LMFDB - Embedded newform 1998.2.k.a.1639.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(1063,1998)] 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("1998.1063"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1998, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1998 = 2 \cdot 3^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1998.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.9541103239$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 666)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1639.15
Character	$\chi$	$=$	1998.1639
Dual form			1998.2.k.a.1063.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} -2.07510i q^{5} +(-1.46218 - 2.53257i) q^{7} +1.00000i q^{8} -2.07510 q^{10} +(-1.24729 + 2.16036i) q^{11} +0.965976i q^{13} +(-2.53257 + 1.46218i) q^{14} +1.00000 q^{16} +(-5.51981 + 3.18686i) q^{17} +(5.19406 + 2.99879i) q^{19} +2.07510i q^{20} +(2.16036 + 1.24729i) q^{22} +(-6.10692 + 3.52583i) q^{23} +0.693968 q^{25} +0.965976 q^{26} +(1.46218 + 2.53257i) q^{28} +(-1.39694 - 0.806522i) q^{29} +(-4.44527 + 2.56648i) q^{31} -1.00000i q^{32} +(3.18686 + 5.51981i) q^{34} +(-5.25533 + 3.03416i) q^{35} +(-5.41023 + 2.78018i) q^{37} +(2.99879 - 5.19406i) q^{38} +2.07510 q^{40} +7.84678 q^{41} +(0.286819 + 0.165595i) q^{43} +(1.24729 - 2.16036i) q^{44} +(3.52583 + 6.10692i) q^{46} +(4.35223 - 7.53829i) q^{47} +(-0.775932 + 1.34395i) q^{49} -0.693968i q^{50} -0.965976i q^{52} +(6.29300 + 10.8998i) q^{53} +(4.48297 + 2.58824i) q^{55} +(2.53257 - 1.46218i) q^{56} +(-0.806522 + 1.39694i) q^{58} +(-5.26958 - 3.04240i) q^{59} +(3.32949 - 1.92228i) q^{61} +(2.56648 + 4.44527i) q^{62} -1.00000 q^{64} +2.00450 q^{65} +9.83943 q^{67} +(5.51981 - 3.18686i) q^{68} +(3.03416 + 5.25533i) q^{70} +(-1.55554 + 2.69428i) q^{71} -12.3747 q^{73} +(2.78018 + 5.41023i) q^{74} +(-5.19406 - 2.99879i) q^{76} +7.29502 q^{77} +(1.65079 - 0.953087i) q^{79} -2.07510i q^{80} -7.84678i q^{82} -10.8429 q^{83} +(6.61306 + 11.4541i) q^{85} +(0.165595 - 0.286819i) q^{86} +(-2.16036 - 1.24729i) q^{88} +(11.9327 - 6.88934i) q^{89} +(2.44640 - 1.41243i) q^{91} +(6.10692 - 3.52583i) q^{92} +(-7.53829 - 4.35223i) q^{94} +(6.22279 - 10.7782i) q^{95} +(4.24112 + 2.44861i) q^{97} +(1.34395 + 0.775932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} - 2 q^{7} + 4 q^{11} + 76 q^{16} - 12 q^{23} - 100 q^{25} + 24 q^{26} + 2 q^{28} - 18 q^{29} + 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} - 72 q^{41} + 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) $ 76 * q - 76 * q^4 - 2 * q^7 + 4 * q^11 + 76 * q^16 - 12 * q^23 - 100 * q^25 + 24 * q^26 + 2 * q^28 - 18 * q^29 + 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 - 72 * q^41 + 6 * q^43 - 4 * q^44 + 20 * q^47 - 36 * q^49 - 14 * q^53 + 6 * q^59 + 16 * q^62 - 76 * q^64 - 32 * q^65 + 40 * q^67 - 2 * q^71 + 28 * q^73 + 2 * q^74 + 24 * q^77 + 6 * q^79 + 64 * q^83 - 12 * q^85 - 4 * q^86 - 60 * q^89 + 42 * q^91 + 12 * q^92 + 14 * q^95 - 12 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1998\mathbb{Z}\right)^\times$.

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$		−	2.07510i		−	0.928012i	−0.885832	−	0.464006i	$-0.846412\pi$
$5$		−	2.07510i		−	0.928012i	0.885832	−	0.464006i	$-0.153588\pi$
$6$		0			0
$7$	−1.46218	−	2.53257i	−0.552652	−	0.957221i	−0.998082	−	0.0619040i	$-0.980283\pi$
$7$	−1.46218	−	2.53257i	−0.552652	−	0.957221i	0.445431	−	0.895316i	$-0.353051\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.07510			−0.656204
$11$	−1.24729	+	2.16036i	−0.376071	+	0.651374i	−0.990487	−	0.137608i	$-0.956058\pi$
$11$	−1.24729	+	2.16036i	−0.376071	+	0.651374i	0.614416	+	0.788982i	$0.289392\pi$
$12$		0			0
$13$			0.965976i			0.267914i	0.990987	+	0.133957i	$0.0427683\pi$
$13$			0.965976i			0.267914i	−0.990987	+	0.133957i	$0.957232\pi$
$14$	−2.53257	+	1.46218i	−0.676857	+	0.390784i
$15$		0			0
$16$	1.00000			0.250000
$17$	−5.51981	+	3.18686i	−1.33875	+	0.772928i	−0.986622	−	0.163024i	$-0.947875\pi$
$17$	−5.51981	+	3.18686i	−1.33875	+	0.772928i	−0.352129	+	0.935952i	$0.614542\pi$
$18$		0			0
$19$	5.19406	+	2.99879i	1.19160	+	0.687970i	0.958669	−	0.284523i	$-0.0918354\pi$
$19$	5.19406	+	2.99879i	1.19160	+	0.687970i	0.232930	+	0.972494i	$0.425169\pi$
$20$			2.07510i			0.464006i
$21$		0			0
$22$	2.16036	+	1.24729i	0.460591	+	0.265922i
$23$	−6.10692	+	3.52583i	−1.27338	+	0.735186i	−0.975623	−	0.219455i	$-0.929572\pi$
$23$	−6.10692	+	3.52583i	−1.27338	+	0.735186i	−0.297757	+	0.954642i	$0.596239\pi$
$24$		0			0
$25$	0.693968			0.138794
$26$	0.965976			0.189444
$27$		0			0
$28$	1.46218	+	2.53257i	0.276326	+	0.478610i
$29$	−1.39694	−	0.806522i	−0.259405	−	0.149767i	0.364658	−	0.931141i	$-0.381186\pi$
$29$	−1.39694	−	0.806522i	−0.259405	−	0.149767i	−0.624063	+	0.781374i	$0.714519\pi$
$30$		0			0
$31$	−4.44527	+	2.56648i	−0.798393	+	0.460953i	−0.842909	−	0.538056i	$-0.819159\pi$
$31$	−4.44527	+	2.56648i	−0.798393	+	0.460953i	0.0445157	+	0.999009i	$0.485826\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	3.18686	+	5.51981i	0.546543	+	0.946640i
$35$	−5.25533	+	3.03416i	−0.888312	+	0.512867i
$36$		0			0
$37$	−5.41023	+	2.78018i	−0.889436	+	0.457060i
$37$	−5.41023	+	2.78018i	−0.889436	+	0.457060i
$38$	2.99879	−	5.19406i	0.486468	−	0.842588i
$39$		0			0
$40$	2.07510			0.328102
$41$	7.84678			1.22546			0.612730	−	0.790292i	$-0.290071\pi$
$41$	7.84678			1.22546			0.612730	+	0.790292i	$0.290071\pi$
$42$		0			0
$43$	0.286819	+	0.165595i	0.0437395	+	0.0252530i	0.521710	−	0.853123i	$-0.325294\pi$
$43$	0.286819	+	0.165595i	0.0437395	+	0.0252530i	−0.477971	+	0.878376i	$0.658628\pi$
$44$	1.24729	−	2.16036i	0.188036	−	0.325687i
$45$		0			0
$46$	3.52583	+	6.10692i	0.519855	+	0.900416i
$47$	4.35223	−	7.53829i	0.634838	−	1.09957i	−0.351711	−	0.936109i	$-0.614400\pi$
$47$	4.35223	−	7.53829i	0.634838	−	1.09957i	0.986549	−	0.163463i	$-0.0522666\pi$
$48$		0			0
$49$	−0.775932	+	1.34395i	−0.110847	+	0.191993i
$50$		−	0.693968i		−	0.0981419i
$51$		0			0
$52$		−	0.965976i		−	0.133957i
$53$	6.29300	+	10.8998i	0.864410	+	1.49720i	0.867631	+	0.497208i	$0.165641\pi$
$53$	6.29300	+	10.8998i	0.864410	+	1.49720i	−0.00322093	+	0.999995i	$0.501025\pi$
$54$		0			0
$55$	4.48297	+	2.58824i	0.604483	+	0.348998i
$56$	2.53257	−	1.46218i	0.338429	−	0.195392i
$57$		0			0
$58$	−0.806522	+	1.39694i	−0.105902	+	0.183427i
$59$	−5.26958	−	3.04240i	−0.686041	−	0.396086i	0.116086	−	0.993239i	$-0.462965\pi$
$59$	−5.26958	−	3.04240i	−0.686041	−	0.396086i	−0.802127	+	0.597153i	$0.796299\pi$
$60$		0			0
$61$	3.32949	−	1.92228i	0.426298	−	0.246123i	−0.271470	−	0.962447i	$-0.587510\pi$
$61$	3.32949	−	1.92228i	0.426298	−	0.246123i	0.697768	+	0.716324i	$0.254177\pi$
$62$	2.56648	+	4.44527i	0.325943	+	0.564549i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.00450			0.248627
$66$		0			0
$67$	9.83943			1.20208			0.601039	−	0.799220i	$-0.294754\pi$
$67$	9.83943			1.20208			0.601039	+	0.799220i	$0.294754\pi$
$68$	5.51981	−	3.18686i	0.669375	−	0.386464i
$69$		0			0
$70$	3.03416	+	5.25533i	0.362652	+	0.628132i
$71$	−1.55554	+	2.69428i	−0.184609	+	0.319752i	−0.943445	−	0.331530i	$-0.892435\pi$
$71$	−1.55554	+	2.69428i	−0.184609	+	0.319752i	0.758836	+	0.651282i	$0.225769\pi$
$72$		0			0
$73$	−12.3747			−1.44835			−0.724177	−	0.689614i	$-0.757780\pi$
$73$	−12.3747			−1.44835			−0.724177	+	0.689614i	$0.757780\pi$
$74$	2.78018	+	5.41023i	0.323190	+	0.628926i
$75$		0			0
$76$	−5.19406	−	2.99879i	−0.595800	−	0.343985i
$77$	7.29502			0.831345
$78$		0			0
$79$	1.65079	−	0.953087i	0.185729	−	0.107231i	−0.404253	−	0.914647i	$-0.632468\pi$
$79$	1.65079	−	0.953087i	0.185729	−	0.107231i	0.589982	+	0.807417i	$0.299135\pi$
$80$		−	2.07510i		−	0.232003i
$81$		0			0
$82$		−	7.84678i		−	0.866531i
$83$	−10.8429			−1.19016			−0.595082	−	0.803665i	$-0.702880\pi$
$83$	−10.8429			−1.19016			−0.595082	+	0.803665i	$0.702880\pi$
$84$		0			0
$85$	6.61306	+	11.4541i	0.717287	+	1.24238i
$86$	0.165595	−	0.286819i	0.0178566	−	0.0309285i
$87$		0			0
$88$	−2.16036	−	1.24729i	−0.230296	−	0.132961i
$89$	11.9327	−	6.88934i	1.26486	−	0.730269i	0.290851	−	0.956768i	$-0.406061\pi$
$89$	11.9327	−	6.88934i	1.26486	−	0.730269i	0.974011	+	0.226499i	$0.0727281\pi$
$90$		0			0
$91$	2.44640	−	1.41243i	0.256452	−	0.148063i
$92$	6.10692	−	3.52583i	0.636690	−	0.367593i
$93$		0			0
$94$	−7.53829	−	4.35223i	−0.777515	−	0.448898i
$95$	6.22279	−	10.7782i	0.638444	−	1.10582i
$96$		0			0
$97$	4.24112	+	2.44861i	0.430620	+	0.248619i	0.699611	−	0.714524i	$-0.253357\pi$
$97$	4.24112	+	2.44861i	0.430620	+	0.248619i	−0.268991	+	0.963143i	$0.586690\pi$
$98$	1.34395	+	0.775932i	0.135760	+	0.0783810i
$99$		0			0
$100$	−0.693968			−0.0693968
$101$	−0.280230	+	0.485372i	−0.0278839	+	0.0482963i	−0.879631	−	0.475657i	$-0.842210\pi$
$101$	−0.280230	+	0.485372i	−0.0278839	+	0.0482963i	0.851747	+	0.523954i	$0.175544\pi$
$102$		0			0
$103$	−8.90739	+	5.14268i	−0.877671	+	0.506724i	−0.869890	−	0.493246i	$-0.835810\pi$
$103$	−8.90739	+	5.14268i	−0.877671	+	0.506724i	−0.00778126	+	0.999970i	$0.502477\pi$
$104$	−0.965976			−0.0947218
$105$		0			0
$106$	10.8998	−	6.29300i	1.05868	−	0.611230i
$107$	−9.12887	+	15.8117i	−0.882521	+	1.52857i	−0.0339922	+	0.999422i	$0.510822\pi$
$107$	−9.12887	+	15.8117i	−0.882521	+	1.52857i	−0.848529	+	0.529149i	$0.822511\pi$
$108$		0			0
$109$	−12.4302	+	7.17656i	−1.19059	+	0.687389i	−0.958441	−	0.285290i	$-0.907910\pi$
$109$	−12.4302	+	7.17656i	−1.19059	+	0.687389i	−0.232152	+	0.972679i	$0.574577\pi$
$110$	2.58824	−	4.48297i	0.246779	−	0.427434i
$111$		0			0
$112$	−1.46218	−	2.53257i	−0.138163	−	0.239305i
$113$	−4.10371	−	2.36928i	−0.386045	−	0.222883i	0.294400	−	0.955682i	$-0.404880\pi$
$113$	−4.10371	−	2.36928i	−0.386045	−	0.222883i	−0.680445	+	0.732799i	$0.738213\pi$
$114$		0			0
$115$	7.31644	+	12.6724i	0.682262	+	1.18171i
$116$	1.39694	+	0.806522i	0.129702	+	0.0748837i
$117$		0			0
$118$	−3.04240	+	5.26958i	−0.280075	+	0.485104i
$119$	16.1419	+	9.31953i	1.47973	+	0.854320i
$120$		0			0
$121$	2.38855	+	4.13709i	0.217141	+	0.376099i
$122$	−1.92228	−	3.32949i	−0.174035	−	0.301438i
$123$		0			0
$124$	4.44527	−	2.56648i	0.399197	−	0.230476i
$125$		−	11.8155i		−	1.05681i
$126$		0			0
$127$	6.78495	+	11.7519i	0.602067	+	1.04281i	0.992508	+	0.122182i	$0.0389893\pi$
$127$	6.78495	+	11.7519i	0.602067	+	1.04281i	−0.390441	+	0.920628i	$0.627677\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$		−	2.00450i		−	0.175806i
$131$	11.3418	+	6.54821i	0.990940	+	0.572120i	0.905555	−	0.424228i	$-0.139455\pi$
$131$	11.3418	+	6.54821i	0.990940	+	0.572120i	0.0853850	+	0.996348i	$0.472788\pi$
$132$		0			0
$133$		−	17.5391i		−	1.52083i
$134$		−	9.83943i		−	0.849997i
$135$		0			0
$136$	−3.18686	−	5.51981i	−0.273271	−	0.473320i
$137$	−4.51361	+	7.81780i	−0.385624	+	0.667920i	−0.991856	−	0.127368i	$-0.959347\pi$
$137$	−4.51361	+	7.81780i	−0.385624	+	0.667920i	0.606232	+	0.795288i	$0.292680\pi$
$138$		0			0
$139$	−11.4771	+	19.8788i	−0.973471	+	1.68610i	−0.288581	+	0.957455i	$0.593183\pi$
$139$	−11.4771	+	19.8788i	−0.973471	+	1.68610i	−0.684890	+	0.728646i	$0.740150\pi$
$140$	5.25533	−	3.03416i	0.444156	−	0.256434i
$141$		0			0
$142$	2.69428	+	1.55554i	0.226099	+	0.130538i
$143$	−2.08686	−	1.20485i	−0.174512	−	0.100755i
$144$		0			0
$145$	−1.67361	+	2.89878i	−0.138986	+	0.240731i
$146$			12.3747i			1.02414i
$147$		0			0
$148$	5.41023	−	2.78018i	0.444718	−	0.228530i
$149$	1.77169	+	3.06866i	0.145143	+	0.251394i	0.929426	−	0.369008i	$-0.120303\pi$
$149$	1.77169	+	3.06866i	0.145143	+	0.251394i	−0.784284	+	0.620403i	$0.786969\pi$
$150$		0			0
$151$	−5.11404	−	8.85777i	−0.416175	−	0.720835i	0.579376	−	0.815060i	$-0.303296\pi$
$151$	−5.11404	−	8.85777i	−0.416175	−	0.720835i	−0.995551	+	0.0942247i	$0.969963\pi$
$152$	−2.99879	+	5.19406i	−0.243234	+	0.421294i
$153$		0			0
$154$		−	7.29502i		−	0.587850i
$155$	5.32569	+	9.22436i	0.427770	+	0.740919i
$156$		0			0
$157$	−1.98168	+	3.43237i	−0.158155	+	0.273933i	−0.934203	−	0.356741i	$-0.883888\pi$
$157$	−1.98168	+	3.43237i	−0.158155	+	0.273933i	0.776048	+	0.630674i	$0.217221\pi$
$158$	−0.953087	−	1.65079i	−0.0758235	−	0.131330i
$159$		0			0
$160$	−2.07510			−0.164051
$161$	17.8588	+	10.3108i	1.40747	+	0.812604i
$162$		0			0
$163$	−12.9105	+	7.45388i	−1.01123	+	0.583833i	−0.911551	−	0.411187i	$-0.865114\pi$
$163$	−12.9105	+	7.45388i	−1.01123	+	0.583833i	−0.0996771	+	0.995020i	$0.531781\pi$
$164$	−7.84678			−0.612730
$165$		0			0
$166$			10.8429i			0.841573i
$167$		−	5.38912i		−	0.417023i	−0.978020	−	0.208511i	$-0.933138\pi$
$167$		−	5.38912i		−	0.417023i	0.978020	−	0.208511i	$-0.0668618\pi$
$168$		0			0
$169$	12.0669			0.928222
$170$	11.4541	−	6.61306i	0.878493	−	0.507198i
$171$		0			0
$172$	−0.286819	−	0.165595i	−0.0218698	−	0.0126265i
$173$	2.77645			0.211089			0.105545	−	0.994415i	$-0.466341\pi$
$173$	2.77645			0.211089			0.105545	+	0.994415i	$0.466341\pi$
$174$		0			0
$175$	−1.01471	−	1.75752i	−0.0767045	−	0.132856i
$176$	−1.24729	+	2.16036i	−0.0940178	+	0.162844i
$177$		0			0
$178$	−6.88934	−	11.9327i	−0.516378	−	0.894393i
$179$		−	6.05390i		−	0.452490i	−0.974070	−	0.226245i	$-0.927355\pi$
$179$		−	6.05390i		−	0.452490i	0.974070	−	0.226245i	$-0.0726450\pi$
$180$		0			0
$181$	3.93255	−	6.81137i	0.292304	−	0.506286i	−0.682050	−	0.731305i	$-0.738911\pi$
$181$	3.93255	−	6.81137i	0.292304	−	0.506286i	0.974354	+	0.225020i	$0.0722447\pi$
$182$	−1.41243	−	2.44640i	−0.104696	−	0.181339i
$183$		0			0
$184$	−3.52583	−	6.10692i	−0.259928	−	0.450208i
$185$	5.76916	+	11.2268i	0.424157	+	0.825407i
$186$		0			0
$187$		−	15.8997i		−	1.16270i
$188$	−4.35223	+	7.53829i	−0.317419	+	0.549786i
$189$		0			0
$190$	−10.7782	−	6.22279i	−0.781932	−	0.451448i
$191$	−7.53550	−	4.35062i	−0.545249	−	0.314800i	0.201954	−	0.979395i	$-0.435271\pi$
$191$	−7.53550	−	4.35062i	−0.545249	−	0.314800i	−0.747204	+	0.664595i	$0.768604\pi$
$192$		0			0
$193$	−8.34933	+	4.82049i	−0.600998	+	0.346986i	−0.769434	−	0.638726i	$-0.779462\pi$
$193$	−8.34933	+	4.82049i	−0.600998	+	0.346986i	0.168436	+	0.985713i	$0.446128\pi$
$194$	2.44861	−	4.24112i	0.175800	−	0.304495i
$195$		0			0
$196$	0.775932	−	1.34395i	0.0554237	−	0.0959967i
$197$	−5.57481	−	9.65586i	−0.397189	−	0.687951i	0.596189	−	0.802844i	$-0.296681\pi$
$197$	−5.57481	−	9.65586i	−0.397189	−	0.687951i	−0.993378	+	0.114893i	$0.963348\pi$
$198$		0			0
$199$		−	6.78425i		−	0.480923i	−0.970659	−	0.240461i	$-0.922701\pi$
$199$		−	6.78425i		−	0.480923i	0.970659	−	0.240461i	$-0.0772987\pi$
$200$			0.693968i			0.0490710i
$201$		0			0
$202$	0.485372	+	0.280230i	0.0341507	+	0.0197169i
$203$			4.71712i			0.331077i
$204$		0			0
$205$		−	16.2828i		−	1.13724i
$206$	5.14268	+	8.90739i	0.358308	+	0.620607i
$207$		0			0
$208$			0.965976i			0.0669784i
$209$	−12.9570	+	7.48071i	−0.896252	+	0.517451i
$210$		0			0
$211$	8.45706	+	14.6480i	0.582208	+	1.00841i	0.995217	+	0.0976866i	$0.0311443\pi$
$211$	8.45706	+	14.6480i	0.582208	+	1.00841i	−0.413010	+	0.910727i	$0.635522\pi$
$212$	−6.29300	−	10.8998i	−0.432205	−	0.748601i
$213$		0			0
$214$	15.8117	+	9.12887i	1.08086	+	0.624037i
$215$	0.343626	−	0.595178i	0.0234351	−	0.0405908i
$216$		0			0
$217$	12.9995	+	7.50529i	0.882467	+	0.509492i
$218$	7.17656	+	12.4302i	0.486058	+	0.841877i
$219$		0			0
$220$	−4.48297	−	2.58824i	−0.302242	−	0.174499i
$221$	−3.07844	−	5.33201i	−0.207078	−	0.358670i
$222$		0			0
$223$	−10.7054	+	18.5423i	−0.716886	+	1.24168i	0.245341	+	0.969437i	$0.421100\pi$
$223$	−10.7054	+	18.5423i	−0.716886	+	1.24168i	−0.962227	+	0.272247i	$0.912233\pi$
$224$	−2.53257	+	1.46218i	−0.169214	+	0.0976959i
$225$		0			0
$226$	−2.36928	+	4.10371i	−0.157602	+	0.272975i
$227$	−21.7648	+	12.5659i	−1.44458	+	0.834028i	−0.998150	−	0.0607919i	$-0.980637\pi$
$227$	−21.7648	+	12.5659i	−1.44458	+	0.834028i	−0.446428	+	0.894820i	$0.647304\pi$
$228$		0			0
$229$	−6.45385			−0.426482			−0.213241	−	0.977000i	$-0.568402\pi$
$229$	−6.45385			−0.426482			−0.213241	+	0.977000i	$0.568402\pi$
$230$	12.6724	−	7.31644i	0.835597	−	0.482432i
$231$		0			0
$232$	0.806522	−	1.39694i	0.0529508	−	0.0917134i
$233$	20.1699			1.32137			0.660686	−	0.750662i	$-0.270265\pi$
$233$	20.1699			1.32137			0.660686	+	0.750662i	$0.270265\pi$
$234$		0			0
$235$	−15.6427	−	9.03131i	−1.02042	−	0.589138i
$236$	5.26958	+	3.04240i	0.343021	+	0.198043i
$237$		0			0
$238$	9.31953	−	16.1419i	0.604095	−	1.04632i
$239$	−4.12334	−	2.38061i	−0.266716	−	0.153989i	0.360678	−	0.932690i	$-0.382545\pi$
$239$	−4.12334	−	2.38061i	−0.266716	−	0.153989i	−0.627395	+	0.778702i	$0.715879\pi$
$240$		0			0
$241$	−5.64101	+	3.25684i	−0.363369	+	0.209791i	−0.670558	−	0.741857i	$-0.733945\pi$
$241$	−5.64101	+	3.25684i	−0.363369	+	0.209791i	0.307188	+	0.951649i	$0.400612\pi$
$242$	4.13709	−	2.38855i	0.265942	−	0.153542i
$243$		0			0
$244$	−3.32949	+	1.92228i	−0.213149	+	0.123062i
$245$	2.78884	+	1.61013i	0.178172	+	0.102868i
$246$		0			0
$247$	−2.89676	+	5.01734i	−0.184317	+	0.319246i
$248$	−2.56648	−	4.44527i	−0.162971	−	0.282275i
$249$		0			0
$250$	−11.8155			−0.747280
$251$		−	5.22002i		−	0.329485i	−0.986337	−	0.164742i	$-0.947321\pi$
$251$		−	5.22002i		−	0.329485i	0.986337	−	0.164742i	$-0.0526793\pi$
$252$		0			0
$253$		−	17.5909i		−	1.10593i
$254$	11.7519	−	6.78495i	0.737378	−	0.425726i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.04659	−	0.604249i	−0.0652844	−	0.0376920i	0.467002	−	0.884256i	$-0.345334\pi$
$257$	−1.04659	−	0.604249i	−0.0652844	−	0.0376920i	−0.532287	+	0.846564i	$0.678667\pi$
$258$		0			0
$259$	14.9517	+	9.63664i	0.929055	+	0.598792i
$260$	−2.00450			−0.124314
$261$		0			0
$262$	6.54821	−	11.3418i	0.404550	−	0.700701i
$263$	−12.0489	−	20.8694i	−0.742970	−	1.28686i	−0.951137	−	0.308768i	$-0.900083\pi$
$263$	−12.0489	−	20.8694i	−0.742970	−	1.28686i	0.208168	−	0.978093i	$-0.433250\pi$
$264$		0			0
$265$	22.6182	−	13.0586i	1.38942	−	0.802183i
$266$	−17.5391			−1.07539
$267$		0			0
$268$	−9.83943			−0.601039
$269$	−15.0540			−0.917857			−0.458928	−	0.888473i	$-0.651767\pi$
$269$	−15.0540			−0.917857			−0.458928	+	0.888473i	$0.651767\pi$
$270$		0			0
$271$	−6.82535	−	11.8219i	−0.414611	−	0.718127i	0.580777	−	0.814063i	$-0.302749\pi$
$271$	−6.82535	−	11.8219i	−0.414611	−	0.718127i	−0.995387	+	0.0959361i	$0.969416\pi$
$272$	−5.51981	+	3.18686i	−0.334688	+	0.193232i
$273$		0			0
$274$	7.81780	+	4.51361i	0.472291	+	0.272677i
$275$	−0.865577	+	1.49922i	−0.0521963	+	0.0904066i
$276$		0			0
$277$	−0.428527	+	0.247410i	−0.0257477	+	0.0148654i	−0.512819	−	0.858497i	$-0.671399\pi$
$277$	−0.428527	+	0.247410i	−0.0257477	+	0.0148654i	0.487071	+	0.873362i	$0.338065\pi$
$278$	19.8788	+	11.4771i	1.19225	+	0.688348i
$279$		0			0
$280$	−3.03416	−	5.25533i	−0.181326	−	0.314066i
$281$		−	32.4144i		−	1.93368i	−0.255385	−	0.966839i	$-0.582202\pi$
$281$		−	32.4144i		−	1.93368i	0.255385	−	0.966839i	$-0.417798\pi$
$282$		0			0
$283$			23.2720i			1.38338i	0.722197	+	0.691688i	$0.243133\pi$
$283$			23.2720i			1.38338i	−0.722197	+	0.691688i	$0.756867\pi$
$284$	1.55554	−	2.69428i	0.0923046	−	0.159876i
$285$		0			0
$286$	−1.20485	+	2.08686i	−0.0712442	+	0.123399i
$287$	−11.4734	−	19.8725i	−0.677253	−	1.17304i
$288$		0			0
$289$	11.8122	−	20.4593i	0.694836	−	1.20349i
$290$	2.89878	+	1.67361i	0.170222	+	0.0982779i
$291$		0			0
$292$	12.3747			0.724177
$293$	16.4919			0.963466			0.481733	−	0.876318i	$-0.340007\pi$
$293$	16.4919			0.963466			0.481733	+	0.876318i	$0.340007\pi$
$294$		0			0
$295$	−6.31327	+	10.9349i	−0.367573	+	0.636655i
$296$	−2.78018	−	5.41023i	−0.161595	−	0.314463i
$297$		0			0
$298$	3.06866	−	1.77169i	0.177763	−	0.102631i
$299$	−3.40587	−	5.89914i	−0.196966	−	0.341156i
$300$		0			0
$301$		−	0.968519i		−	0.0558245i
$302$	−8.85777	+	5.11404i	−0.509708	+	0.294280i
$303$		0			0
$304$	5.19406	+	2.99879i	0.297900	+	0.171993i
$305$	−3.98893	−	6.90903i	−0.228405	−	0.395610i
$306$		0			0
$307$	19.9087			1.13625			0.568125	−	0.822942i	$-0.307669\pi$
$307$	19.9087			1.13625			0.568125	+	0.822942i	$0.307669\pi$
$308$	−7.29502			−0.415672
$309$		0			0
$310$	9.22436	−	5.32569i	0.523909	−	0.302479i
$311$	7.25454	+	4.18841i	0.411367	+	0.237503i	0.691377	−	0.722494i	$-0.257004\pi$
$311$	7.25454	+	4.18841i	0.411367	+	0.237503i	−0.280010	+	0.959997i	$0.590338\pi$
$312$		0			0
$313$			2.70871i			0.153105i	0.997066	+	0.0765526i	$0.0243913\pi$
$313$			2.70871i			0.153105i	−0.997066	+	0.0765526i	$0.975609\pi$
$314$	3.43237	+	1.98168i	0.193700	+	0.111833i
$315$		0			0
$316$	−1.65079	+	0.953087i	−0.0928645	+	0.0536153i
$317$	7.39929			0.415586			0.207793	−	0.978173i	$-0.433372\pi$
$317$	7.39929			0.415586			0.207793	+	0.978173i	$0.433372\pi$
$318$		0			0
$319$	3.48476	−	2.01193i	0.195109	−	0.112646i
$320$			2.07510i			0.116002i
$321$		0			0
$322$	10.3108	−	17.8588i	0.574598	−	0.995232i
$323$	−38.2270			−2.12701
$324$		0			0
$325$			0.670357i			0.0371847i
$326$	7.45388	+	12.9105i	0.412832	+	0.715046i
$327$		0			0
$328$			7.84678i			0.433266i
$329$	−25.4550			−1.40338
$330$		0			0
$331$			0.437608i			0.0240531i	0.999928	+	0.0120266i	$0.00382826\pi$
$331$			0.437608i			0.0240531i	−0.999928	+	0.0120266i	$0.996172\pi$
$332$	10.8429			0.595082
$333$		0			0
$334$	−5.38912			−0.294880
$335$		−	20.4178i		−	1.11554i
$336$		0			0
$337$	2.65082			0.144400			0.0721998	−	0.997390i	$-0.476998\pi$
$337$	2.65082			0.144400			0.0721998	+	0.997390i	$0.476998\pi$
$338$		−	12.0669i		−	0.656352i
$339$		0			0
$340$	−6.61306	−	11.4541i	−0.358643	−	0.621188i
$341$		−	12.8045i		−	0.693404i
$342$		0			0
$343$	−15.9323			−0.860263
$344$	−0.165595	+	0.286819i	−0.00892829	+	0.0154643i
$345$		0			0
$346$		−	2.77645i		−	0.149263i
$347$	−1.84812	+	1.06701i	−0.0992125	+	0.0572804i	−0.548785	−	0.835963i	$-0.684910\pi$
$347$	−1.84812	+	1.06701i	−0.0992125	+	0.0572804i	0.449573	+	0.893244i	$0.351576\pi$
$348$		0			0
$349$	−0.0108863			−0.000582733			−0.000291366	−	1.00000i	$-0.500093\pi$
$349$	−0.0108863			−0.000582733			−0.000291366		1.00000i	$0.500093\pi$
$350$	−1.75752	+	1.01471i	−0.0939435	+	0.0542383i
$351$		0			0
$352$	2.16036	+	1.24729i	0.115148	+	0.0664806i
$353$			29.4755i			1.56882i	0.620240	+	0.784412i	$0.287035\pi$
$353$			29.4755i			1.56882i	−0.620240	+	0.784412i	$0.712965\pi$
$354$		0			0
$355$	5.59090	+	3.22791i	0.296734	+	0.171320i
$356$	−11.9327	+	6.88934i	−0.632431	+	0.365134i
$357$		0			0
$358$	−6.05390			−0.319959
$359$	−18.3714			−0.969608			−0.484804	−	0.874623i	$-0.661109\pi$
$359$	−18.3714			−0.969608			−0.484804	+	0.874623i	$0.661109\pi$
$360$		0			0
$361$	8.48551	+	14.6973i	0.446606	+	0.773544i
$362$	−6.81137	−	3.93255i	−0.357998	−	0.206690i
$363$		0			0
$364$	−2.44640	+	1.41243i	−0.128226	+	0.0740314i
$365$			25.6788i			1.34409i
$366$		0			0
$367$	−12.8321	−	22.2258i	−0.669829	−	1.16018i	−0.977952	−	0.208831i	$-0.933034\pi$
$367$	−12.8321	−	22.2258i	−0.669829	−	1.16018i	0.308123	−	0.951347i	$-0.400299\pi$
$368$	−6.10692	+	3.52583i	−0.318345	+	0.183797i
$369$		0			0
$370$	11.2268	−	5.76916i	0.583651	−	0.299924i
$371$	18.4030	−	31.8749i	0.955436	−	1.65486i
$372$		0			0
$373$	27.9016			1.44469			0.722346	−	0.691532i	$-0.243064\pi$
$373$	27.9016			1.44469			0.722346	+	0.691532i	$0.243064\pi$
$374$	−15.8997			−0.822156
$375$		0			0
$376$	7.53829	+	4.35223i	0.388757	+	0.224449i
$377$	0.779081	−	1.34941i	0.0401247	−	0.0694981i
$378$		0			0
$379$	−8.28061	−	14.3424i	−0.425346	−	0.736722i	0.571106	−	0.820876i	$-0.306514\pi$
$379$	−8.28061	−	14.3424i	−0.425346	−	0.736722i	−0.996453	+	0.0841544i	$0.973181\pi$
$380$	−6.22279	+	10.7782i	−0.319222	+	0.552909i
$381$		0			0
$382$	−4.35062	+	7.53550i	−0.222597	+	0.385550i
$383$			20.4913i			1.04705i	0.852009	+	0.523527i	$0.175384\pi$
$383$			20.4913i			1.04705i	−0.852009	+	0.523527i	$0.824616\pi$
$384$		0			0
$385$		−	15.1379i		−	0.771498i
$386$	4.82049	+	8.34933i	0.245356	+	0.424970i
$387$		0			0
$388$	−4.24112	−	2.44861i	−0.215310	−	0.124309i
$389$	−22.4403	+	12.9559i	−1.13777	+	0.656890i	−0.945877	−	0.324526i	$-0.894795\pi$
$389$	−22.4403	+	12.9559i	−1.13777	+	0.656890i	−0.191891	+	0.981416i	$0.561462\pi$
$390$		0			0
$391$	22.4727	−	38.9238i	1.13649	−	1.96846i
$392$	−1.34395	−	0.775932i	−0.0678799	−	0.0391905i
$393$		0			0
$394$	−9.65586	+	5.57481i	−0.486455	+	0.280855i
$395$	−1.97775	−	3.42556i	−0.0995113	−	0.172359i
$396$		0			0
$397$	−9.32207			−0.467861			−0.233931	−	0.972253i	$-0.575159\pi$
$397$	−9.32207			−0.467861			−0.233931	+	0.972253i	$0.575159\pi$
$398$	−6.78425			−0.340064
$399$		0			0
$400$	0.693968			0.0346984
$401$	−6.01297	+	3.47159i	−0.300274	+	0.173363i	−0.642566	−	0.766231i	$-0.722130\pi$
$401$	−6.01297	+	3.47159i	−0.300274	+	0.173363i	0.342292	+	0.939594i	$0.388797\pi$
$402$		0			0
$403$	−2.47916	−	4.29402i	−0.123496	−	0.213900i
$404$	0.280230	−	0.485372i	0.0139419	−	0.0241482i
$405$		0			0
$406$	4.71712			0.234107
$407$	0.741895	−	15.1557i	0.0367744	−	0.751243i
$408$		0			0
$409$	−28.0121	−	16.1728i	−1.38511	−	0.799693i	−0.392351	−	0.919816i	$-0.628338\pi$
$409$	−28.0121	−	16.1728i	−1.38511	−	0.799693i	−0.992759	+	0.120122i	$0.961671\pi$
$410$	−16.2828			−0.804152
$411$		0			0
$412$	8.90739	−	5.14268i	0.438836	−	0.253362i
$413$			17.7941i			0.875590i
$414$		0			0
$415$			22.5001i			1.10449i
$416$	0.965976			0.0473609
$417$		0			0
$418$	7.48071	+	12.9570i	0.365893	+	0.633746i
$419$	17.0524	−	29.5355i	0.833062	−	1.44291i	−0.0625364	−	0.998043i	$-0.519919\pi$
$419$	17.0524	−	29.5355i	0.833062	−	1.44291i	0.895599	−	0.444863i	$-0.146748\pi$
$420$		0			0
$421$	−1.49015	−	0.860340i	−0.0726256	−	0.0419304i	0.463247	−	0.886229i	$-0.346684\pi$
$421$	−1.49015	−	0.860340i	−0.0726256	−	0.0419304i	−0.535873	+	0.844299i	$0.680017\pi$
$422$	14.6480	−	8.45706i	0.713056	−	0.411683i
$423$		0			0
$424$	−10.8998	+	6.29300i	−0.529341	+	0.305615i
$425$	−3.83057	+	2.21158i	−0.185810	+	0.107277i
$426$		0			0
$427$	−9.73663	−	5.62145i	−0.471189	−	0.272041i
$428$	9.12887	−	15.8117i	0.441261	−	0.764286i
$429$		0			0
$430$	−0.595178	−	0.343626i	−0.0287020	−	0.0165711i
$431$	7.18439	+	4.14791i	0.346060	+	0.199798i	0.662949	−	0.748665i	$-0.269305\pi$
$431$	7.18439	+	4.14791i	0.346060	+	0.199798i	−0.316889	+	0.948463i	$0.602638\pi$
$432$		0			0
$433$	−17.3517			−0.833867			−0.416934	−	0.908937i	$-0.636895\pi$
$433$	−17.3517			−0.833867			−0.416934	+	0.908937i	$0.636895\pi$
$434$	7.50529	−	12.9995i	0.360265	−	0.623998i
$435$		0			0
$436$	12.4302	−	7.17656i	0.595297	−	0.343695i
$437$	−42.2929			−2.02314
$438$		0			0
$439$	−27.8441	+	16.0758i	−1.32893	+	0.767257i	−0.985134	−	0.171789i	$-0.945045\pi$
$439$	−27.8441	+	16.0758i	−1.32893	+	0.767257i	−0.343794	+	0.939045i	$0.611712\pi$
$440$	−2.58824	+	4.48297i	−0.123390	+	0.213717i
$441$		0			0
$442$	−5.33201	+	3.07844i	−0.253618	+	0.146426i
$443$	−9.47241	+	16.4067i	−0.450048	+	0.779506i	−0.998388	−	0.0567494i	$-0.981926\pi$
$443$	−9.47241	+	16.4067i	−0.450048	+	0.779506i	0.548341	+	0.836255i	$0.315260\pi$
$444$		0			0
$445$	−14.2961	−	24.7615i	−0.677698	−	1.17381i
$446$	18.5423	+	10.7054i	0.878003	+	0.506915i
$447$		0			0
$448$	1.46218	+	2.53257i	0.0690814	+	0.119653i
$449$	11.7990	+	6.81218i	0.556832	+	0.321487i	0.751873	−	0.659308i	$-0.229151\pi$
$449$	11.7990	+	6.81218i	0.556832	+	0.321487i	−0.195041	+	0.980795i	$0.562484\pi$
$450$		0			0
$451$	−9.78718	+	16.9519i	−0.460860	+	0.798233i
$452$	4.10371	+	2.36928i	0.193022	+	0.111441i
$453$		0			0
$454$	12.5659	+	21.7648i	0.589747	+	1.02147i
$455$	−2.93093	−	5.07652i	−0.137404	−	0.237991i
$456$		0			0
$457$	8.61765	−	4.97540i	0.403117	−	0.232740i	−0.284711	−	0.958613i	$-0.591898\pi$
$457$	8.61765	−	4.97540i	0.403117	−	0.232740i	0.687828	+	0.725874i	$0.258564\pi$
$458$			6.45385i			0.301569i
$459$		0			0
$460$	−7.31644	−	12.6724i	−0.341131	−	0.590856i
$461$		−	22.0486i		−	1.02691i	−0.858117	−	0.513454i	$-0.828366\pi$
$461$		−	22.0486i		−	1.02691i	0.858117	−	0.513454i	$-0.171634\pi$
$462$		0			0
$463$			13.4512i			0.625129i	0.949897	+	0.312565i	$0.101188\pi$
$463$			13.4512i			0.625129i	−0.949897	+	0.312565i	$0.898812\pi$
$464$	−1.39694	−	0.806522i	−0.0648512	−	0.0374418i
$465$		0			0
$466$		−	20.1699i		−	0.934352i
$467$			11.8425i			0.548005i	0.961729	+	0.274003i	$0.0883477\pi$
$467$			11.8425i			0.548005i	−0.961729	+	0.274003i	$0.911652\pi$
$468$		0			0
$469$	−14.3870	−	24.9190i	−0.664330	−	1.15065i
$470$	−9.03131	+	15.6427i	−0.416583	+	0.721543i
$471$		0			0
$472$	3.04240	−	5.26958i	0.140038	−	0.242552i
$473$	−0.715492	+	0.413089i	−0.0328983	+	0.0189939i
$474$		0			0
$475$	3.60451	+	2.08107i	0.165386	+	0.0954859i
$476$	−16.1419	−	9.31953i	−0.739863	−	0.427160i
$477$		0			0
$478$	−2.38061	+	4.12334i	−0.108887	+	0.188597i
$479$		−	9.31385i		−	0.425561i	−0.977100	−	0.212780i	$-0.931748\pi$
$479$		−	9.31385i		−	0.425561i	0.977100	−	0.212780i	$-0.0682519\pi$
$480$		0			0
$481$	−2.68559	−	5.22615i	−0.122453	−	0.238292i
$482$	3.25684	+	5.64101i	0.148345	+	0.256941i
$483$		0			0
$484$	−2.38855	−	4.13709i	−0.108571	−	0.188050i
$485$	5.08111	−	8.80074i	0.230721	−	0.399621i
$486$		0			0
$487$			28.3740i			1.28575i	0.765972	+	0.642874i	$0.222258\pi$
$487$			28.3740i			1.28575i	−0.765972	+	0.642874i	$0.777742\pi$
$488$	1.92228	+	3.32949i	0.0870177	+	0.150719i
$489$		0			0
$490$	1.61013	−	2.78884i	0.0727385	−	0.125987i
$491$	16.0415	+	27.7847i	0.723942	+	1.25390i	0.959408	+	0.282022i	$0.0910051\pi$
$491$	16.0415	+	27.7847i	0.723942	+	1.25390i	−0.235466	+	0.971883i	$0.575662\pi$
$492$		0			0
$493$	10.2811			0.463038
$494$	5.01734	+	2.89676i	0.225741	+	0.130331i
$495$		0			0
$496$	−4.44527	+	2.56648i	−0.199598	+	0.115238i
$497$	9.09794			0.408098
$498$		0			0
$499$		−	17.8888i		−	0.800812i	−0.916338	−	0.400406i	$-0.868869\pi$
$499$		−	17.8888i		−	0.800812i	0.916338	−	0.400406i	$-0.131131\pi$
$500$			11.8155i			0.528407i
$501$		0			0
$502$	−5.22002			−0.232981
$503$	−20.1448	+	11.6306i	−0.898212	+	0.518583i	−0.876620	−	0.481184i	$-0.840207\pi$
$503$	−20.1448	+	11.6306i	−0.898212	+	0.518583i	−0.0215923	+	0.999767i	$0.506874\pi$
$504$		0			0
$505$	1.00719	+	0.581504i	0.0448196	+	0.0258766i
$506$	−17.5909			−0.782010
$507$		0			0
$508$	−6.78495	−	11.7519i	−0.301033	−	0.521405i
$509$	−11.2233	+	19.4393i	−0.497462	+	0.861630i	−0.999996	−	0.00292796i	$-0.999068\pi$
$509$	−11.2233	+	19.4393i	−0.497462	+	0.861630i	0.502534	+	0.864558i	$0.332401\pi$
$510$		0			0
$511$	18.0941	+	31.3399i	0.800436	+	1.38639i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−0.604249	+	1.04659i	−0.0266523	+	0.0461631i
$515$	10.6716	+	18.4837i	0.470246	+	0.814489i
$516$		0			0
$517$	10.8570	+	18.8048i	0.477489	+	0.827034i
$518$	9.63664	−	14.9517i	0.423410	−	0.656941i
$519$		0			0
$520$			2.00450i			0.0879030i
$521$	4.75508	−	8.23605i	0.208324	−	0.360828i	−0.742863	−	0.669444i	$-0.766532\pi$
$521$	4.75508	−	8.23605i	0.208324	−	0.360828i	0.951187	+	0.308616i	$0.0998658\pi$
$522$		0			0
$523$	−8.58415	−	4.95606i	−0.375359	−	0.216713i	0.300438	−	0.953801i	$-0.402867\pi$
$523$	−8.58415	−	4.95606i	−0.375359	−	0.216713i	−0.675797	+	0.737088i	$0.736200\pi$
$524$	−11.3418	−	6.54821i	−0.495470	−	0.286060i
$525$		0			0
$526$	−20.8694	+	12.0489i	−0.909948	+	0.525359i
$527$	16.3580	−	28.3329i	0.712566	−	1.23420i
$528$		0			0
$529$	13.3629	−	23.1453i	0.580998	−	1.00632i
$530$	−13.0586	−	22.6182i	−0.567229	−	0.982470i
$531$		0			0
$532$			17.5391i			0.760415i
$533$			7.57980i			0.328318i
$534$		0			0
$535$	32.8108	+	18.9433i	1.41853	+	0.818990i
$536$			9.83943i			0.424999i
$537$		0			0
$538$			15.0540i			0.649023i
$539$	−1.93562	−	3.35259i	−0.0833730	−	0.144406i
$540$		0			0
$541$		−	30.8724i		−	1.32731i	−0.748040	−	0.663653i	$-0.769005\pi$
$541$		−	30.8724i		−	1.32731i	0.748040	−	0.663653i	$-0.230995\pi$
$542$	−11.8219	+	6.82535i	−0.507792	+	0.293174i
$543$		0			0
$544$	3.18686	+	5.51981i	0.136636	+	0.236660i
$545$	14.8921	+	25.7938i	0.637906	+	1.10489i
$546$		0			0
$547$	−3.81046	−	2.19997i	−0.162924	−	0.0940640i	0.416321	−	0.909218i	$-0.363319\pi$
$547$	−3.81046	−	2.19997i	−0.162924	−	0.0940640i	−0.579245	+	0.815154i	$0.696652\pi$
$548$	4.51361	−	7.81780i	0.192812	−	0.333960i
$549$		0			0
$550$	1.49922	+	0.865577i	0.0639271	+	0.0369083i
$551$	−4.83718	−	8.37825i	−0.206071	−	0.356925i
$552$		0			0
$553$	−4.82751	−	2.78717i	−0.205287	−	0.118522i
$554$	0.247410	+	0.428527i	0.0105114	+	0.0182064i
$555$		0			0
$556$	11.4771	−	19.8788i	0.486736	−	0.843051i
$557$	−3.30729	+	1.90946i	−0.140134	+	0.0809065i	−0.568428	−	0.822733i	$-0.692448\pi$
$557$	−3.30729	+	1.90946i	−0.140134	+	0.0809065i	0.428294	+	0.903640i	$0.359115\pi$
$558$		0			0
$559$	−0.159961	+	0.277061i	−0.00676563	+	0.0117184i
$560$	−5.25533	+	3.03416i	−0.222078	+	0.128217i
$561$		0			0
$562$	−32.4144			−1.36732
$563$	9.90220	−	5.71704i	0.417328	−	0.240945i	−0.276605	−	0.960984i	$-0.589209\pi$
$563$	9.90220	−	5.71704i	0.417328	−	0.240945i	0.693934	+	0.720039i	$0.255876\pi$
$564$		0			0
$565$	−4.91648	+	8.51560i	−0.206838	+	0.358254i
$566$	23.2720			0.978194
$567$		0			0
$568$	−2.69428	−	1.55554i	−0.113050	−	0.0652692i
$569$	−26.2859	−	15.1762i	−1.10196	−	0.636217i	−0.165226	−	0.986256i	$-0.552835\pi$
$569$	−26.2859	−	15.1762i	−1.10196	−	0.636217i	−0.936735	+	0.350038i	$0.886169\pi$
$570$		0			0
$571$	−12.1777	+	21.0923i	−0.509619	+	0.882686i	0.490319	+	0.871543i	$0.336880\pi$
$571$	−12.1777	+	21.0923i	−0.509619	+	0.882686i	−0.999938	+	0.0111430i	$0.996453\pi$
$572$	2.08686	+	1.20485i	0.0872560	+	0.0503773i
$573$		0			0
$574$	−19.8725	+	11.4734i	−0.829462	+	0.478890i
$575$	−4.23800	+	2.44681i	−0.176737	+	0.102039i
$576$		0			0
$577$	−5.16764	+	2.98354i	−0.215132	+	0.124206i	−0.603694	−	0.797216i	$-0.706305\pi$
$577$	−5.16764	+	2.98354i	−0.215132	+	0.124206i	0.388562	+	0.921422i	$0.372972\pi$
$578$	−20.4593	−	11.8122i	−0.850996	−	0.491323i
$579$		0			0
$580$	1.67361	−	2.89878i	0.0694930	−	0.120365i
$581$	15.8543	+	27.4604i	0.657746	+	1.13925i
$582$		0			0
$583$	−31.3967			−1.30032
$584$		−	12.3747i		−	0.512071i
$585$		0			0
$586$		−	16.4919i		−	0.681273i
$587$	−18.6025	+	10.7401i	−0.767806	+	0.443293i	−0.832091	−	0.554639i	$-0.812857\pi$
$587$	−18.6025	+	10.7401i	−0.767806	+	0.443293i	0.0642855	+	0.997932i	$0.479523\pi$
$588$		0			0
$589$	−30.7853			−1.26849
$590$	10.9349	+	6.31327i	0.450183	+	0.259913i
$591$		0			0
$592$	−5.41023	+	2.78018i	−0.222359	+	0.114265i
$593$	−14.6839			−0.602995			−0.301497	−	0.953467i	$-0.597486\pi$
$593$	−14.6839			−0.602995			−0.301497	+	0.953467i	$0.597486\pi$
$594$		0			0
$595$	19.3389	−	33.4960i	0.792819	−	1.37320i
$596$	−1.77169	−	3.06866i	−0.0725713	−	0.125697i
$597$		0			0
$598$	−5.89914	+	3.40587i	−0.241234	+	0.139276i
$599$	−37.2774			−1.52311			−0.761557	−	0.648098i	$-0.775565\pi$
$599$	−37.2774			−1.52311			−0.761557	+	0.648098i	$0.775565\pi$
$600$		0			0
$601$	21.2614			0.867272			0.433636	−	0.901088i	$-0.357230\pi$
$601$	21.2614			0.867272			0.433636	+	0.901088i	$0.357230\pi$
$602$	−0.968519			−0.0394739
$603$		0			0
$604$	5.11404	+	8.85777i	0.208087	+	0.360418i
$605$	8.58488	−	4.95648i	0.349025	−	0.201510i
$606$		0			0
$607$	30.9306	+	17.8578i	1.25543	+	0.724824i	0.972183	−	0.234222i	$-0.0752542\pi$
$607$	30.9306	+	17.8578i	1.25543	+	0.724824i	0.283250	+	0.959046i	$0.408588\pi$
$608$	2.99879	−	5.19406i	0.121617	−	0.210647i
$609$		0			0
$610$	−6.90903	+	3.98893i	−0.279738	+	0.161507i
$611$	7.28181	+	4.20415i	0.294590	+	0.170082i
$612$		0			0
$613$	−4.63356	−	8.02556i	−0.187148	−	0.324149i	0.757151	−	0.653240i	$-0.226591\pi$
$613$	−4.63356	−	8.02556i	−0.187148	−	0.324149i	−0.944298	+	0.329091i	$0.893258\pi$
$614$		−	19.9087i		−	0.803450i
$615$		0			0
$616$			7.29502i			0.293925i
$617$	−10.6162	+	18.3879i	−0.427393	+	0.740267i	−0.996641	−	0.0818993i	$-0.973901\pi$
$617$	−10.6162	+	18.3879i	−0.427393	+	0.740267i	0.569247	+	0.822166i	$0.307235\pi$
$618$		0			0
$619$	15.2987	−	26.4981i	0.614907	−	1.06505i	−0.375494	−	0.926825i	$-0.622527\pi$
$619$	15.2987	−	26.4981i	0.614907	−	1.06505i	0.990401	−	0.138225i	$-0.0441397\pi$
$620$	−5.32569	−	9.22436i	−0.213885	−	0.370459i
$621$		0			0
$622$	4.18841	−	7.25454i	0.167940	−	0.290881i
$623$	−34.8955	−	20.1469i	−1.39806	−	0.807168i
$624$		0			0
$625$	−21.0486			−0.841943
$626$	2.70871			0.108262
$627$		0			0
$628$	1.98168	−	3.43237i	0.0790776	−	0.136966i
$629$	21.0034	−	32.5878i	0.837459	−	1.29936i
$630$		0			0
$631$	−24.2862	+	14.0216i	−0.966817	+	0.558192i	−0.898264	−	0.439455i	$-0.855171\pi$
$631$	−24.2862	+	14.0216i	−0.966817	+	0.558192i	−0.0685526	+	0.997648i	$0.521838\pi$
$632$	0.953087	+	1.65079i	0.0379118	+	0.0656651i
$633$		0			0
$634$		−	7.39929i		−	0.293863i
$635$	24.3863	−	14.0794i	0.967741	−	0.558725i
$636$		0			0
$637$	−1.29823	−	0.749532i	−0.0514376	−	0.0296975i
$638$	−2.01193	−	3.48476i	−0.0796530	−	0.137963i
$639$		0			0
$640$	2.07510			0.0820255
$641$	29.6377			1.17062			0.585310	−	0.810810i	$-0.300973\pi$
$641$	29.6377			1.17062			0.585310	+	0.810810i	$0.300973\pi$
$642$		0			0
$643$	28.4800	−	16.4429i	1.12314	−	0.648445i	0.180940	−	0.983494i	$-0.442086\pi$
$643$	28.4800	−	16.4429i	1.12314	−	0.648445i	0.942201	+	0.335049i	$0.108753\pi$
$644$	−17.8588	−	10.3108i	−0.703735	−	0.406302i
$645$		0			0
$646$			38.2270i			1.50402i
$647$	−27.5906	−	15.9294i	−1.08470	−	0.626250i	−0.152538	−	0.988298i	$-0.548745\pi$
$647$	−27.5906	−	15.9294i	−1.08470	−	0.626250i	−0.932160	+	0.362047i	$0.882078\pi$
$648$		0			0
$649$	13.1454	−	7.58948i	0.516001	−	0.297913i
$650$	0.670357			0.0262936
$651$		0			0
$652$	12.9105	−	7.45388i	0.505614	−	0.291916i
$653$			7.38487i			0.288992i	0.989505	+	0.144496i	$0.0461561\pi$
$653$			7.38487i			0.288992i	−0.989505	+	0.144496i	$0.953844\pi$
$654$		0			0
$655$	13.5882	−	23.5354i	0.530934	−	0.919604i
$656$	7.84678			0.306365
$657$		0			0
$658$			25.4550i			0.992338i
$659$	22.1651	+	38.3911i	0.863431	+	1.49551i	0.868597	+	0.495520i	$0.165022\pi$
$659$	22.1651	+	38.3911i	0.863431	+	1.49551i	−0.00516561	+	0.999987i	$0.501644\pi$
$660$		0			0
$661$			18.8130i			0.731741i	0.930666	+	0.365870i	$0.119229\pi$
$661$			18.8130i			0.731741i	−0.930666	+	0.365870i	$0.880771\pi$
$662$	0.437608			0.0170081
$663$		0			0
$664$		−	10.8429i		−	0.420787i
$665$	−36.3953			−1.41135
$666$		0			0
$667$	11.3746			0.440428
$668$			5.38912i			0.208511i
$669$		0			0
$670$	−20.4178			−0.788807
$671$			9.59056i			0.370239i
$672$		0			0
$673$	22.9828	+	39.8073i	0.885921	+	1.53446i	0.844654	+	0.535312i	$0.179806\pi$
$673$	22.9828	+	39.8073i	0.885921	+	1.53446i	0.0412668	+	0.999148i	$0.486861\pi$
$674$		−	2.65082i		−	0.102106i
$675$		0			0
$676$	−12.0669			−0.464111
$677$	24.4206	−	42.2977i	0.938561	−	1.62563i	0.170402	−	0.985375i	$-0.445493\pi$
$677$	24.4206	−	42.2977i	0.938561	−	1.62563i	0.768158	−	0.640260i	$-0.221173\pi$
$678$		0			0
$679$		−	14.3212i		−	0.549598i
$680$	−11.4541	+	6.61306i	−0.439247	+	0.253599i
$681$		0			0
$682$	−12.8045			−0.490310
$683$	−25.0780	+	14.4788i	−0.959582	+	0.554015i	−0.896044	−	0.443965i	$-0.853572\pi$
$683$	−25.0780	+	14.4788i	−0.959582	+	0.554015i	−0.0635373	+	0.997979i	$0.520238\pi$
$684$		0			0
$685$	16.2227	+	9.36619i	0.619838	+	0.357864i
$686$			15.9323i			0.608298i
$687$		0			0
$688$	0.286819	+	0.165595i	0.0109349	+	0.00631326i
$689$	−10.5290	+	6.07889i	−0.401121	+	0.231587i
$690$		0			0
$691$	−20.9594			−0.797334			−0.398667	−	0.917096i	$-0.630527\pi$
$691$	−20.9594			−0.797334			−0.398667	+	0.917096i	$0.630527\pi$
$692$	−2.77645			−0.105545
$693$		0			0
$694$	1.06701	+	1.84812i	0.0405033	+	0.0701538i
$695$	41.2506	+	23.8160i	1.56472	+	0.903393i
$696$		0			0
$697$	−43.3127	+	25.0066i	−1.64059	+	0.947193i
$698$			0.0108863i			0.000412054i
$699$		0			0
$700$	1.01471	+	1.75752i	0.0383523	+	0.0664281i
$701$	31.9608	−	18.4526i	1.20714	−	0.696945i	0.245009	−	0.969521i	$-0.421209\pi$
$701$	31.9608	−	18.4526i	1.20714	−	0.696945i	0.962134	+	0.272576i	$0.0878757\pi$
$702$		0			0
$703$	−36.4382	−	1.78370i	−1.37429	−	0.0672736i
$704$	1.24729	−	2.16036i	0.0470089	−	0.0814218i
$705$		0			0
$706$	29.4755			1.10933
$707$	1.63898			0.0616403
$708$		0			0
$709$	−39.8517	−	23.0084i	−1.49666	−	0.864099i	−0.496671	−	0.867939i	$-0.665444\pi$
$709$	−39.8517	−	23.0084i	−1.49666	−	0.864099i	−0.999993	+	0.00384026i	$0.998778\pi$
$710$	3.22791	−	5.59090i	0.121141	−	0.209823i
$711$		0			0
$712$	6.88934	+	11.9327i	0.258189	+	0.447197i
$713$	18.0979	−	31.3465i	0.677772	−	1.17394i
$714$		0			0
$715$	−2.50018	+	4.33044i	−0.0935015	+	0.161949i
$716$			6.05390i			0.226245i
$717$		0			0
$718$			18.3714i			0.685616i
$719$	15.5745	+	26.9759i	0.580832	+	1.00603i	0.995381	+	0.0960034i	$0.0306060\pi$
$719$	15.5745	+	26.9759i	0.580832	+	1.00603i	−0.414549	+	0.910027i	$0.636061\pi$
$720$		0			0
$721$	26.0484	+	15.0390i	0.970093	+	0.560083i
$722$	14.6973	−	8.48551i	0.546978	−	0.315798i
$723$		0			0
$724$	−3.93255	+	6.81137i	−0.146152	+	0.253143i
$725$	−0.969430	−	0.559701i	−0.0360037	−	0.0207868i
$726$		0			0
$727$	22.5417	−	13.0144i	0.836025	−	0.482679i	−0.0198862	−	0.999802i	$-0.506330\pi$
$727$	22.5417	−	13.0144i	0.836025	−	0.482679i	0.855911	+	0.517123i	$0.172997\pi$
$728$	1.41243	+	2.44640i	0.0523481	+	0.0906696i
$729$		0			0
$730$	25.6788			0.950416
$731$	−2.11092			−0.0780751
$732$		0			0
$733$	14.0275			0.518116			0.259058	−	0.965862i	$-0.416588\pi$
$733$	14.0275			0.518116			0.259058	+	0.965862i	$0.416588\pi$
$734$	−22.2258	+	12.8321i	−0.820370	+	0.473641i
$735$		0			0
$736$	3.52583	+	6.10692i	0.129964	+	0.225104i
$737$	−12.2726	+	21.2567i	−0.452066	+	0.783002i
$738$		0			0
$739$	−31.7058			−1.16632			−0.583158	−	0.812359i	$-0.698183\pi$
$739$	−31.7058			−1.16632			−0.583158	+	0.812359i	$0.698183\pi$
$740$	−5.76916	−	11.2268i	−0.212078	−	0.412704i
$741$		0			0
$742$	−31.8749	−	18.4030i	−1.17016	−	0.675595i
$743$	−39.9145			−1.46432			−0.732160	−	0.681133i	$-0.761488\pi$
$743$	−39.9145			−1.46432			−0.732160	+	0.681133i	$0.761488\pi$
$744$		0			0
$745$	6.36777	−	3.67643i	0.233297	−	0.134694i
$746$		−	27.9016i		−	1.02155i
$747$		0			0
$748$			15.8997i			0.581352i
$749$	53.3921			1.95091
$750$		0			0
$751$	−21.5366	−	37.3024i	−0.785880	−	1.36118i	−0.928472	−	0.371402i	$-0.878877\pi$
$751$	−21.5366	−	37.3024i	−0.785880	−	1.36118i	0.142592	−	0.989782i	$-0.454456\pi$
$752$	4.35223	−	7.53829i	0.158710	−	0.274893i
$753$		0			0
$754$	−1.34941	−	0.779081i	−0.0491425	−	0.0283725i
$755$	−18.3807	+	10.6121i	−0.668944	+	0.386215i
$756$		0			0
$757$	39.2580	−	22.6656i	1.42686	−	0.823797i	0.429986	−	0.902836i	$-0.358519\pi$
$757$	39.2580	−	22.6656i	1.42686	−	0.823797i	0.996872	+	0.0790390i	$0.0251852\pi$
$758$	−14.3424	+	8.28061i	−0.520941	+	0.300765i
$759$		0			0
$760$	10.7782	+	6.22279i	0.390966	+	0.225724i
$761$	21.3517	−	36.9823i	0.774000	−	1.34061i	−0.161355	−	0.986896i	$-0.551587\pi$
$761$	21.3517	−	36.9823i	0.774000	−	1.34061i	0.935355	−	0.353710i	$-0.115080\pi$
$762$		0			0
$763$	36.3502	+	20.9868i	1.31597	+	0.759774i
$764$	7.53550	+	4.35062i	0.272625	+	0.157400i
$765$		0			0
$766$	20.4913			0.740379
$767$	2.93888	−	5.09029i	0.106117	−	0.183800i
$768$		0			0
$769$	−27.2910	+	15.7565i	−0.984139	+	0.568193i	−0.903517	−	0.428552i	$-0.859024\pi$
$769$	−27.2910	+	15.7565i	−0.984139	+	0.568193i	−0.0806222	+	0.996745i	$0.525691\pi$
$770$	−15.1379			−0.545532
$771$		0			0
$772$	8.34933	−	4.82049i	0.300499	−	0.173493i
$773$	17.8946	−	30.9944i	0.643626	−	1.11479i	−0.340991	−	0.940066i	$-0.610763\pi$
$773$	17.8946	−	30.9944i	0.643626	−	1.11479i	0.984617	−	0.174726i	$-0.0559039\pi$
$774$		0			0
$775$	−3.08487	+	1.78105i	−0.110812	+	0.0639773i
$776$	−2.44861	+	4.24112i	−0.0879000	+	0.152247i
$777$		0			0
$778$	12.9559	+	22.4403i	0.464492	+	0.804523i
$779$	40.7566	+	23.5308i	1.46026	+	0.843080i
$780$		0			0
$781$	−3.88042	−	6.72108i	−0.138852	−	0.240499i
$782$	−38.9238	−	22.4727i	−1.39191	−	0.803621i
$783$		0			0
$784$	−0.775932	+	1.34395i	−0.0277119	+	0.0479983i
$785$	7.12250	+	4.11218i	0.254213	+	0.146770i
$786$		0			0
$787$	−14.4367	−	25.0050i	−0.514611	−	0.891332i	−0.999856	−	0.0169544i	$-0.994603\pi$
$787$	−14.4367	−	25.0050i	−0.514611	−	0.891332i	0.485245	−	0.874378i	$-0.338730\pi$
$788$	5.57481	+	9.65586i	0.198594	+	0.343976i
$789$		0			0
$790$	−3.42556	+	1.97775i	−0.121876	+	0.0703651i
$791$			13.8572i			0.492706i
$792$		0			0
$793$	1.85688	+	3.21621i	0.0659398	+	0.114211i
$794$			9.32207i			0.330828i
$795$		0			0
$796$			6.78425i			0.240461i
$797$	7.45836	+	4.30608i	0.264189	+	0.152529i	0.626244	−	0.779627i	$-0.284591\pi$
$797$	7.45836	+	4.30608i	0.264189	+	0.152529i	−0.362055	+	0.932157i	$0.617925\pi$
$798$		0			0
$799$			55.4799i			1.96274i
$800$		−	0.693968i		−	0.0245355i
$801$		0			0
$802$	3.47159	+	6.01297i	0.122586	+	0.212325i
$803$	15.4349	−	26.7340i	0.544684	−	0.943421i
$804$		0			0
$805$	21.3959	−	37.0588i	0.754106	−	1.30615i
$806$	−4.29402	+	2.47916i	−0.151250	+	0.0873245i
$807$		0			0
$808$	−0.485372	−	0.280230i	−0.0170753	−	0.00985845i
$809$	32.9827	+	19.0426i	1.15961	+	0.669500i	0.951210	−	0.308544i	$-0.0998415\pi$
$809$	32.9827	+	19.0426i	1.15961	+	0.669500i	0.208399	+	0.978044i	$0.433175\pi$
$810$		0			0
$811$	−1.25518	+	2.17403i	−0.0440752	+	0.0763405i	−0.887221	−	0.461344i	$-0.847367\pi$
$811$	−1.25518	+	2.17403i	−0.0440752	+	0.0763405i	0.843146	+	0.537684i	$0.180701\pi$
$812$		−	4.71712i		−	0.165538i
$813$		0			0
$814$	−15.1557	−	0.741895i	−0.531209	−	0.0260034i
$815$	15.4675	+	26.7905i	0.541804	+	0.938432i
$816$		0			0
$817$	0.993171	+	1.72022i	0.0347467	+	0.0601830i
$818$	−16.1728	+	28.0121i	−0.565469	+	0.979420i
$819$		0			0
$820$			16.2828i			0.568621i
$821$	7.37137	+	12.7676i	0.257262	+	0.445592i	0.965508	−	0.260375i	$-0.0838462\pi$
$821$	7.37137	+	12.7676i	0.257262	+	0.445592i	−0.708245	+	0.705967i	$0.750513\pi$
$822$		0			0
$823$	−7.35430	+	12.7380i	−0.256355	+	0.444020i	−0.965263	−	0.261282i	$-0.915855\pi$
$823$	−7.35430	+	12.7380i	−0.256355	+	0.444020i	0.708908	+	0.705301i	$0.249188\pi$
$824$	−5.14268	−	8.90739i	−0.179154	−	0.310304i
$825$		0			0
$826$	17.7941			0.619136
$827$	6.22156	+	3.59202i	0.216345	+	0.124907i	0.604257	−	0.796790i	$-0.293470\pi$
$827$	6.22156	+	3.59202i	0.216345	+	0.124907i	−0.387912	+	0.921697i	$0.626803\pi$
$828$		0			0
$829$	47.5246	−	27.4384i	1.65060	−	0.952974i	0.673773	−	0.738939i	$-0.264673\pi$
$829$	47.5246	−	27.4384i	1.65060	−	0.952974i	0.976826	−	0.214035i	$-0.0686606\pi$
$830$	22.5001			0.780990
$831$		0			0
$832$		−	0.965976i		−	0.0334892i
$833$		−	9.89116i		−	0.342708i
$834$		0			0
$835$	−11.1830			−0.387002
$836$	12.9570	−	7.48071i	0.448126	−	0.258726i
$837$		0			0
$838$	−29.5355	−	17.0524i	−1.02029	−	0.589064i
$839$	18.4848			0.638165			0.319082	−	0.947727i	$-0.396625\pi$
$839$	18.4848			0.638165			0.319082	+	0.947727i	$0.396625\pi$
$840$		0			0
$841$	−13.1990	−	22.8614i	−0.455139	−	0.788325i
$842$	−0.860340	+	1.49015i	−0.0296493	+	0.0513540i
$843$		0			0
$844$	−8.45706	−	14.6480i	−0.291104	−	0.504207i
$845$		−	25.0400i		−	0.861401i
$846$		0			0
$847$	6.98498	−	12.0983i	0.240007	−	0.415704i
$848$	6.29300	+	10.8998i	0.216103	+	0.374301i
$849$		0			0
$850$	2.21158	+	3.83057i	0.0758566	+	0.131388i
$851$	23.2374	−	36.0539i	0.796566	−	1.23591i
$852$		0			0
$853$		−	31.2396i		−	1.06962i	−0.844971	−	0.534812i	$-0.820382\pi$
$853$		−	31.2396i		−	1.06962i	0.844971	−	0.534812i	$-0.179618\pi$
$854$	−5.62145	+	9.73663i	−0.192362	+	0.333181i
$855$		0			0
$856$	−15.8117	−	9.12887i	−0.540432	−	0.312018i
$857$	−5.55472	−	3.20702i	−0.189746	−	0.109550i	0.402118	−	0.915588i	$-0.368274\pi$
$857$	−5.55472	−	3.20702i	−0.189746	−	0.109550i	−0.591864	+	0.806038i	$0.701608\pi$
$858$		0			0
$859$	9.71896	−	5.61125i	0.331607	−	0.191453i	−0.324947	−	0.945732i	$-0.605347\pi$
$859$	9.71896	−	5.61125i	0.331607	−	0.191453i	0.656554	+	0.754279i	$0.272013\pi$
$860$	−0.343626	+	0.595178i	−0.0117176	+	0.0202954i
$861$		0			0
$862$	4.14791	−	7.18439i	0.141278	−	0.244701i
$863$	10.1464	+	17.5740i	0.345386	+	0.598226i	0.985424	−	0.170117i	$-0.0544146\pi$
$863$	10.1464	+	17.5740i	0.345386	+	0.598226i	−0.640038	+	0.768344i	$0.721081\pi$
$864$		0			0
$865$		−	5.76140i		−	0.195893i
$866$			17.3517i			0.589633i
$867$		0			0
$868$	−12.9995	−	7.50529i	−0.441233	−	0.254746i
$869$			4.75509i			0.161305i
$870$		0			0
$871$			9.50465i			0.322053i
$872$	−7.17656	−	12.4302i	−0.243029	−	0.420938i
$873$		0			0
$874$			42.2929i			1.43058i
$875$	−29.9237	+	17.2764i	−1.01160	+	0.584050i
$876$		0			0
$877$	8.83272	+	15.2987i	0.298260	+	0.516601i	0.975738	−	0.218942i	$-0.0702605\pi$
$877$	8.83272	+	15.2987i	0.298260	+	0.516601i	−0.677478	+	0.735543i	$0.736927\pi$
$878$	16.0758	+	27.8441i	0.542532	+	0.939694i
$879$		0			0
$880$	4.48297	+	2.58824i	0.151121	+	0.0872496i
$881$	−20.2235	+	35.0281i	−0.681347	+	1.18013i	0.293223	+	0.956044i	$0.405272\pi$
$881$	−20.2235	+	35.0281i	−0.681347	+	1.18013i	−0.974570	+	0.224083i	$0.928061\pi$
$882$		0			0
$883$	−11.9594	−	6.90475i	−0.402465	−	0.232363i	0.285082	−	0.958503i	$-0.407979\pi$
$883$	−11.9594	−	6.90475i	−0.402465	−	0.232363i	−0.687547	+	0.726140i	$0.741312\pi$
$884$	3.07844	+	5.33201i	0.103539	+	0.179335i
$885$		0			0
$886$	16.4067	+	9.47241i	0.551194	+	0.318232i
$887$	−8.37557	−	14.5069i	−0.281224	−	0.487094i	0.690462	−	0.723368i	$-0.257407\pi$
$887$	−8.37557	−	14.5069i	−0.281224	−	0.487094i	−0.971687	+	0.236274i	$0.924074\pi$
$888$		0			0
$889$	19.8416	−	34.3667i	0.665466	−	1.15262i
$890$	−24.7615	+	14.2961i	−0.830008	+	0.479205i
$891$		0			0
$892$	10.7054	−	18.5423i	0.358443	−	0.620842i
$893$	45.2115	−	26.1029i	1.51295	−	0.873499i
$894$		0			0
$895$	−12.5624			−0.419916
$896$	2.53257	−	1.46218i	0.0846071	−	0.0488480i
$897$		0			0
$898$	6.81218	−	11.7990i	0.227326	−	0.393739i
$899$	8.27968			0.276143
$900$		0			0
$901$	−69.4724	−	40.1099i	−2.31446	−	1.33625i
$902$	16.9519	+	9.78718i	0.564436	+	0.325877i
$903$		0			0
$904$	2.36928	−	4.10371i	0.0788010	−	0.136487i
$905$	−14.1343	−	8.16043i	−0.469839	−	0.271262i
$906$		0			0
$907$	−5.95086	+	3.43573i	−0.197595	+	0.114082i	−0.595533	−	0.803331i	$-0.703059\pi$
$907$	−5.95086	+	3.43573i	−0.197595	+	0.114082i	0.397938	+	0.917412i	$0.369726\pi$
$908$	21.7648	−	12.5659i	0.722289	−	0.417014i
$909$		0			0
$910$	−5.07652	+	2.93093i	−0.168285	+	0.0971594i
$911$	23.7057	+	13.6865i	0.785406	+	0.453455i	0.838343	−	0.545143i	$-0.183525\pi$
$911$	23.7057	+	13.6865i	0.785406	+	0.453455i	−0.0529365	+	0.998598i	$0.516858\pi$
$912$		0			0
$913$	13.5242	−	23.4246i	0.447586	−	0.775242i
$914$	−4.97540	−	8.61765i	−0.164572	−	0.285047i
$915$		0			0
$916$	6.45385			0.213241
$917$		−	38.2986i		−	1.26473i
$918$		0			0
$919$		−	23.1609i		−	0.764009i	−0.924161	−	0.382004i	$-0.875234\pi$
$919$		−	23.1609i		−	0.764009i	0.924161	−	0.382004i	$-0.124766\pi$
$920$	−12.6724	+	7.31644i	−0.417798	+	0.241216i
$921$		0			0
$922$	−22.0486			−0.726133
$923$	−2.60261	−	1.50262i	−0.0856661	−	0.0494593i
$924$		0			0
$925$	−3.75453	+	1.92936i	−0.123448	+	0.0634370i
$926$	13.4512			0.442033
$927$		0			0
$928$	−0.806522	+	1.39694i	−0.0264754	+	0.0458567i
$929$	−11.7720	−	20.3898i	−0.386228	−	0.668966i	0.605711	−	0.795685i	$-0.292889\pi$
$929$	−11.7720	−	20.3898i	−0.386228	−	0.668966i	−0.991939	+	0.126719i	$0.959555\pi$
$930$		0			0
$931$	−8.06047	+	4.65372i	−0.264171	+	0.152519i
$932$	−20.1699			−0.660686
$933$		0			0
$934$	11.8425			0.387498
$935$	−32.9935			−1.07900
$936$		0			0
$937$	12.5828	+	21.7940i	0.411061	+	0.711978i	0.995006	−	0.0998150i	$-0.0318251\pi$
$937$	12.5828	+	21.7940i	0.411061	+	0.711978i	−0.583945	+	0.811793i	$0.698492\pi$
$938$	−24.9190	+	14.3870i	−0.813635	+	0.469752i
$939$		0			0
$940$	15.6427	+	9.03131i	0.510208	+	0.294569i
$941$	8.26816	−	14.3209i	0.269534	−	0.466847i	−0.699207	−	0.714919i	$-0.746464\pi$
$941$	8.26816	−	14.3209i	0.269534	−	0.466847i	0.968742	+	0.248072i	$0.0797969\pi$
$942$		0			0
$943$	−47.9196	+	27.6664i	−1.56048	+	0.900942i
$944$	−5.26958	−	3.04240i	−0.171510	−	0.0990215i
$945$		0			0
$946$	0.413089	+	0.715492i	0.0134307	+	0.0232626i
$947$		−	18.2880i		−	0.594281i	−0.954834	−	0.297141i	$-0.903967\pi$
$947$		−	18.2880i		−	0.594281i	0.954834	−	0.297141i	$-0.0960330\pi$
$948$		0			0
$949$		−	11.9537i		−	0.388034i
$950$	2.08107	−	3.60451i	0.0675187	−	0.116946i
$951$		0			0
$952$	−9.31953	+	16.1419i	−0.302048	+	0.523162i
$953$	19.9492	+	34.5531i	0.646219	+	1.11928i	0.984018	+	0.178066i	$0.0569841\pi$
$953$	19.9492	+	34.5531i	0.646219	+	1.11928i	−0.337799	+	0.941218i	$0.609683\pi$
$954$		0			0
$955$	−9.02797	+	15.6369i	−0.292138	+	0.505998i
$956$	4.12334	+	2.38061i	0.133358	+	0.0769944i
$957$		0			0
$958$	−9.31385			−0.300917
$959$	26.3988			0.852462
$960$		0			0
$961$	−2.32641	+	4.02945i	−0.0750453	+	0.129982i
$962$	−5.22615	+	2.68559i	−0.168498	+	0.0865870i
$963$		0			0
$964$	5.64101	−	3.25684i	0.181685	−	0.104896i
$965$	10.0030	+	17.3257i	0.322007	+	0.557733i
$966$		0			0
$967$		−	10.2031i		−	0.328111i	−0.986451	−	0.164055i	$-0.947542\pi$
$967$		−	10.2031i		−	0.328111i	0.986451	−	0.164055i	$-0.0524576\pi$
$968$	−4.13709	+	2.38855i	−0.132971	+	0.0767710i
$969$		0			0
$970$	−8.80074	−	5.08111i	−0.282575	−	0.163145i
$971$	18.9059	+	32.7460i	0.606720	+	1.05087i	0.991777	+	0.127977i	$0.0408484\pi$
$971$	18.9059	+	32.7460i	0.606720	+	1.05087i	−0.385057	+	0.922893i	$0.625818\pi$
$972$		0			0
$973$	67.1260			2.15196
$974$	28.3740			0.909161
$975$		0			0
$976$	3.32949	−	1.92228i	0.106575	−	0.0615308i
$977$	10.4748	+	6.04761i	0.335118	+	0.193480i	0.658111	−	0.752921i	$-0.271356\pi$
$977$	10.4748	+	6.04761i	0.335118	+	0.193480i	−0.322993	+	0.946401i	$0.604689\pi$
$978$		0			0
$979$			34.3719i			1.09853i
$980$	−2.78884	−	1.61013i	−0.0890861	−	0.0514339i
$981$		0			0
$982$	27.7847	−	16.0415i	0.886644	−	0.511904i
$983$	−28.1841			−0.898933			−0.449467	−	0.893297i	$-0.648386\pi$
$983$	−28.1841			−0.898933			−0.449467	+	0.893297i	$0.648386\pi$
$984$		0			0
$985$	−20.0369	+	11.5683i	−0.638427	+	0.368596i
$986$		−	10.2811i		−	0.327417i
$987$		0			0
$988$	2.89676	−	5.01734i	0.0921583	−	0.159623i
$989$	−2.33544			−0.0742627
$990$		0			0
$991$			0.284061i			0.00902349i	0.999990	+	0.00451174i	$0.00143614\pi$
$991$			0.284061i			0.00902349i	−0.999990	+	0.00451174i	$0.998564\pi$
$992$	2.56648	+	4.44527i	0.0814857	+	0.141137i
$993$		0			0
$994$		−	9.09794i		−	0.288569i
$995$	−14.0780			−0.446302
$996$		0			0
$997$		−	43.4781i		−	1.37697i	−0.725253	−	0.688483i	$-0.758277\pi$
$997$		−	43.4781i		−	1.37697i	0.725253	−	0.688483i	$-0.241723\pi$
$998$	−17.8888			−0.566260
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.k.a.1639.15		76
3.2	odd	2		666.2.k.a.529.33	yes	76
9.4	even	3		1998.2.t.a.307.24		76
9.5	odd	6		666.2.t.a.85.12	yes	76
37.27	even	6		1998.2.t.a.397.24		76
111.101	odd	6		666.2.t.a.619.12	yes	76
333.175	even	6	inner	1998.2.k.a.1063.24		76
333.212	odd	6		666.2.k.a.175.14	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.14	✓	76	333.212	odd	6
666.2.k.a.529.33	yes	76	3.2	odd	2
666.2.t.a.85.12	yes	76	9.5	odd	6
666.2.t.a.619.12	yes	76	111.101	odd	6
1998.2.k.a.1063.24		76	333.175	even	6	inner
1998.2.k.a.1639.15		76	1.1	even	1	trivial
1998.2.t.a.307.24		76	9.4	even	3
1998.2.t.a.397.24		76	37.27	even	6

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:	\( N \)	\(=\)	\( 1998 = 2 \cdot 3^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1998.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} -2.07510i q^{5} +(-1.46218 - 2.53257i) q^{7} +1.00000i q^{8} -2.07510 q^{10} +(-1.24729 + 2.16036i) q^{11} +0.965976i q^{13} +(-2.53257 + 1.46218i) q^{14} +1.00000 q^{16} +(-5.51981 + 3.18686i) q^{17} +(5.19406 + 2.99879i) q^{19} +2.07510i q^{20} +(2.16036 + 1.24729i) q^{22} +(-6.10692 + 3.52583i) q^{23} +0.693968 q^{25} +0.965976 q^{26} +(1.46218 + 2.53257i) q^{28} +(-1.39694 - 0.806522i) q^{29} +(-4.44527 + 2.56648i) q^{31} -1.00000i q^{32} +(3.18686 + 5.51981i) q^{34} +(-5.25533 + 3.03416i) q^{35} +(-5.41023 + 2.78018i) q^{37} +(2.99879 - 5.19406i) q^{38} +2.07510 q^{40} +7.84678 q^{41} +(0.286819 + 0.165595i) q^{43} +(1.24729 - 2.16036i) q^{44} +(3.52583 + 6.10692i) q^{46} +(4.35223 - 7.53829i) q^{47} +(-0.775932 + 1.34395i) q^{49} -0.693968i q^{50} -0.965976i q^{52} +(6.29300 + 10.8998i) q^{53} +(4.48297 + 2.58824i) q^{55} +(2.53257 - 1.46218i) q^{56} +(-0.806522 + 1.39694i) q^{58} +(-5.26958 - 3.04240i) q^{59} +(3.32949 - 1.92228i) q^{61} +(2.56648 + 4.44527i) q^{62} -1.00000 q^{64} +2.00450 q^{65} +9.83943 q^{67} +(5.51981 - 3.18686i) q^{68} +(3.03416 + 5.25533i) q^{70} +(-1.55554 + 2.69428i) q^{71} -12.3747 q^{73} +(2.78018 + 5.41023i) q^{74} +(-5.19406 - 2.99879i) q^{76} +7.29502 q^{77} +(1.65079 - 0.953087i) q^{79} -2.07510i q^{80} -7.84678i q^{82} -10.8429 q^{83} +(6.61306 + 11.4541i) q^{85} +(0.165595 - 0.286819i) q^{86} +(-2.16036 - 1.24729i) q^{88} +(11.9327 - 6.88934i) q^{89} +(2.44640 - 1.41243i) q^{91} +(6.10692 - 3.52583i) q^{92} +(-7.53829 - 4.35223i) q^{94} +(6.22279 - 10.7782i) q^{95} +(4.24112 + 2.44861i) q^{97} +(1.34395 + 0.775932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} - 2 q^{7} + 4 q^{11} + 76 q^{16} - 12 q^{23} - 100 q^{25} + 24 q^{26} + 2 q^{28} - 18 q^{29} + 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} - 72 q^{41} + 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) \) 76 * q - 76 * q^4 - 2 * q^7 + 4 * q^11 + 76 * q^16 - 12 * q^23 - 100 * q^25 + 24 * q^26 + 2 * q^28 - 18 * q^29 + 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 - 72 * q^41 + 6 * q^43 - 4 * q^44 + 20 * q^47 - 36 * q^49 - 14 * q^53 + 6 * q^59 + 16 * q^62 - 76 * q^64 - 32 * q^65 + 40 * q^67 - 2 * q^71 + 28 * q^73 + 2 * q^74 + 24 * q^77 + 6 * q^79 + 64 * q^83 - 12 * q^85 - 4 * q^86 - 60 * q^89 + 42 * q^91 + 12 * q^92 + 14 * q^95 - 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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