200810\pi$
$60$		−	6.04090i		−	0.779876i
$61$	−4.24621			−0.543672			−0.271836	−	0.962344i	$-0.587631\pi$
$61$	−4.24621			−0.543672			−0.271836	+	0.962344i	$0.587631\pi$
$62$			8.10887i			1.02983i
$63$	15.6847	−	4.05444i	1.97608	−	0.510811i
$64$	1.00000			0.125000
$65$			3.39228i			0.420761i
$66$	−9.12311			−1.12298
$67$		−	0.371834i		−	0.0454268i	−0.999742	−	0.0227134i	$-0.992769\pi$
$67$		−	0.371834i		−	0.0454268i	0.999742	−	0.0227134i	$-0.00723052\pi$
$68$	7.12311			0.863803
$69$	−12.2462	+	7.73704i	−1.47427	+	0.931430i
$70$	5.12311	−	1.32431i	0.612328	−	0.158285i
$71$	15.3693			1.82400			0.912001	−	0.410188i	$-0.134537\pi$
$71$	15.3693			1.82400			0.912001	+	0.410188i	$0.134537\pi$
$72$	−6.12311			−0.721615
$73$			12.0818i			1.41407i	0.707180	+	0.707033i	$0.249967\pi$
$73$			12.0818i			1.41407i	−0.707180	+	0.707033i	$0.750033\pi$
$74$			1.69614i			0.197172i
$75$		−	3.02045i		−	0.348771i
$76$	4.00000			0.458831
$77$	−2.00000	−	7.73704i	−0.227921	−	0.881717i
$78$	5.12311			0.580077
$79$		−	3.97292i		−	0.446988i	−0.974705	−	0.223494i	$-0.928254\pi$
$79$		−	3.97292i		−	0.446988i	0.974705	−	0.223494i	$-0.0717464\pi$
$80$	−2.00000			−0.223607
$81$	10.1231			1.12479
$82$			3.39228i			0.374615i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$	−2.00000	−	7.73704i	−0.218218	−	0.844180i
$85$	−14.2462			−1.54522
$86$			3.02045i			0.325703i
$87$		−	6.04090i		−	0.647652i
$88$			3.02045i			0.321981i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	12.2462			1.29086
$91$	1.12311	+	4.34475i	0.117733	+	0.455454i
$92$	2.56155	+	4.05444i	0.267060	+	0.422704i
$93$	−24.4924			−2.53975
$94$		−	7.36520i		−	0.759663i
$95$	−8.00000			−0.820783
$96$			3.02045i			0.308273i
$97$	4.24621			0.431137			0.215569	−	0.976489i	$-0.430839\pi$
$97$	4.24621			0.431137			0.215569	+	0.976489i	$0.430839\pi$
$98$	6.12311	−	3.39228i	0.618527	−	0.342672i
$99$		−	18.4945i		−	1.85877i
$100$	−1.00000			−0.100000
$101$		−	5.08842i		−	0.506317i	−0.967425	−	0.253159i	$-0.918531\pi$
$101$		−	5.08842i		−	0.506317i	0.967425	−	0.253159i	$-0.0814694\pi$
$102$			21.5150i			2.13030i
$103$	−10.8769			−1.07173			−0.535866	−	0.844303i	$-0.680015\pi$
$103$	−10.8769			−1.07173			−0.535866	+	0.844303i	$0.680015\pi$
$104$		−	1.69614i		−	0.166320i
$105$	4.00000	+	15.4741i	0.390360	+	1.51011i
$106$		−	13.7779i		−	1.33823i
$107$		−	14.3586i		−	1.38810i	−0.719929	−	0.694048i	$-0.755826\pi$
$107$		−	14.3586i		−	1.38810i	0.719929	−	0.694048i	$-0.244174\pi$
$108$		−	9.43318i		−	0.907708i
$109$		−	17.1702i		−	1.64461i	−0.569048	−	0.822304i	$-0.692688\pi$
$109$		−	17.1702i		−	1.64461i	0.569048	−	0.822304i	$-0.307312\pi$
$110$		−	6.04090i		−	0.575977i
$111$	−5.12311			−0.486264
$112$	−2.56155	+	0.662153i	−0.242044	+	0.0625676i
$113$		−	6.78456i		−	0.638238i	−0.947715	−	0.319119i	$-0.896613\pi$
$113$		−	6.78456i		−	0.638238i	0.947715	−	0.319119i	$-0.103387\pi$
$114$			12.0818i			1.13156i
$115$	−5.12311	−	8.10887i	−0.477732	−	0.756156i
$116$	−2.00000			−0.185695
$117$			10.3857i			0.960154i
$118$		−	9.06134i		−	0.834164i
$119$	−18.2462	+	4.71659i	−1.67263	+	0.432369i
$120$		−	6.04090i		−	0.551456i
$121$	1.87689			0.170627
$122$	−4.24621			−0.384434
$123$	−10.2462			−0.923870
$124$			8.10887i			0.728198i
$125$	12.0000			1.07331
$126$	15.6847	−	4.05444i	1.39730	−	0.361198i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	1.00000			0.0883883
$129$	−9.12311			−0.803245
$130$			3.39228i			0.297523i
$131$			3.02045i			0.263898i	0.991257	+	0.131949i	$0.0421235\pi$
$131$			3.02045i			0.263898i	−0.991257	+	0.131949i	$0.957877\pi$
$132$	−9.12311			−0.794064
$133$	−10.2462	+	2.64861i	−0.888459	+	0.229664i
$134$		−	0.371834i		−	0.0321216i
$135$			18.8664i			1.62376i
$136$	7.12311			0.610801
$137$			20.7713i			1.77461i	0.461181	+	0.887306i	$0.347426\pi$
$137$			20.7713i			1.77461i	−0.461181	+	0.887306i	$0.652574\pi$
$138$	−12.2462	+	7.73704i	−1.04247	+	0.658620i
$139$			15.1022i			1.28096i	0.767977	+	0.640478i	$0.221264\pi$
$139$			15.1022i			1.28096i	−0.767977	+	0.640478i	$0.778736\pi$
$140$	5.12311	−	1.32431i	0.432981	−	0.111924i
$141$	22.2462			1.87347
$142$	15.3693			1.28976
$143$	5.12311			0.428416
$144$	−6.12311			−0.510259
$145$	4.00000			0.332182
$146$			12.0818i			0.999896i
$147$	10.2462	+	18.4945i	0.845093	+	1.52540i
$148$			1.69614i			0.139422i
$149$			17.1702i			1.40664i	0.710874	+	0.703319i	$0.248300\pi$
$149$			17.1702i			1.40664i	−0.710874	+	0.703319i	$0.751700\pi$
$150$		−	3.02045i		−	0.246619i
$151$	5.12311			0.416912			0.208456	−	0.978032i	$-0.433156\pi$
$151$	5.12311			0.416912			0.208456	+	0.978032i	$0.433156\pi$
$152$	4.00000			0.324443
$153$	−43.6155			−3.52611
$154$	−2.00000	−	7.73704i	−0.161165	−	0.623468i
$155$		−	16.2177i		−	1.30264i
$156$	5.12311			0.410177
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$		−	3.97292i		−	0.316069i
$159$	41.6155			3.30033
$160$	−2.00000			−0.158114
$161$	−9.24621	−	8.68951i	−0.728704	−	0.684829i
$162$	10.1231			0.795346
$163$	−16.4924			−1.29179			−0.645893	−	0.763428i	$-0.723515\pi$
$163$	−16.4924			−1.29179			−0.645893	+	0.763428i	$0.723515\pi$
$164$			3.39228i			0.264893i
$165$	18.2462			1.42047
$166$	4.00000			0.310460
$167$		−	19.4470i		−	1.50485i	−0.658676	−	0.752427i	$-0.728883\pi$
$167$		−	19.4470i		−	1.50485i	0.658676	−	0.752427i	$-0.271117\pi$
$168$	−2.00000	−	7.73704i	−0.154303	−	0.596925i
$169$	10.1231			0.778700
$170$	−14.2462			−1.09263
$171$	−24.4924			−1.87298
$172$			3.02045i			0.230307i
$173$			6.99337i			0.531696i	0.964015	+	0.265848i	$0.0856519\pi$
$173$			6.99337i			0.531696i	−0.964015	+	0.265848i	$0.914348\pi$
$174$		−	6.04090i		−	0.457959i
$175$	2.56155	−	0.662153i	0.193635	−	0.0500541i
$176$			3.02045i			0.227675i
$177$	27.3693			2.05720
$178$	2.00000			0.149906
$179$	14.2462			1.06481			0.532406	−	0.846489i	$-0.321288\pi$
$179$	14.2462			1.06481			0.532406	+	0.846489i	$0.321288\pi$
$180$	12.2462			0.912779
$181$	8.24621			0.612936			0.306468	−	0.951881i	$-0.400853\pi$
$181$	8.24621			0.612936			0.306468	+	0.951881i	$0.400853\pi$
$182$	1.12311	+	4.34475i	0.0832501	+	0.322055i
$183$		−	12.8255i		−	0.948085i
$184$	2.56155	+	4.05444i	0.188840	+	0.298897i
$185$		−	3.39228i		−	0.249406i
$186$	−24.4924			−1.79587
$187$			21.5150i			1.57333i
$188$		−	7.36520i		−	0.537163i
$189$	6.24621	+	24.1636i	0.454345	+	1.75764i
$190$	−8.00000			−0.580381
$191$			20.1907i			1.46095i	0.682942	+	0.730473i	$0.260700\pi$
$191$			20.1907i			1.46095i	−0.682942	+	0.730473i	$0.739300\pi$
$192$			3.02045i			0.217982i
$193$	−5.36932			−0.386492			−0.193246	−	0.981150i	$-0.561902\pi$
$193$	−5.36932			−0.386492			−0.193246	+	0.981150i	$0.561902\pi$
$194$	4.24621			0.304860
$195$	−10.2462			−0.733746
$196$	6.12311	−	3.39228i	0.437365	−	0.242306i
$197$	−20.2462			−1.44248			−0.721241	−	0.692684i	$-0.756428\pi$
$197$	−20.2462			−1.44248			−0.721241	+	0.692684i	$0.756428\pi$
$198$		−	18.4945i		−	1.31435i
$199$	−12.4924			−0.885564			−0.442782	−	0.896629i	$-0.646009\pi$
$199$	−12.4924			−0.885564			−0.442782	+	0.896629i	$0.646009\pi$
$200$	−1.00000			−0.0707107
$201$	1.12311			0.0792178
$202$		−	5.08842i		−	0.358020i
$203$	5.12311	−	1.32431i	0.359572	−	0.0929481i
$204$			21.5150i			1.50635i
$205$		−	6.78456i		−	0.473855i
$206$	−10.8769			−0.757829
$207$	−15.6847	−	24.8257i	−1.09016	−	1.72551i
$208$		−	1.69614i		−	0.117606i
$209$			12.0818i			0.835715i
$210$	4.00000	+	15.4741i	0.276026	+	1.06781i
$211$	−6.24621			−0.430007			−0.215003	−	0.976613i	$-0.568976\pi$
$211$	−6.24621			−0.430007			−0.215003	+	0.976613i	$0.568976\pi$
$212$		−	13.7779i		−	0.946272i
$213$			46.4222i			3.18080i
$214$		−	14.3586i		−	0.981532i
$215$		−	6.04090i		−	0.411986i
$216$		−	9.43318i		−	0.641846i
$217$	−5.36932	−	20.7713i	−0.364493	−	1.41005i
$218$		−	17.1702i		−	1.16291i
$219$	−36.4924			−2.46593
$220$		−	6.04090i		−	0.407277i
$221$		−	12.0818i		−	0.812709i
$222$	−5.12311			−0.343840
$223$			3.22925i			0.216247i	0.994137	+	0.108123i	$0.0344842\pi$
$223$			3.22925i			0.216247i	−0.994137	+	0.108123i	$0.965516\pi$
$224$	−2.56155	+	0.662153i	−0.171151	+	0.0442420i
$225$	6.12311			0.408207
$226$		−	6.78456i		−	0.451302i
$227$	−6.24621			−0.414576			−0.207288	−	0.978280i	$-0.566464\pi$
$227$	−6.24621			−0.414576			−0.207288	+	0.978280i	$0.566464\pi$
$228$			12.0818i			0.800136i
$229$	−7.75379			−0.512385			−0.256192	−	0.966626i	$-0.582468\pi$
$229$	−7.75379			−0.512385			−0.256192	+	0.966626i	$0.582468\pi$
$230$	−5.12311	−	8.10887i	−0.337808	−	0.534683i
$231$	23.3693	−	6.04090i	1.53759	−	0.397462i
$232$	−2.00000			−0.131306
$233$	−16.2462			−1.06432			−0.532162	−	0.846642i	$-0.678620\pi$
$233$	−16.2462			−1.06432			−0.532162	+	0.846642i	$0.678620\pi$
$234$			10.3857i			0.678931i
$235$			14.7304i			0.960906i
$236$		−	9.06134i		−	0.589843i
$237$	12.0000			0.779484
$238$	−18.2462	+	4.71659i	−1.18273	+	0.305731i
$239$	17.6155			1.13945			0.569727	−	0.821834i	$-0.307049\pi$
$239$	17.6155			1.13945			0.569727	+	0.821834i	$0.307049\pi$
$240$		−	6.04090i		−	0.389938i
$241$	20.2462			1.30417			0.652087	−	0.758145i	$-0.273894\pi$
$241$	20.2462			1.30417			0.652087	+	0.758145i	$0.273894\pi$
$242$	1.87689			0.120651
$243$			2.27678i			0.146055i
$244$	−4.24621			−0.271836
$245$	−12.2462	+	6.78456i	−0.782382	+	0.433450i
$246$	−10.2462			−0.653275
$247$		−	6.78456i		−	0.431691i
$248$			8.10887i			0.514914i
$249$			12.0818i			0.765652i
$250$	12.0000			0.758947
$251$	26.7386			1.68773			0.843864	−	0.536557i	$-0.180276\pi$
$251$	26.7386			1.68773			0.843864	+	0.536557i	$0.180276\pi$
$252$	15.6847	−	4.05444i	0.988041	−	0.255405i
$253$	−12.2462	+	7.73704i	−0.769913	+	0.486423i
$254$		0			0
$255$		−	43.0299i		−	2.69464i
$256$	1.00000			0.0625000
$257$		−	17.3790i		−	1.08407i	−0.840355	−	0.542037i	$-0.817653\pi$
$257$		−	17.3790i		−	1.08407i	0.840355	−	0.542037i	$-0.182347\pi$
$258$	−9.12311			−0.567980
$259$	−1.12311	−	4.34475i	−0.0697864	−	0.269970i
$260$			3.39228i			0.210380i
$261$	12.2462			0.758021
$262$			3.02045i			0.186604i
$263$		−	7.36520i		−	0.454158i	−0.973876	−	0.227079i	$-0.927082\pi$
$263$		−	7.36520i		−	0.454158i	0.973876	−	0.227079i	$-0.0729175\pi$
$264$	−9.12311			−0.561488
$265$			27.5559i			1.69274i
$266$	−10.2462	+	2.64861i	−0.628236	+	0.162397i
$267$			6.04090i			0.369697i
$268$		−	0.371834i		−	0.0227134i
$269$		−	19.0752i		−	1.16303i	−0.813535	−	0.581517i	$-0.802460\pi$
$269$		−	19.0752i		−	1.16303i	0.813535	−	0.581517i	$-0.197540\pi$
$270$			18.8664i			1.14817i
$271$			1.32431i			0.0804459i	0.999191	+	0.0402230i	$0.0128068\pi$
$271$			1.32431i			0.0804459i	−0.999191	+	0.0402230i	$0.987193\pi$
$272$	7.12311			0.431902
$273$	−13.1231	+	3.39228i	−0.794246	+	0.205310i
$274$			20.7713i			1.25484i
$275$		−	3.02045i		−	0.182140i
$276$	−12.2462	+	7.73704i	−0.737135	+	0.465715i
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$			15.1022i			0.905772i
$279$		−	49.6515i		−	2.97256i
$280$	5.12311	−	1.32431i	0.306164	−	0.0791425i
$281$			5.29723i			0.316006i	0.987439	+	0.158003i	$0.0505056\pi$
$281$			5.29723i			0.316006i	−0.987439	+	0.158003i	$0.949494\pi$
$282$	22.2462			1.32474
$283$	−20.0000			−1.18888			−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000			−1.18888			−0.594438	+	0.804141i	$0.702626\pi$
$284$	15.3693			0.912001
$285$		−	24.1636i		−	1.43133i
$286$	5.12311			0.302936
$287$	−2.24621	−	8.68951i	−0.132590	−	0.512926i
$288$	−6.12311			−0.360807
$289$	33.7386			1.98463
$290$	4.00000			0.234888
$291$			12.8255i			0.751842i
$292$			12.0818i			0.707033i
$293$	18.4924			1.08034			0.540169	−	0.841556i	$-0.318360\pi$
$293$	18.4924			1.08034			0.540169	+	0.841556i	$0.318360\pi$
$294$	10.2462	+	18.4945i	0.597571	+	1.07862i
$295$			18.1227i			1.05514i
$296$			1.69614i			0.0985862i
$297$	28.4924			1.65330
$298$			17.1702i			0.994644i
$299$	6.87689	−	4.34475i	0.397701	−	0.251264i
$300$		−	3.02045i		−	0.174386i
$301$	−2.00000	−	7.73704i	−0.115278	−	0.445955i
$302$	5.12311			0.294802
$303$	15.3693			0.882944
$304$	4.00000			0.229416
$305$	8.49242			0.486275
$306$	−43.6155			−2.49333
$307$			18.4945i			1.05554i	0.849388	+	0.527769i	$0.176971\pi$
$307$			18.4945i			1.05554i	−0.849388	+	0.527769i	$0.823029\pi$
$308$	−2.00000	−	7.73704i	−0.113961	−	0.440859i
$309$		−	32.8531i		−	1.86895i
$310$		−	16.2177i		−	0.921106i
$311$		−	12.6624i		−	0.718021i	−0.933334	−	0.359010i	$-0.883114\pi$
$311$		−	12.6624i		−	0.718021i	0.933334	−	0.359010i	$-0.116886\pi$
$312$	5.12311			0.290039
$313$	−18.4924			−1.04525			−0.522627	−	0.852562i	$-0.675048\pi$
$313$	−18.4924			−1.04525			−0.522627	+	0.852562i	$0.675048\pi$
$314$	−10.0000			−0.564333
$315$	−31.3693	+	8.10887i	−1.76746	+	0.456883i
$316$		−	3.97292i		−	0.223494i
$317$	−7.75379			−0.435496			−0.217748	−	0.976005i	$-0.569871\pi$
$317$	−7.75379			−0.435496			−0.217748	+	0.976005i	$0.569871\pi$
$318$	41.6155			2.33368
$319$		−	6.04090i		−	0.338225i
$320$	−2.00000			−0.111803
$321$	43.3693			2.42064
$322$	−9.24621	−	8.68951i	−0.515271	−	0.484247i
$323$	28.4924			1.58536
$324$	10.1231			0.562395
$325$			1.69614i			0.0940850i
$326$	−16.4924			−0.913431
$327$	51.8617			2.86796
$328$			3.39228i			0.187307i
$329$	4.87689	+	18.8664i	0.268872	+	1.04014i
$330$	18.2462			1.00442
$331$	−14.2462			−0.783043			−0.391521	−	0.920169i	$-0.628051\pi$
$331$	−14.2462			−0.783043			−0.391521	+	0.920169i	$0.628051\pi$
$332$	4.00000			0.219529
$333$		−	10.3857i		−	0.569130i
$334$		−	19.4470i		−	1.06409i
$335$			0.743668i			0.0406309i
$336$	−2.00000	−	7.73704i	−0.109109	−	0.422090i
$337$		−	10.5945i		−	0.577117i	−0.957462	−	0.288558i	$-0.906824\pi$
$337$		−	10.5945i		−	0.577117i	0.957462	−	0.288558i	$-0.0931759\pi$
$338$	10.1231			0.550624
$339$	20.4924			1.11300
$340$	−14.2462			−0.772609
$341$	−24.4924			−1.32634
$342$	−24.4924			−1.32440
$343$	−13.4384	+	12.7439i	−0.725608	+	0.688108i
$344$			3.02045i			0.162852i
$345$	24.4924	−	15.4741i	1.31863	−	0.833096i
$346$			6.99337i			0.375966i
$347$	16.4924			0.885360			0.442680	−	0.896680i	$-0.354028\pi$
$347$	16.4924			0.885360			0.442680	+	0.896680i	$0.354028\pi$
$348$		−	6.04090i		−	0.323826i
$349$		−	12.2906i		−	0.657901i	−0.944347	−	0.328950i	$-0.893305\pi$
$349$		−	12.2906i		−	0.657901i	0.944347	−	0.328950i	$-0.106695\pi$
$350$	2.56155	−	0.662153i	0.136921	−	0.0353936i
$351$	−16.0000			−0.854017
$352$			3.02045i			0.160990i
$353$		−	13.5691i		−	0.722212i	−0.932525	−	0.361106i	$-0.882399\pi$
$353$		−	13.5691i		−	0.722212i	0.932525	−	0.361106i	$-0.117601\pi$
$354$	27.3693			1.45466
$355$	−30.7386			−1.63144
$356$	2.00000			0.106000
$357$	−14.2462	−	55.1117i	−0.753989	−	2.91682i
$358$	14.2462			0.752936
$359$			23.5829i			1.24466i	0.782755	+	0.622330i	$0.213814\pi$
$359$			23.5829i			1.24466i	−0.782755	+	0.622330i	$0.786186\pi$
$360$	12.2462			0.645432
$361$	−3.00000			−0.157895
$362$	8.24621			0.433411
$363$			5.66906i			0.297549i
$364$	1.12311	+	4.34475i	0.0588667	+	0.227727i
$365$		−	24.1636i		−	1.26478i
$366$		−	12.8255i		−	0.670398i
$367$	2.87689			0.150173			0.0750863	−	0.997177i	$-0.476077\pi$
$367$	2.87689			0.150173			0.0750863	+	0.997177i	$0.476077\pi$
$368$	2.56155	+	4.05444i	0.133530	+	0.211352i
$369$		−	20.7713i		−	1.08131i
$370$		−	3.39228i		−	0.176356i
$371$	9.12311	+	35.2929i	0.473648	+	1.83232i
$372$	−24.4924			−1.26987
$373$		−	18.6576i		−	0.966051i	−0.875606	−	0.483026i	$-0.839538\pi$
$373$		−	18.6576i		−	0.966051i	0.875606	−	0.483026i	$-0.160462\pi$
$374$			21.5150i			1.11251i
$375$			36.2454i			1.87170i
$376$		−	7.36520i		−	0.379831i
$377$			3.39228i			0.174711i
$378$	6.24621	+	24.1636i	0.321270	+	1.24284i
$379$			18.4945i			0.950000i	0.879986	+	0.475000i	$0.157552\pi$
$379$			18.4945i			0.950000i	−0.879986	+	0.475000i	$0.842448\pi$
$380$	−8.00000			−0.410391
$381$		0			0
$382$			20.1907i			1.03304i
$383$	18.8769			0.964564			0.482282	−	0.876016i	$-0.339808\pi$
$383$	18.8769			0.964564			0.482282	+	0.876016i	$0.339808\pi$
$384$			3.02045i			0.154137i
$385$	4.00000	+	15.4741i	0.203859	+	0.788632i
$386$	−5.36932			−0.273291
$387$		−	18.4945i		−	0.940129i
$388$	4.24621			0.215569
$389$		−	11.8730i		−	0.601984i	−0.953627	−	0.300992i	$-0.902682\pi$
$389$		−	11.8730i		−	0.601984i	0.953627	−	0.300992i	$-0.0973178\pi$
$390$	−10.2462			−0.518837
$391$	18.2462	+	28.8802i	0.922751	+	1.46053i
$392$	6.12311	−	3.39228i	0.309264	−	0.171336i
$393$	−9.12311			−0.460200
$394$	−20.2462			−1.01999
$395$			7.94584i			0.399799i
$396$		−	18.4945i		−	0.929385i
$397$		−	23.9548i		−	1.20226i	−0.799153	−	0.601128i	$-0.794718\pi$
$397$		−	23.9548i		−	1.20226i	0.799153	−	0.601128i	$-0.205282\pi$
$398$	−12.4924			−0.626189
$399$	−8.00000	−	30.9481i	−0.400501	−	1.54935i
$400$	−1.00000			−0.0500000
$401$		−	15.4741i		−	0.772738i	−0.922344	−	0.386369i	$-0.873729\pi$
$401$		−	15.4741i		−	0.772738i	0.922344	−	0.386369i	$-0.126271\pi$
$402$	1.12311			0.0560154
$403$	13.7538			0.685125
$404$		−	5.08842i		−	0.253159i
$405$	−20.2462			−1.00604
$406$	5.12311	−	1.32431i	0.254255	−	0.0657242i
$407$	−5.12311			−0.253943
$408$			21.5150i			1.06515i
$409$		−	3.39228i		−	0.167738i	−0.996477	−	0.0838688i	$-0.973272\pi$
$409$		−	3.39228i		−	0.167738i	0.996477	−	0.0838688i	$-0.0267277\pi$
$410$		−	6.78456i		−	0.335066i
$411$	−62.7386			−3.09467
$412$	−10.8769			−0.535866
$413$	6.00000	+	23.2111i	0.295241	+	1.14214i
$414$	−15.6847	−	24.8257i	−0.770859	−	1.22012i
$415$	−8.00000			−0.392705
$416$		−	1.69614i		−	0.0831602i
$417$	−45.6155			−2.23380
$418$			12.0818i			0.590940i
$419$	8.49242			0.414882			0.207441	−	0.978248i	$-0.433487\pi$
$419$	8.49242			0.414882			0.207441	+	0.978248i	$0.433487\pi$
$420$	4.00000	+	15.4741i	0.195180	+	0.755057i
$421$			23.9548i			1.16748i	0.811939	+	0.583742i	$0.198412\pi$
$421$			23.9548i			1.16748i	−0.811939	+	0.583742i	$0.801588\pi$
$422$	−6.24621			−0.304061
$423$			45.0979i			2.19274i
$424$		−	13.7779i		−	0.669116i
$425$	−7.12311			−0.345521
$426$			46.4222i			2.24916i
$427$	10.8769	−	2.81164i	0.526370	−	0.136065i
$428$		−	14.3586i		−	0.694048i
$429$			15.4741i			0.747095i
$430$		−	6.04090i		−	0.291318i
$431$		−	8.85254i		−	0.426412i	−0.977007	−	0.213206i	$-0.931609\pi$
$431$		−	8.85254i		−	0.426412i	0.977007	−	0.213206i	$-0.0683905\pi$
$432$		−	9.43318i		−	0.453854i
$433$	27.6155			1.32712			0.663559	−	0.748124i	$-0.269045\pi$
$433$	27.6155			1.32712			0.663559	+	0.748124i	$0.269045\pi$
$434$	−5.36932	−	20.7713i	−0.257735	−	0.997054i
$435$			12.0818i			0.579278i
$436$		−	17.1702i		−	0.822304i
$437$	10.2462	+	16.2177i	0.490143	+	0.775800i
$438$	−36.4924			−1.74368
$439$			26.9752i			1.28746i	0.765254	+	0.643729i	$0.222613\pi$
$439$			26.9752i			1.28746i	−0.765254	+	0.643729i	$0.777387\pi$
$440$		−	6.04090i		−	0.287988i
$441$	−37.4924	+	20.7713i	−1.78535	+	0.989110i
$442$		−	12.0818i		−	0.574672i
$443$	7.50758			0.356696			0.178348	−	0.983967i	$-0.442925\pi$
$443$	7.50758			0.356696			0.178348	+	0.983967i	$0.442925\pi$
$444$	−5.12311			−0.243132
$445$	−4.00000			−0.189618
$446$			3.22925i			0.152910i
$447$	−51.8617			−2.45298
$448$	−2.56155	+	0.662153i	−0.121022	+	0.0312838i
$449$	15.1231			0.713703			0.356852	−	0.934161i	$-0.383850\pi$
$449$	15.1231			0.713703			0.356852	+	0.934161i	$0.383850\pi$
$450$	6.12311			0.288646
$451$	−10.2462			−0.482475
$452$		−	6.78456i		−	0.319119i
$453$			15.4741i			0.727035i
$454$	−6.24621			−0.293149
$455$	−2.24621	−	8.68951i	−0.105304	−	0.407370i
$456$			12.0818i			0.565782i
$457$		−	41.1250i		−	1.92375i	−0.273496	−	0.961873i	$-0.588180\pi$
$457$		−	41.1250i		−	1.92375i	0.273496	−	0.961873i	$-0.411820\pi$
$458$	−7.75379			−0.362311
$459$		−	67.1935i		−	3.13633i
$460$	−5.12311	−	8.10887i	−0.238866	−	0.378078i
$461$			15.6829i			0.730424i	0.930924	+	0.365212i	$0.119004\pi$
$461$			15.6829i			0.730424i	−0.930924	+	0.365212i	$0.880996\pi$
$462$	23.3693	−	6.04090i	1.08724	−	0.281048i
$463$	8.63068			0.401102			0.200551	−	0.979683i	$-0.435727\pi$
$463$	8.63068			0.401102			0.200551	+	0.979683i	$0.435727\pi$
$464$	−2.00000			−0.0928477
$465$	48.9848			2.27162
$466$	−16.2462			−0.752591
$467$	−7.50758			−0.347409			−0.173705	−	0.984798i	$-0.555574\pi$
$467$	−7.50758			−0.347409			−0.173705	+	0.984798i	$0.555574\pi$
$468$			10.3857i			0.480077i
$469$	0.246211	+	0.952473i	0.0113690	+	0.0439811i
$470$			14.7304i			0.679463i
$471$		−	30.2045i		−	1.39175i
$472$		−	9.06134i		−	0.417082i
$473$	−9.12311			−0.419481
$474$	12.0000			0.551178
$475$	−4.00000			−0.183533
$476$	−18.2462	+	4.71659i	−0.836314	+	0.216184i
$477$			84.3637i			3.86275i
$478$	17.6155			0.805716
$479$	−13.1231			−0.599610			−0.299805	−	0.954001i	$-0.596922\pi$
$479$	−13.1231			−0.599610			−0.299805	+	0.954001i	$0.596922\pi$
$480$		−	6.04090i		−	0.275728i
$481$	2.87689			0.131175
$482$	20.2462			0.922190
$483$	26.2462	−	27.9277i	1.19424	−	1.27075i
$484$	1.87689			0.0853134
$485$	−8.49242			−0.385621
$486$			2.27678i			0.103277i
$487$	28.4924			1.29111			0.645557	−	0.763712i	$-0.276625\pi$
$487$	28.4924			1.29111			0.645557	+	0.763712i	$0.276625\pi$
$488$	−4.24621			−0.192217
$489$		−	49.8145i		−	2.25269i
$490$	−12.2462	+	6.78456i	−0.553227	+	0.306495i
$491$	−34.7386			−1.56773			−0.783866	−	0.620930i	$-0.786755\pi$
$491$	−34.7386			−1.56773			−0.783866	+	0.620930i	$0.786755\pi$
$492$	−10.2462			−0.461935
$493$	−14.2462			−0.641617
$494$		−	6.78456i		−	0.305252i
$495$			36.9890i			1.66253i
$496$			8.10887i			0.364099i
$497$	−39.3693	+	10.1768i	−1.76596	+	0.456494i
$498$			12.0818i			0.541398i
$499$	40.4924			1.81269			0.906345	−	0.422539i	$-0.138861\pi$
$499$	40.4924			1.81269			0.906345	+	0.422539i	$0.138861\pi$
$500$	12.0000			0.536656
$501$	58.7386			2.62425
$502$	26.7386			1.19340
$503$	−9.61553			−0.428735			−0.214368	−	0.976753i	$-0.568769\pi$
$503$	−9.61553			−0.428735			−0.214368	+	0.976753i	$0.568769\pi$
$504$	15.6847	−	4.05444i	0.698650	−	0.180599i
$505$			10.1768i			0.452864i
$506$	−12.2462	+	7.73704i	−0.544410	+	0.343953i
$507$			30.5763i			1.35794i
$508$		0			0
$509$		−	8.48071i		−	0.375901i	−0.982179	−	0.187950i	$-0.939816\pi$
$509$		−	8.48071i		−	0.375901i	0.982179	−	0.187950i	$-0.0601844\pi$
$510$		−	43.0299i		−	1.90540i
$511$	−8.00000	−	30.9481i	−0.353899	−	1.36907i
$512$	1.00000			0.0441942
$513$		−	37.7327i		−	1.66594i
$514$		−	17.3790i		−	0.766556i
$515$	21.7538			0.958586
$516$	−9.12311			−0.401622
$517$	22.2462			0.978387
$518$	−1.12311	−	4.34475i	−0.0493464	−	0.190898i
$519$	−21.1231			−0.927201
$520$			3.39228i			0.148761i
$521$	−21.3693			−0.936207			−0.468103	−	0.883674i	$-0.655063\pi$
$521$	−21.3693			−0.936207			−0.468103	+	0.883674i	$0.655063\pi$
$522$	12.2462			0.536002
$523$	16.4924			0.721163			0.360582	−	0.932728i	$-0.382578\pi$
$523$	16.4924			0.721163			0.360582	+	0.932728i	$0.382578\pi$
$524$			3.02045i			0.131949i
$525$	2.00000	+	7.73704i	0.0872872	+	0.337672i
$526$		−	7.36520i		−	0.321138i
$527$			57.7603i			2.51608i
$528$	−9.12311			−0.397032
$529$	−9.87689	+	20.7713i	−0.429430	+	0.903100i
$530$			27.5559i			1.19695i
$531$			55.4836i			2.40778i
$532$	−10.2462	+	2.64861i	−0.444230	+	0.114832i
$533$	5.75379			0.249224
$534$			6.04090i			0.261415i
$535$			28.7171i			1.24155i
$536$		−	0.371834i		−	0.0160608i
$537$			43.0299i			1.85688i
$538$		−	19.0752i		−	0.822389i
$539$	10.2462	+	18.4945i	0.441336	+	0.796615i
$540$			18.8664i			0.811879i
$541$	12.7386			0.547677			0.273838	−	0.961776i	$-0.411707\pi$
$541$	12.7386			0.547677			0.273838	+	0.961776i	$0.411707\pi$
$542$			1.32431i			0.0568839i
$543$			24.9073i			1.06887i
$544$	7.12311			0.305401
$545$			34.3404i			1.47098i
$546$	−13.1231	+	3.39228i	−0.561617	+	0.145176i
$547$	−16.4924			−0.705165			−0.352583	−	0.935781i	$-0.614696\pi$
$547$	−16.4924			−0.705165			−0.352583	+	0.935781i	$0.614696\pi$
$548$			20.7713i			0.887306i
$549$	26.0000			1.10965
$550$		−	3.02045i		−	0.128792i
$551$	−8.00000			−0.340811
$552$	−12.2462	+	7.73704i	−0.521233	+	0.329310i
$553$	2.63068	+	10.1768i	0.111868	+	0.432764i
$554$	−10.0000			−0.424859
$555$	10.2462			0.434927
$556$			15.1022i			0.640478i
$557$		−	22.0498i		−	0.934281i	−0.884183	−	0.467141i	$-0.845284\pi$
$557$		−	22.0498i		−	0.934281i	0.884183	−	0.467141i	$-0.154716\pi$
$558$		−	49.6515i		−	2.10191i
$559$	5.12311			0.216684
$560$	5.12311	−	1.32431i	0.216491	−	0.0559622i
$561$	−64.9848			−2.74366
$562$			5.29723i			0.223450i
$563$	−42.7386			−1.80122			−0.900609	−	0.434630i	$-0.856879\pi$
$563$	−42.7386			−1.80122			−0.900609	+	0.434630i	$0.856879\pi$
$564$	22.2462			0.936734
$565$			13.5691i			0.570858i
$566$	−20.0000			−0.840663
$567$	−25.9309	+	6.70305i	−1.08899	+	0.281502i
$568$	15.3693			0.644882
$569$		−	3.39228i		−	0.142212i	−0.997469	−	0.0711059i	$-0.977347\pi$
$569$		−	3.39228i		−	0.142212i	0.997469	−	0.0711059i	$-0.0226528\pi$
$570$		−	24.1636i		−	1.01210i
$571$		−	12.4536i		−	0.521168i	−0.965451	−	0.260584i	$-0.916085\pi$
$571$		−	12.4536i		−	0.521168i	0.965451	−	0.260584i	$-0.0839151\pi$
$572$	5.12311			0.214208
$573$	−60.9848			−2.54768
$574$	−2.24621	−	8.68951i	−0.0937550	−	0.362693i
$575$	−2.56155	−	4.05444i	−0.106824	−	0.169082i
$576$	−6.12311			−0.255129
$577$		−	34.7580i		−	1.44700i	−0.690326	−	0.723498i	$-0.742533\pi$
$577$		−	34.7580i		−	1.44700i	0.690326	−	0.723498i	$-0.257467\pi$
$578$	33.7386			1.40334
$579$		−	16.2177i		−	0.673986i
$580$	4.00000			0.166091
$581$	−10.2462	+	2.64861i	−0.425084	+	0.109883i
$582$			12.8255i			0.531632i
$583$	41.6155			1.72354
$584$			12.0818i			0.499948i
$585$		−	20.7713i		−	0.858788i
$586$	18.4924			0.763915
$587$			10.2226i			0.421933i	0.977493	+	0.210966i	$0.0676611\pi$
$587$			10.2226i			0.421933i	−0.977493	+	0.210966i	$0.932339\pi$
$588$	10.2462	+	18.4945i	0.422547	+	0.762701i
$589$			32.4355i			1.33648i
$590$			18.1227i			0.746099i
$591$		−	61.1526i		−	2.51548i
$592$			1.69614i			0.0697110i
$593$			24.1636i			0.992279i	0.868243	+	0.496140i	$0.165250\pi$
$593$			24.1636i			0.992279i	−0.868243	+	0.496140i	$0.834750\pi$
$594$	28.4924			1.16906
$595$	36.4924	−	9.43318i	1.49604	−	0.386723i
$596$			17.1702i			0.703319i
$597$		−	37.7327i		−	1.54430i
$598$	6.87689	−	4.34475i	0.281217	−	0.177670i
$599$	12.4924			0.510427			0.255213	−	0.966885i	$-0.417854\pi$
$599$	12.4924			0.510427			0.255213	+	0.966885i	$0.417854\pi$
$600$		−	3.02045i		−	0.123309i
$601$		−	43.0299i		−	1.75523i	−0.479368	−	0.877614i	$-0.659134\pi$
$601$		−	43.0299i		−	1.75523i	0.479368	−	0.877614i	$-0.340866\pi$
$602$	−2.00000	−	7.73704i	−0.0815139	−	0.315338i
$603$			2.27678i			0.0927176i
$604$	5.12311			0.208456
$605$	−3.75379			−0.152613
$606$	15.3693			0.624336
$607$		−	14.1498i		−	0.574321i	−0.957882	−	0.287161i	$-0.907289\pi$
$607$		−	14.1498i		−	0.574321i	0.957882	−	0.287161i	$-0.0927114\pi$
$608$	4.00000			0.162221
$609$	4.00000	+	15.4741i	0.162088	+	0.627041i
$610$	8.49242			0.343848
$611$	−12.4924			−0.505389
$612$	−43.6155			−1.76305
$613$		−	15.6829i		−	0.633425i	−0.948522	−	0.316713i	$-0.897421\pi$
$613$		−	15.6829i		−	0.633425i	0.948522	−	0.316713i	$-0.102579\pi$
$614$			18.4945i			0.746378i
$615$	20.4924			0.826334
$616$	−2.00000	−	7.73704i	−0.0805823	−	0.311734i
$617$		−	5.29723i		−	0.213258i	−0.994299	−	0.106629i	$-0.965994\pi$
$617$		−	5.29723i		−	0.213258i	0.994299	−	0.106629i	$-0.0340058\pi$
$618$		−	32.8531i		−	1.32155i
$619$	22.2462			0.894151			0.447075	−	0.894496i	$-0.352466\pi$
$619$	22.2462			0.894151			0.447075	+	0.894496i	$0.352466\pi$
$620$		−	16.2177i		−	0.651320i
$621$	38.2462	−	24.1636i	1.53477	−	0.969651i
$622$		−	12.6624i		−	0.507717i
$623$	−5.12311	+	1.32431i	−0.205253	+	0.0530572i
$624$	5.12311			0.205088
$625$	−19.0000			−0.760000
$626$	−18.4924			−0.739106
$627$	−36.4924			−1.45737
$628$	−10.0000			−0.399043
$629$			12.0818i			0.481733i
$630$	−31.3693	+	8.10887i	−1.24978	+	0.323065i
$631$			30.3675i			1.20891i	0.796639	+	0.604456i	$0.206609\pi$
$631$			30.3675i			1.20891i	−0.796639	+	0.604456i	$0.793391\pi$
$632$		−	3.97292i		−	0.158034i
$633$		−	18.8664i		−	0.749870i
$634$	−7.75379			−0.307942
$635$		0			0
$636$	41.6155			1.65016
$637$	−5.75379	−	10.3857i	−0.227973	−	0.411494i
$638$		−	6.04090i		−	0.239161i
$639$	−94.1080			−3.72285
$640$	−2.00000			−0.0790569
$641$		−	22.2586i		−	0.879163i	−0.898203	−	0.439582i	$-0.855127\pi$
$641$		−	22.2586i		−	0.879163i	0.898203	−	0.439582i	$-0.144873\pi$
$642$	43.3693			1.71165
$643$	−26.7386			−1.05447			−0.527234	−	0.849720i	$-0.676771\pi$
$643$	−26.7386			−1.05447			−0.527234	+	0.849720i	$0.676771\pi$
$644$	−9.24621	−	8.68951i	−0.364352	−	0.342415i
$645$	18.2462			0.718444
$646$	28.4924			1.12102
$647$			6.62153i			0.260319i	0.991493	+	0.130160i	$0.0415490\pi$
$647$			6.62153i			0.260319i	−0.991493	+	0.130160i	$0.958451\pi$
$648$	10.1231			0.397673
$649$	27.3693			1.07434
$650$			1.69614i			0.0665281i
$651$	62.7386	−	16.2177i	2.45892	−	0.635623i
$652$	−16.4924			−0.645893
$653$	28.7386			1.12463			0.562315	−	0.826923i	$-0.309911\pi$
$653$	28.7386			1.12463			0.562315	+	0.826923i	$0.309911\pi$
$654$	51.8617			2.02795
$655$		−	6.04090i		−	0.236037i
$656$			3.39228i			0.132446i
$657$		−	73.9781i		−	2.88616i
$658$	4.87689	+	18.8664i	0.190121	+	0.735487i
$659$		−	24.5354i		−	0.955764i	−0.878424	−	0.477882i	$-0.841405\pi$
$659$		−	24.5354i		−	0.955764i	0.878424	−	0.477882i	$-0.158595\pi$
$660$	18.2462			0.710233
$661$	−38.4924			−1.49718			−0.748591	−	0.663032i	$-0.769269\pi$
$661$	−38.4924			−1.49718			−0.748591	+	0.663032i	$0.769269\pi$
$662$	−14.2462			−0.553695
$663$	36.4924			1.41725
$664$	4.00000			0.155230
$665$	20.4924	−	5.29723i	0.794662	−	0.205418i
$666$		−	10.3857i		−	0.402436i
$667$	−5.12311	−	8.10887i	−0.198367	−	0.313977i
$668$		−	19.4470i		−	0.752427i
$669$	−9.75379			−0.377103
$670$			0.743668i			0.0287304i
$671$		−	12.8255i		−	0.495121i
$672$	−2.00000	−	7.73704i	−0.0771517	−	0.298463i
$673$	−16.8769			−0.650556			−0.325278	−	0.945618i	$-0.605458\pi$
$673$	−16.8769			−0.650556			−0.325278	+	0.945618i	$0.605458\pi$
$674$		−	10.5945i		−	0.408083i
$675$			9.43318i			0.363083i
$676$	10.1231			0.389350
$677$	18.4924			0.710722			0.355361	−	0.934729i	$-0.384358\pi$
$677$	18.4924			0.710722			0.355361	+	0.934729i	$0.384358\pi$
$678$	20.4924			0.787007
$679$	−10.8769	+	2.81164i	−0.417417	+	0.107901i
$680$	−14.2462			−0.546317
$681$		−	18.8664i		−	0.722960i
$682$	−24.4924			−0.937863
$683$	−8.49242			−0.324954			−0.162477	−	0.986712i	$-0.551948\pi$
$683$	−8.49242			−0.324954			−0.162477	+	0.986712i	$0.551948\pi$
$684$	−24.4924			−0.936491
$685$		−	41.5426i		−	1.58726i
$686$	−13.4384	+	12.7439i	−0.513082	+	0.486566i
$687$		−	23.4199i		−	0.893525i
$688$			3.02045i			0.115153i
$689$	−23.3693			−0.890300
$690$	24.4924	−	15.4741i	0.932411	−	0.589088i
$691$		−	43.4018i		−	1.65108i	−0.564343	−	0.825541i	$-0.690870\pi$
$691$		−	43.4018i		−	1.65108i	0.564343	−	0.825541i	$-0.309130\pi$
$692$			6.99337i			0.265848i
$693$	12.2462	+	47.3747i	0.465195	+	1.79962i
$694$	16.4924			0.626044
$695$		−	30.2045i		−	1.14572i
$696$		−	6.04090i		−	0.228980i
$697$			24.1636i			0.915261i
$698$		−	12.2906i		−	0.465206i
$699$		−	49.0708i		−	1.85603i
$700$	2.56155	−	0.662153i	0.0968176	−	0.0250270i
$701$		−	27.7647i		−	1.04866i	−0.851516	−	0.524329i	$-0.824316\pi$
$701$		−	27.7647i		−	1.04866i	0.851516	−	0.524329i	$-0.175684\pi$
$702$	−16.0000			−0.603881
$703$			6.78456i			0.255885i
$704$			3.02045i			0.113837i
$705$	−44.4924			−1.67568
$706$		−	13.5691i		−	0.510681i
$707$	3.36932	+	13.0343i	0.126716	+	0.490204i
$708$	27.3693			1.02860
$709$			27.7647i			1.04272i	0.853336	+	0.521362i	$0.174576\pi$
$709$			27.7647i			1.04272i	−0.853336	+	0.521362i	$0.825424\pi$
$710$	−30.7386			−1.15360
$711$			24.3266i			0.912319i
$712$	2.00000			0.0749532
$713$	−32.8769	+	20.7713i	−1.23125	+	0.777891i
$714$	−14.2462	−	55.1117i	−0.533151	−	2.06250i
$715$	−10.2462			−0.383187
$716$	14.2462			0.532406
$717$			53.2068i			1.98704i
$718$			23.5829i			0.880108i
$719$			45.8416i			1.70960i	0.518955	+	0.854801i	$0.326321\pi$
$719$			45.8416i			1.70960i	−0.518955	+	0.854801i	$0.673679\pi$
$720$	12.2462			0.456389
$721$	27.8617	−	7.20217i	1.03763	−	0.268223i
$722$	−3.00000			−0.111648
$723$			61.1526i			2.27429i
$724$	8.24621			0.306468
$725$	2.00000			0.0742781
$726$			5.66906i			0.210399i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	1.12311	+	4.34475i	0.0416251	+	0.161027i
$729$	23.4924			0.870090
$730$		−	24.1636i		−	0.894334i
$731$			21.5150i			0.795760i
$732$		−	12.8255i		−	0.474043i
$733$	42.4924			1.56949			0.784747	−	0.619817i	$-0.212793\pi$
$733$	42.4924			1.56949			0.784747	+	0.619817i	$0.212793\pi$
$734$	2.87689			0.106188
$735$	−20.4924	−	36.9890i	−0.755874	−	1.36436i
$736$	2.56155	+	4.05444i	0.0944201	+	0.149448i
$737$	1.12311			0.0413701
$738$		−	20.7713i		−	0.764602i
$739$	−28.0000			−1.03000			−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000			−1.03000			−0.514998	+	0.857191i	$0.672207\pi$
$740$		−	3.39228i		−	0.124703i
$741$	20.4924			0.752808
$742$	9.12311	+	35.2929i	0.334920	+	1.29564i
$743$			36.0823i			1.32373i	0.749622	+	0.661866i	$0.230235\pi$
$743$			36.0823i			1.32373i	−0.749622	+	0.661866i	$0.769765\pi$
$744$	−24.4924			−0.897936
$745$		−	34.3404i		−	1.25814i
$746$		−	18.6576i		−	0.683101i
$747$	−24.4924			−0.896131
$748$			21.5150i			0.786665i
$749$	9.50758	+	36.7802i	0.347399	+	1.34392i
$750$			36.2454i			1.32349i
$751$		−	34.9211i		−	1.27429i	−0.770745	−	0.637144i	$-0.780116\pi$
$751$		−	34.9211i		−	1.27429i	0.770745	−	0.637144i	$-0.219884\pi$
$752$		−	7.36520i		−	0.268581i
$753$			80.7627i			2.94315i
$754$			3.39228i			0.123540i
$755$	−10.2462			−0.372898
$756$	6.24621	+	24.1636i	0.227173	+	0.878821i
$757$		−	8.89831i		−	0.323415i	−0.986839	−	0.161707i	$-0.948300\pi$
$757$		−	8.89831i		−	0.323415i	0.986839	−	0.161707i	$-0.0517001\pi$
$758$			18.4945i			0.671751i
$759$	−23.3693	−	36.9890i	−0.848252	−	1.34262i
$760$	−8.00000			−0.290191
$761$		−	16.9614i		−	0.614851i	−0.951572	−	0.307425i	$-0.900533\pi$
$761$		−	16.9614i		−	0.614851i	0.951572	−	0.307425i	$-0.0994674\pi$
$762$		0			0
$763$	11.3693	+	43.9824i	0.411597	+	1.59227i
$764$			20.1907i			0.730473i
$765$	87.2311			3.15385
$766$	18.8769			0.682050
$767$	−15.3693			−0.554954
$768$			3.02045i			0.108991i
$769$	2.63068			0.0948649			0.0474324	−	0.998874i	$-0.484896\pi$
$769$	2.63068			0.0948649			0.0474324	+	0.998874i	$0.484896\pi$
$770$	4.00000	+	15.4741i	0.144150	+	0.557647i
$771$	52.4924			1.89047
$772$	−5.36932			−0.193246
$773$	35.7538			1.28597			0.642987	−	0.765877i	$-0.277695\pi$
$773$	35.7538			1.28597			0.642987	+	0.765877i	$0.277695\pi$
$774$		−	18.4945i		−	0.664772i
$775$		−	8.10887i		−	0.291279i
$776$	4.24621			0.152430
$777$	13.1231	−	3.39228i	0.470789	−	0.121697i
$778$		−	11.8730i		−	0.425667i
$779$			13.5691i			0.486164i
$780$	−10.2462			−0.366873
$781$			46.4222i			1.66112i
$782$	18.2462	+	28.8802i	0.652483	+	1.03275i
$783$			18.8664i			0.674229i
$784$	6.12311	−	3.39228i	0.218682	−	0.121153i
$785$	20.0000			0.713831
$786$	−9.12311			−0.325410
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	−20.2462			−0.721241
$789$	22.2462			0.791986
$790$			7.94584i			0.282700i
$791$	4.49242	+	17.3790i	0.159732	+	0.617927i
$792$		−	18.4945i		−	0.657174i
$793$			7.20217i			0.255757i
$794$		−	23.9548i		−	0.850123i
$795$	−83.2311			−2.95190
$796$	−12.4924			−0.442782
$797$	1.50758			0.0534011			0.0267006	−	0.999643i	$-0.491500\pi$
$797$	1.50758			0.0534011			0.0267006	+	0.999643i	$0.491500\pi$
$798$	−8.00000	−	30.9481i	−0.283197	−	1.09555i
$799$		−	52.4631i		−	1.85601i
$800$	−1.00000			−0.0353553
$801$	−12.2462			−0.432699
$802$		−	15.4741i		−	0.546409i
$803$	−36.4924			−1.28779
$804$	1.12311			0.0396089
$805$	18.4924	+	17.3790i	0.651772	+	0.612530i
$806$	13.7538			0.484457
$807$	57.6155			2.02816
$808$		−	5.08842i		−	0.179010i
$809$	23.1231			0.812965			0.406483	−	0.913659i	$-0.366755\pi$
$809$	23.1231			0.812965			0.406483	+	0.913659i	$0.366755\pi$
$810$	−20.2462			−0.711379
$811$		−	28.3453i		−	0.995338i	−0.867367	−	0.497669i	$-0.834189\pi$
$811$		−	28.3453i		−	0.995338i	0.867367	−	0.497669i	$-0.165811\pi$
$812$	5.12311	−	1.32431i	0.179786	−	0.0464741i
$813$	−4.00000			−0.140286
$814$	−5.12311			−0.179565
$815$	32.9848			1.15541
$816$			21.5150i			0.753175i
$817$			12.0818i			0.422688i
$818$		−	3.39228i		−	0.118608i
$819$	−6.87689	−	26.6034i	−0.240298	−	0.929598i
$820$		−	6.78456i		−	0.236927i
$821$	−45.2311			−1.57857			−0.789287	−	0.614024i	$-0.789550\pi$
$821$	−45.2311			−1.57857			−0.789287	+	0.614024i	$0.789550\pi$
$822$	−62.7386			−2.18826
$823$	3.50758			0.122266			0.0611332	−	0.998130i	$-0.480529\pi$
$823$	3.50758			0.122266			0.0611332	+	0.998130i	$0.480529\pi$
$824$	−10.8769			−0.378915
$825$	9.12311			0.317626
$826$	6.00000	+	23.2111i	0.208767	+	0.807618i
$827$		−	12.4536i		−	0.433055i	−0.976277	−	0.216528i	$-0.930527\pi$
$827$		−	12.4536i		−	0.433055i	0.976277	−	0.216528i	$-0.0694731\pi$
$828$	−15.6847	−	24.8257i	−0.545080	−	0.862754i
$829$		−	20.9801i		−	0.728669i	−0.931268	−	0.364335i	$-0.881296\pi$
$829$		−	20.9801i		−	0.728669i	0.931268	−	0.364335i	$-0.118704\pi$
$830$	−8.00000			−0.277684
$831$		−	30.2045i		−	1.04778i
$832$		−	1.69614i		−	0.0588031i
$833$	43.6155	−	24.1636i	1.51119	−	0.837219i
$834$	−45.6155			−1.57954
$835$			38.8940i			1.34598i
$836$			12.0818i			0.417858i
$837$	76.4924			2.64396
$838$	8.49242			0.293366
$839$	−19.8617			−0.685703			−0.342852	−	0.939390i	$-0.611393\pi$
$839$	−19.8617			−0.685703			−0.342852	+	0.939390i	$0.611393\pi$
$840$	4.00000	+	15.4741i	0.138013	+	0.533906i
$841$	−25.0000			−0.862069
$842$			23.9548i			0.825536i
$843$	−16.0000			−0.551069
$844$	−6.24621			−0.215003
$845$	−20.2462			−0.696491
$846$			45.0979i			1.55050i
$847$	−4.80776	+	1.24279i	−0.165197	+	0.0427028i
$848$		−	13.7779i		−	0.473136i
$849$		−	60.4090i		−	2.07323i
$850$	−7.12311			−0.244321
$851$	−6.87689	+	4.34475i	−0.235737	+	0.148936i
$852$			46.4222i			1.59040i
$853$			27.7647i			0.950644i	0.879812	+	0.475322i	$0.157668\pi$
$853$			27.7647i			0.950644i	−0.879812	+	0.475322i	$0.842332\pi$
$854$	10.8769	−	2.81164i	0.372200	−	0.0962125i
$855$	48.9848			1.67525
$856$		−	14.3586i		−	0.490766i
$857$			13.9867i			0.477778i	0.971047	+	0.238889i	$0.0767832\pi$
$857$			13.9867i			0.477778i	−0.971047	+	0.238889i	$0.923217\pi$
$858$			15.4741i			0.528276i
$859$		−	5.25145i		−	0.179177i	−0.995979	−	0.0895886i	$-0.971445\pi$
$859$		−	5.25145i		−	0.179177i	0.995979	−	0.0895886i	$-0.0285552\pi$
$860$		−	6.04090i		−	0.205993i
$861$	26.2462	−	6.78456i	0.894468	−	0.231217i
$862$		−	8.85254i		−	0.301519i
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$		−	9.43318i		−	0.320923i
$865$		−	13.9867i		−	0.475563i
$866$	27.6155			0.938414
$867$			101.906i			3.46090i
$868$	−5.36932	−	20.7713i	−0.182246	−	0.705024i
$869$	12.0000			0.407072
$870$			12.0818i			0.409611i
$871$	−0.630683			−0.0213699
$872$		−	17.1702i		−	0.581457i
$873$	−26.0000			−0.879967
$874$	10.2462	+	16.2177i	0.346583	+	0.548573i
$875$	−30.7386	+	7.94584i	−1.03916	+	0.268618i
$876$	−36.4924			−1.23296
$877$	2.49242			0.0841631			0.0420816	−	0.999114i	$-0.486601\pi$
$877$	2.49242			0.0841631			0.0420816	+	0.999114i	$0.486601\pi$
$878$			26.9752i			0.910370i
$879$			55.8554i			1.88396i
$880$		−	6.04090i		−	0.203639i
$881$	1.36932			0.0461335			0.0230667	−	0.999734i	$-0.492657\pi$
$881$	1.36932			0.0461335			0.0230667	+	0.999734i	$0.492657\pi$
$882$	−37.4924	+	20.7713i	−1.26244	+	0.699406i
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		−	12.0818i		−	0.406355i
$885$	−54.7386			−1.84002
$886$	7.50758			0.252222
$887$			4.71659i			0.158368i	0.996860	+	0.0791838i	$0.0252314\pi$
$887$			4.71659i			0.158368i	−0.996860	+	0.0791838i	$0.974769\pi$
$888$	−5.12311			−0.171920
$889$		0			0
$890$	−4.00000			−0.134080
$891$			30.5763i			1.02435i
$892$			3.22925i			0.108123i
$893$		−	29.4608i		−	0.985868i
$894$	−51.8617			−1.73452
$895$	−28.4924			−0.952397
$896$	−2.56155	+	0.662153i	−0.0855755	+	0.0221210i
$897$	13.1231	+	20.7713i	0.438168	+	0.693534i
$898$	15.1231			0.504665
$899$		−	16.2177i		−	0.540892i
$900$	6.12311			0.204104
$901$		−	98.1417i		−	3.26957i
$902$	−10.2462			−0.341162
$903$	23.3693	−	6.04090i	0.777682	−	0.201028i
$904$		−	6.78456i		−	0.225651i
$905$	−16.4924			−0.548227
$906$			15.4741i			0.514092i
$907$		−	0.789443i		−	0.0262130i	−0.999914	−	0.0131065i	$-0.995828\pi$
$907$		−	0.789443i		−	0.0262130i	0.999914	−	0.0131065i	$-0.00417205\pi$
$908$	−6.24621			−0.207288
$909$			31.1570i			1.03341i
$910$	−2.24621	−	8.68951i	−0.0744612	−	0.288054i
$911$		−	8.85254i		−	0.293298i	−0.989189	−	0.146649i	$-0.953151\pi$
$911$		−	8.85254i		−	0.293298i	0.989189	−	0.146649i	$-0.0468487\pi$
$912$			12.0818i			0.400068i
$913$			12.0818i			0.399849i
$914$		−	41.1250i		−	1.36029i
$915$			25.6509i			0.847993i
$916$	−7.75379			−0.256192
$917$	−2.00000	−	7.73704i	−0.0660458	−	0.255499i
$918$		−	67.1935i		−	2.21772i
$919$			21.6780i			0.715091i	0.933896	+	0.357546i	$0.116386\pi$
$919$			21.6780i			0.715091i	−0.933896	+	0.357546i	$0.883614\pi$
$920$	−5.12311	−	8.10887i	−0.168904	−	0.267342i
$921$	−55.8617			−1.84071
$922$			15.6829i			0.516488i
$923$		−	26.0685i		−	0.858056i
$924$	23.3693	−	6.04090i	0.768794	−	0.198731i
$925$		−	1.69614i		−	0.0557688i
$926$	8.63068			0.283622
$927$	66.6004			2.18744
$928$	−2.00000			−0.0656532
$929$			35.8278i			1.17547i	0.809053	+	0.587735i	$0.199980\pi$
$929$			35.8278i			1.17547i	−0.809053	+	0.587735i	$0.800020\pi$
$930$	48.9848			1.60628
$931$	24.4924	−	13.5691i	0.802707	−	0.444710i
$932$	−16.2462			−0.532162
$933$	38.2462			1.25212
$934$	−7.50758			−0.245655
$935$		−	43.0299i		−	1.40723i
$936$			10.3857i			0.339466i
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$	0.246211	+	0.952473i	0.00803908	+	0.0310993i
$939$		−	55.8554i		−	1.82277i
$940$			14.7304i			0.480453i
$941$	−8.73863			−0.284871			−0.142436	−	0.989804i	$-0.545493\pi$
$941$	−8.73863			−0.284871			−0.142436	+	0.989804i	$0.545493\pi$
$942$		−	30.2045i		−	0.984115i
$943$	−13.7538	+	8.68951i	−0.447885	+	0.282969i
$944$		−	9.06134i		−	0.294922i
$945$	−12.4924	−	48.3272i	−0.406379	−	1.57208i
$946$	−9.12311			−0.296618
$947$	−52.9848			−1.72178			−0.860888	−	0.508794i	$-0.830091\pi$
$947$	−52.9848			−1.72178			−0.860888	+	0.508794i	$0.830091\pi$
$948$	12.0000			0.389742
$949$	20.4924			0.665212
$950$	−4.00000			−0.129777
$951$		−	23.4199i		−	0.759443i
$952$	−18.2462	+	4.71659i	−0.591363	+	0.152866i
$953$			31.3658i			1.01604i	0.861346	+	0.508018i	$0.169622\pi$
$953$			31.3658i			1.01604i	−0.861346	+	0.508018i	$0.830378\pi$
$954$			84.3637i			2.73138i
$955$		−	40.3813i		−	1.30671i
$956$	17.6155			0.569727
$957$	18.2462			0.589816
$958$	−13.1231			−0.423988
$959$	−13.7538	−	53.2068i	−0.444133	−	1.71814i
$960$		−	6.04090i		−	0.194969i
$961$	−34.7538			−1.12109
$962$	2.87689			0.0927548
$963$			87.9190i			2.83315i
$964$	20.2462			0.652087
$965$	10.7386			0.345689
$966$	26.2462	−	27.9277i	0.844458	−	0.898559i
$967$	−51.8617			−1.66776			−0.833881	−	0.551945i	$-0.813886\pi$
$967$	−51.8617			−1.66776			−0.833881	+	0.551945i	$0.813886\pi$
$968$	1.87689			0.0603257
$969$			86.0599i			2.76464i
$970$	−8.49242			−0.272675
$971$	−39.2311			−1.25898			−0.629492	−	0.777007i	$-0.716737\pi$
$971$	−39.2311			−1.25898			−0.629492	+	0.777007i	$0.716737\pi$
$972$			2.27678i			0.0730277i
$973$	−10.0000	−	38.6852i	−0.320585	−	1.24019i
$974$	28.4924			0.912956
$975$	−5.12311			−0.164071
$976$	−4.24621			−0.135918
$977$		−	32.8531i		−	1.05106i	−0.850774	−	0.525532i	$-0.823866\pi$
$977$		−	32.8531i		−	1.05106i	0.850774	−	0.525532i	$-0.176134\pi$
$978$		−	49.8145i		−	1.59289i
$979$			6.04090i			0.193068i
$980$	−12.2462	+	6.78456i	−0.391191	+	0.216725i
$981$			105.135i			3.35670i
$982$	−34.7386			−1.10855
$983$	44.4924			1.41909			0.709544	−	0.704661i	$-0.248901\pi$
$983$	44.4924			1.41909			0.709544	+	0.704661i	$0.248901\pi$
$984$	−10.2462			−0.326637
$985$	40.4924			1.29020
$986$	−14.2462			−0.453692
$987$	−56.9848	+	14.7304i	−1.81385	+	0.468874i
$988$		−	6.78456i		−	0.215846i
$989$	−12.2462	+	7.73704i	−0.389407	+	0.246023i
$990$			36.9890i			1.17559i
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$			8.10887i			0.257457i
$993$		−	43.0299i		−	1.36551i
$994$	−39.3693	+	10.1768i	−1.24872	+	0.322790i
$995$	24.9848			0.792073
$996$			12.0818i			0.382826i
$997$		−	5.08842i		−	0.161152i	−0.996748	−	0.0805760i	$-0.974324\pi$
$997$		−	5.08842i		−	0.161152i	0.996748	−	0.0805760i	$-0.0256760\pi$
$998$	40.4924			1.28177
$999$	16.0000			0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.c.c.321.4	yes	4
3.2	odd	2		2898.2.g.b.2575.2		4
4.3	odd	2		2576.2.f.b.321.1		4
7.6	odd	2		322.2.c.d.321.1	yes	4
21.20	even	2		2898.2.g.a.2575.4		4
23.22	odd	2		322.2.c.d.321.4	yes	4
28.27	even	2		2576.2.f.e.321.4		4
69.68	even	2		2898.2.g.a.2575.3		4
92.91	even	2		2576.2.f.e.321.1		4
161.160	even	2	inner	322.2.c.c.321.1	✓	4
483.482	odd	2		2898.2.g.b.2575.1		4
644.643	odd	2		2576.2.f.b.321.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.c.c.321.1	✓	4	161.160	even	2	inner
322.2.c.c.321.4	yes	4	1.1	even	1	trivial
322.2.c.d.321.1	yes	4	7.6	odd	2
322.2.c.d.321.4	yes	4	23.22	odd	2
2576.2.f.b.321.1		4	4.3	odd	2
2576.2.f.b.321.4		4	644.643	odd	2
2576.2.f.e.321.1		4	92.91	even	2
2576.2.f.e.321.4		4	28.27	even	2
2898.2.g.a.2575.3		4	69.68	even	2
2898.2.g.a.2575.4		4	21.20	even	2
2898.2.g.b.2575.1		4	483.482	odd	2
2898.2.g.b.2575.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.02045i q^{3} +1.00000 q^{4} -2.00000 q^{5} +3.02045i q^{6} +(-2.56155 + 0.662153i) q^{7} +1.00000 q^{8} -6.12311 q^{9} -2.00000 q^{10} +3.02045i q^{11} +3.02045i q^{12} -1.69614i q^{13} +(-2.56155 + 0.662153i) q^{14} -6.04090i q^{15} +1.00000 q^{16} +7.12311 q^{17} -6.12311 q^{18} +4.00000 q^{19} -2.00000 q^{20} +(-2.00000 - 7.73704i) q^{21} +3.02045i q^{22} +(2.56155 + 4.05444i) q^{23} +3.02045i q^{24} -1.00000 q^{25} -1.69614i q^{26} -9.43318i q^{27} +(-2.56155 + 0.662153i) q^{28} -2.00000 q^{29} -6.04090i q^{30} +8.10887i q^{31} +1.00000 q^{32} -9.12311 q^{33} +7.12311 q^{34} +(5.12311 - 1.32431i) q^{35} -6.12311 q^{36} +1.69614i q^{37} +4.00000 q^{38} +5.12311 q^{39} -2.00000 q^{40} +3.39228i q^{41} +(-2.00000 - 7.73704i) q^{42} +3.02045i q^{43} +3.02045i q^{44} +12.2462 q^{45} +(2.56155 + 4.05444i) q^{46} -7.36520i q^{47} +3.02045i q^{48} +(6.12311 - 3.39228i) q^{49} -1.00000 q^{50} +21.5150i q^{51} -1.69614i q^{52} -13.7779i q^{53} -9.43318i q^{54} -6.04090i q^{55} +(-2.56155 + 0.662153i) q^{56} +12.0818i q^{57} -2.00000 q^{58} -9.06134i q^{59} -6.04090i q^{60} -4.24621 q^{61} +8.10887i q^{62} +(15.6847 - 4.05444i) q^{63} +1.00000 q^{64} +3.39228i q^{65} -9.12311 q^{66} -0.371834i q^{67} +7.12311 q^{68} +(-12.2462 + 7.73704i) q^{69} +(5.12311 - 1.32431i) q^{70} +15.3693 q^{71} -6.12311 q^{72} +12.0818i q^{73} +1.69614i q^{74} -3.02045i q^{75} +4.00000 q^{76} +(-2.00000 - 7.73704i) q^{77} +5.12311 q^{78} -3.97292i q^{79} -2.00000 q^{80} +10.1231 q^{81} +3.39228i q^{82} +4.00000 q^{83} +(-2.00000 - 7.73704i) q^{84} -14.2462 q^{85} +3.02045i q^{86} -6.04090i q^{87} +3.02045i q^{88} +2.00000 q^{89} +12.2462 q^{90} +(1.12311 + 4.34475i) q^{91} +(2.56155 + 4.05444i) q^{92} -24.4924 q^{93} -7.36520i q^{94} -8.00000 q^{95} +3.02045i q^{96} +4.24621 q^{97} +(6.12311 - 3.39228i) q^{98} -18.4945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} - 8 q^{5} - 2 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{10} - 2 q^{14} + 4 q^{16} + 12 q^{17} - 8 q^{18} + 16 q^{19} - 8 q^{20} - 8 q^{21} + 2 q^{23} - 4 q^{25} - 2 q^{28} - 8 q^{29} + 4 q^{32}+ \cdots + 8 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 - 8 * q^5 - 2 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^10 - 2 * q^14 + 4 * q^16 + 12 * q^17 - 8 * q^18 + 16 * q^19 - 8 * q^20 - 8 * q^21 + 2 * q^23 - 4 * q^25 - 2 * q^28 - 8 * q^29 + 4 * q^32 - 20 * q^33 + 12 * q^34 + 4 * q^35 - 8 * q^36 + 16 * q^38 + 4 * q^39 - 8 * q^40 - 8 * q^42 + 16 * q^45 + 2 * q^46 + 8 * q^49 - 4 * q^50 - 2 * q^56 - 8 * q^58 + 16 * q^61 + 38 * q^63 + 4 * q^64 - 20 * q^66 + 12 * q^68 - 16 * q^69 + 4 * q^70 + 12 * q^71 - 8 * q^72 + 16 * q^76 - 8 * q^77 + 4 * q^78 - 8 * q^80 + 24 * q^81 + 16 * q^83 - 8 * q^84 - 24 * q^85 + 8 * q^89 + 16 * q^90 - 12 * q^91 + 2 * q^92 - 32 * q^93 - 32 * q^95 - 16 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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