LMFDB - Embedded newform 1998.2.h.b.1099.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(1009,1998)] 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("1998.1009"); 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, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$15.9541103239$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 666)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1099.17
Character	$\chi$	$=$	1998.1099
Dual form			1998.2.h.b.1009.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +4.07867 q^{5} +(-2.47419 - 4.28542i) q^{7} +1.00000 q^{8} +4.07867 q^{10} +(1.34686 - 2.33282i) q^{11} -2.87378 q^{13} +(-2.47419 - 4.28542i) q^{14} +1.00000 q^{16} +(2.71933 + 4.71002i) q^{17} +(0.179633 - 0.311133i) q^{19} +4.07867 q^{20} +(1.34686 - 2.33282i) q^{22} +(-0.147957 - 0.256269i) q^{23} +11.6356 q^{25} -2.87378 q^{26} +(-2.47419 - 4.28542i) q^{28} +(1.72918 - 2.99502i) q^{29} +(0.980010 + 1.69743i) q^{31} +1.00000 q^{32} +(2.71933 + 4.71002i) q^{34} +(-10.0914 - 17.4788i) q^{35} +(-6.08268 - 0.0307620i) q^{37} +(0.179633 - 0.311133i) q^{38} +4.07867 q^{40} -2.46495 q^{41} +(3.92593 - 6.79991i) q^{43} +(1.34686 - 2.33282i) q^{44} +(-0.147957 - 0.256269i) q^{46} +(3.83844 - 6.64837i) q^{47} +(-8.74321 + 15.1437i) q^{49} +11.6356 q^{50} -2.87378 q^{52} +(-2.45992 - 4.26070i) q^{53} +(5.49339 - 9.51483i) q^{55} +(-2.47419 - 4.28542i) q^{56} +(1.72918 - 2.99502i) q^{58} +(3.27974 - 5.68067i) q^{59} +(-2.07388 - 3.59207i) q^{61} +(0.980010 + 1.69743i) q^{62} +1.00000 q^{64} -11.7212 q^{65} -0.566061 q^{67} +(2.71933 + 4.71002i) q^{68} +(-10.0914 - 17.4788i) q^{70} +(-5.34228 + 9.25310i) q^{71} +8.59878 q^{73} +(-6.08268 - 0.0307620i) q^{74} +(0.179633 - 0.311133i) q^{76} -13.3295 q^{77} +(7.09273 + 12.2850i) q^{79} +4.07867 q^{80} -2.46495 q^{82} -12.4880 q^{83} +(11.0913 + 19.2106i) q^{85} +(3.92593 - 6.79991i) q^{86} +(1.34686 - 2.33282i) q^{88} +(9.19327 + 15.9232i) q^{89} +(7.11027 + 12.3153i) q^{91} +(-0.147957 - 0.256269i) q^{92} +(3.83844 - 6.64837i) q^{94} +(0.732663 - 1.26901i) q^{95} +(0.696052 - 1.20560i) q^{97} +(-8.74321 + 15.1437i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{2} + 36 q^{4} + 8 q^{5} + 4 q^{7} + 36 q^{8} + 8 q^{10} - 3 q^{11} - 2 q^{13} + 4 q^{14} + 36 q^{16} - 3 q^{17} + 9 q^{19} + 8 q^{20} - 3 q^{22} - 11 q^{23} + 44 q^{25} - 2 q^{26} + 4 q^{28}+ \cdots - 12 q^{98}+O(q^{100}) $ 36 * q + 36 * q^2 + 36 * q^4 + 8 * q^5 + 4 * q^7 + 36 * q^8 + 8 * q^10 - 3 * q^11 - 2 * q^13 + 4 * q^14 + 36 * q^16 - 3 * q^17 + 9 * q^19 + 8 * q^20 - 3 * q^22 - 11 * q^23 + 44 * q^25 - 2 * q^26 + 4 * q^28 + 12 * q^29 + 16 * q^31 + 36 * q^32 - 3 * q^34 - 3 * q^35 + 8 * q^37 + 9 * q^38 + 8 * q^40 - 12 * q^41 + 4 * q^43 - 3 * q^44 - 11 * q^46 + 5 * q^47 - 12 * q^49 + 44 * q^50 - 2 * q^52 - 8 * q^53 + 9 * q^55 + 4 * q^56 + 12 * q^58 + 12 * q^59 - 15 * q^61 + 16 * q^62 + 36 * q^64 - 52 * q^65 + 28 * q^67 - 3 * q^68 - 3 * q^70 + 22 * q^73 + 8 * q^74 + 9 * q^76 + 50 * q^77 + 16 * q^79 + 8 * q^80 - 12 * q^82 + 15 * q^85 + 4 * q^86 - 3 * q^88 - 3 * q^89 + 37 * q^91 - 11 * q^92 + 5 * q^94 - 3 * q^95 + 11 * q^97 - 12 * q^98

Character values

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

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	4.07867			1.82404			0.912019	−	0.410148i	$-0.134523\pi$
$5$	4.07867			1.82404			0.912019	+	0.410148i	$0.134523\pi$
$6$		0			0
$7$	−2.47419	−	4.28542i	−0.935155	−	1.61974i	−0.774357	−	0.632749i	$-0.781927\pi$
$7$	−2.47419	−	4.28542i	−0.935155	−	1.61974i	−0.160798	−	0.986987i	$-0.551407\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	4.07867			1.28979
$11$	1.34686	−	2.33282i	0.406093	−	0.703373i	−0.588355	−	0.808603i	$-0.700224\pi$
$11$	1.34686	−	2.33282i	0.406093	−	0.703373i	0.994448	+	0.105229i	$0.0335577\pi$
$12$		0			0
$13$	−2.87378			−0.797043			−0.398521	−	0.917159i	$-0.630476\pi$
$13$	−2.87378			−0.797043			−0.398521	+	0.917159i	$0.630476\pi$
$14$	−2.47419	−	4.28542i	−0.661255	−	1.14533i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.71933	+	4.71002i	0.659535	+	1.14235i	0.980736	+	0.195337i	$0.0625799\pi$
$17$	2.71933	+	4.71002i	0.659535	+	1.14235i	−0.321202	+	0.947011i	$0.604087\pi$
$18$		0			0
$19$	0.179633	−	0.311133i	0.0412105	−	0.0713788i	−0.844684	−	0.535265i	$-0.820212\pi$
$19$	0.179633	−	0.311133i	0.0412105	−	0.0713788i	0.885895	+	0.463886i	$0.153545\pi$
$20$	4.07867			0.912019
$21$		0			0
$22$	1.34686	−	2.33282i	0.287151	−	0.497360i
$23$	−0.147957	−	0.256269i	−0.0308511	−	0.0534357i	0.850188	−	0.526480i	$-0.176488\pi$
$23$	−0.147957	−	0.256269i	−0.0308511	−	0.0534357i	−0.881039	+	0.473044i	$0.843155\pi$
$24$		0			0
$25$	11.6356			2.32711
$26$	−2.87378			−0.563594
$27$		0			0
$28$	−2.47419	−	4.28542i	−0.467578	−	0.809868i
$29$	1.72918	−	2.99502i	0.321100	−	0.556161i	−0.659615	−	0.751603i	$-0.729281\pi$
$29$	1.72918	−	2.99502i	0.321100	−	0.556161i	0.980715	+	0.195442i	$0.0626141\pi$
$30$		0			0
$31$	0.980010	+	1.69743i	0.176015	+	0.304867i	0.940512	−	0.339760i	$-0.110346\pi$
$31$	0.980010	+	1.69743i	0.176015	+	0.304867i	−0.764497	+	0.644627i	$0.777013\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.71933	+	4.71002i	0.466361	+	0.807762i
$35$	−10.0914	−	17.4788i	−1.70576	−	2.95446i
$36$		0			0
$37$	−6.08268	−	0.0307620i	−0.999987	−	0.00505725i
$37$	−6.08268	−	0.0307620i	−0.999987	−	0.00505725i
$38$	0.179633	−	0.311133i	0.0291403	−	0.0504724i
$39$		0			0
$40$	4.07867			0.644895
$41$	−2.46495			−0.384960			−0.192480	−	0.981301i	$-0.561653\pi$
$41$	−2.46495			−0.384960			−0.192480	+	0.981301i	$0.561653\pi$
$42$		0			0
$43$	3.92593	−	6.79991i	0.598699	−	1.03698i	−0.394314	−	0.918976i	$-0.629018\pi$
$43$	3.92593	−	6.79991i	0.598699	−	1.03698i	0.993013	−	0.118001i	$-0.0376487\pi$
$44$	1.34686	−	2.33282i	0.203046	−	0.351687i
$45$		0			0
$46$	−0.147957	−	0.256269i	−0.0218150	−	0.0377848i
$47$	3.83844	−	6.64837i	0.559893	−	0.969764i	−0.437611	−	0.899164i	$-0.644175\pi$
$47$	3.83844	−	6.64837i	0.559893	−	0.969764i	0.997505	−	0.0705996i	$-0.0224913\pi$
$48$		0			0
$49$	−8.74321	+	15.1437i	−1.24903	+	2.16338i
$50$	11.6356			1.64552
$51$		0			0
$52$	−2.87378			−0.398521
$53$	−2.45992	−	4.26070i	−0.337896	−	0.585252i	0.646141	−	0.763218i	$-0.276382\pi$
$53$	−2.45992	−	4.26070i	−0.337896	−	0.585252i	−0.984037	+	0.177966i	$0.943048\pi$
$54$		0			0
$55$	5.49339	−	9.51483i	0.740728	−	1.28298i
$56$	−2.47419	−	4.28542i	−0.330627	−	0.572663i
$57$		0			0
$58$	1.72918	−	2.99502i	0.227052	−	0.393265i
$59$	3.27974	−	5.68067i	0.426985	−	0.739560i	−0.569618	−	0.821909i	$-0.692909\pi$
$59$	3.27974	−	5.68067i	0.426985	−	0.739560i	0.996604	+	0.0823492i	$0.0262423\pi$
$60$		0			0
$61$	−2.07388	−	3.59207i	−0.265534	−	0.459918i	0.702170	−	0.712010i	$-0.252215\pi$
$61$	−2.07388	−	3.59207i	−0.265534	−	0.459918i	−0.967703	+	0.252092i	$0.918881\pi$
$62$	0.980010	+	1.69743i	0.124461	+	0.215574i
$63$		0			0
$64$	1.00000			0.125000
$65$	−11.7212			−1.45384
$66$		0			0
$67$	−0.566061			−0.0691553			−0.0345777	−	0.999402i	$-0.511009\pi$
$67$	−0.566061			−0.0691553			−0.0345777	+	0.999402i	$0.511009\pi$
$68$	2.71933	+	4.71002i	0.329767	+	0.571174i
$69$		0			0
$70$	−10.0914	−	17.4788i	−1.20615	−	2.08912i
$71$	−5.34228	+	9.25310i	−0.634012	+	1.09814i	0.352712	+	0.935732i	$0.385260\pi$
$71$	−5.34228	+	9.25310i	−0.634012	+	1.09814i	−0.986724	+	0.162409i	$0.948074\pi$
$72$		0			0
$73$	8.59878			1.00641			0.503206	−	0.864167i	$-0.332154\pi$
$73$	8.59878			1.00641			0.503206	+	0.864167i	$0.332154\pi$
$74$	−6.08268	−	0.0307620i	−0.707098	−	0.00357601i
$75$		0			0
$76$	0.179633	−	0.311133i	0.0206053	−	0.0356894i
$77$	−13.3295			−1.51904
$78$		0			0
$79$	7.09273	+	12.2850i	0.797995	+	1.38217i	0.920920	+	0.389751i	$0.127439\pi$
$79$	7.09273	+	12.2850i	0.797995	+	1.38217i	−0.122925	+	0.992416i	$0.539228\pi$
$80$	4.07867			0.456009
$81$		0			0
$82$	−2.46495			−0.272208
$83$	−12.4880			−1.37074			−0.685368	−	0.728197i	$-0.740359\pi$
$83$	−12.4880			−1.37074			−0.685368	+	0.728197i	$0.740359\pi$
$84$		0			0
$85$	11.0913	+	19.2106i	1.20302	+	2.08368i
$86$	3.92593	−	6.79991i	0.423344	−	0.733253i
$87$		0			0
$88$	1.34686	−	2.33282i	0.143575	−	0.248680i
$89$	9.19327	+	15.9232i	0.974485	+	1.68786i	0.681626	+	0.731701i	$0.261273\pi$
$89$	9.19327	+	15.9232i	0.974485	+	1.68786i	0.292859	+	0.956156i	$0.405393\pi$
$90$		0			0
$91$	7.11027	+	12.3153i	0.745358	+	1.29100i
$92$	−0.147957	−	0.256269i	−0.0154256	−	0.0267179i
$93$		0			0
$94$	3.83844	−	6.64837i	0.395904	−	0.685727i
$95$	0.732663	−	1.26901i	0.0751696	−	0.130198i
$96$		0			0
$97$	0.696052	−	1.20560i	0.0706734	−	0.122410i	−0.828523	−	0.559955i	$-0.810819\pi$
$97$	0.696052	−	1.20560i	0.0706734	−	0.122410i	0.899197	+	0.437545i	$0.144152\pi$
$98$	−8.74321	+	15.1437i	−0.883198	+	1.52974i
$99$		0			0
$100$	11.6356			1.16356
$101$	−1.38693	+	2.40224i	−0.138005	+	0.239032i	−0.926741	−	0.375700i	$-0.877402\pi$
$101$	−1.38693	+	2.40224i	−0.138005	+	0.239032i	0.788736	+	0.614732i	$0.210736\pi$
$102$		0			0
$103$	−0.774343	−	1.34120i	−0.0762983	−	0.132152i	0.825352	−	0.564619i	$-0.190977\pi$
$103$	−0.774343	−	1.34120i	−0.0762983	−	0.132152i	−0.901650	+	0.432466i	$0.857643\pi$
$104$	−2.87378			−0.281797
$105$		0			0
$106$	−2.45992	−	4.26070i	−0.238928	−	0.413836i
$107$	5.19514	−	8.99825i	0.502234	−	0.869894i	−0.497763	−	0.867313i	$-0.665845\pi$
$107$	5.19514	−	8.99825i	0.502234	−	0.869894i	0.999997	−	0.00258098i	$-0.000821551\pi$
$108$		0			0
$109$	−9.23262	−	15.9914i	−0.884325	−	1.53170i	−0.846485	−	0.532412i	$-0.821286\pi$
$109$	−9.23262	−	15.9914i	−0.884325	−	1.53170i	−0.0378394	−	0.999284i	$-0.512048\pi$
$110$	5.49339	−	9.51483i	0.523774	−	0.907203i
$111$		0			0
$112$	−2.47419	−	4.28542i	−0.233789	−	0.404934i
$113$	−7.99901	+	13.8547i	−0.752483	+	1.30334i	0.194132	+	0.980975i	$0.437811\pi$
$113$	−7.99901	+	13.8547i	−0.752483	+	1.30334i	−0.946616	+	0.322364i	$0.895522\pi$
$114$		0			0
$115$	−0.603468	−	1.04524i	−0.0562736	−	0.0974688i
$116$	1.72918	−	2.99502i	0.160550	−	0.278081i
$117$		0			0
$118$	3.27974	−	5.68067i	0.301924	−	0.522948i
$119$	13.4563	−	23.3069i	1.23353	−	2.13654i
$120$		0			0
$121$	1.87195	+	3.24232i	0.170177	+	0.294756i
$122$	−2.07388	−	3.59207i	−0.187761	−	0.325211i
$123$		0			0
$124$	0.980010	+	1.69743i	0.0880075	+	0.152434i
$125$	27.0643			2.42071
$126$		0			0
$127$	7.60717	+	13.1760i	0.675027	+	1.16918i	0.976461	+	0.215694i	$0.0692014\pi$
$127$	7.60717	+	13.1760i	0.675027	+	1.16918i	−0.301434	+	0.953487i	$0.597465\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−11.7212			−1.02802
$131$	0.447688	−	0.775418i	0.0391146	−	0.0677486i	−0.845805	−	0.533492i	$-0.820880\pi$
$131$	0.447688	−	0.775418i	0.0391146	−	0.0677486i	0.884920	+	0.465743i	$0.154213\pi$
$132$		0			0
$133$	−1.77778			−0.154153
$134$	−0.566061			−0.0489002
$135$		0			0
$136$	2.71933	+	4.71002i	0.233181	+	0.403881i
$137$	−3.53417	+	6.12135i	−0.301944	+	0.522983i	−0.976576	−	0.215172i	$-0.930969\pi$
$137$	−3.53417	+	6.12135i	−0.301944	+	0.522983i	0.674632	+	0.738154i	$0.264302\pi$
$138$		0			0
$139$	−3.83262	+	6.63828i	−0.325078	+	0.563052i	−0.981528	−	0.191318i	$-0.938724\pi$
$139$	−3.83262	+	6.63828i	−0.325078	+	0.563052i	0.656450	+	0.754370i	$0.272057\pi$
$140$	−10.0914	−	17.4788i	−0.852879	−	1.47723i
$141$		0			0
$142$	−5.34228	+	9.25310i	−0.448314	+	0.776503i
$143$	−3.87057	+	6.70402i	−0.323673	+	0.560618i
$144$		0			0
$145$	7.05274	−	12.2157i	0.585698	−	1.01446i
$146$	8.59878			0.711640
$147$		0			0
$148$	−6.08268	−	0.0307620i	−0.499994	−	0.00252862i
$149$	1.76498	+	3.05704i	0.144593	+	0.250442i	0.929221	−	0.369525i	$-0.120479\pi$
$149$	1.76498	+	3.05704i	0.144593	+	0.250442i	−0.784628	+	0.619967i	$0.787146\pi$
$150$		0			0
$151$	−1.13793	−	1.97095i	−0.0926032	−	0.160393i	0.816003	−	0.578048i	$-0.196185\pi$
$151$	−1.13793	−	1.97095i	−0.0926032	−	0.160393i	−0.908606	+	0.417655i	$0.862852\pi$
$152$	0.179633	−	0.311133i	0.0145701	−	0.0252362i
$153$		0			0
$154$	−13.3295			−1.07412
$155$	3.99714	+	6.92325i	0.321058	+	0.556089i
$156$		0			0
$157$	5.17802	−	8.96859i	0.413251	−	0.715772i	−0.581992	−	0.813194i	$-0.697727\pi$
$157$	5.17802	−	8.96859i	0.413251	−	0.715772i	0.995243	+	0.0974227i	$0.0310599\pi$
$158$	7.09273	+	12.2850i	0.564267	+	0.977340i
$159$		0			0
$160$	4.07867			0.322447
$161$	−0.732146	+	1.26811i	−0.0577012	+	0.0999414i
$162$		0			0
$163$	0.937663	+	1.62408i	0.0734434	+	0.127208i	0.900408	−	0.435046i	$-0.143268\pi$
$163$	0.937663	+	1.62408i	0.0734434	+	0.127208i	−0.826965	+	0.562254i	$0.809935\pi$
$164$	−2.46495			−0.192480
$165$		0			0
$166$	−12.4880			−0.969257
$167$	20.0417			1.55088			0.775438	−	0.631424i	$-0.217529\pi$
$167$	20.0417			1.55088			0.775438	+	0.631424i	$0.217529\pi$
$168$		0			0
$169$	−4.74140			−0.364723
$170$	11.0913	+	19.2106i	0.850661	+	1.47339i
$171$		0			0
$172$	3.92593	−	6.79991i	0.299349	−	0.518488i
$173$	13.9219			1.05846			0.529231	−	0.848478i	$-0.322481\pi$
$173$	13.9219			1.05846			0.529231	+	0.848478i	$0.322481\pi$
$174$		0			0
$175$	−28.7886	−	49.8633i	−2.17621	−	3.76931i
$176$	1.34686	−	2.33282i	0.101523	−	0.175843i
$177$		0			0
$178$	9.19327	+	15.9232i	0.689065	+	1.19349i
$179$	−24.6042			−1.83900			−0.919502	−	0.393086i	$-0.871407\pi$
$179$	−24.6042			−1.83900			−0.919502	+	0.393086i	$0.871407\pi$
$180$		0			0
$181$	0.918274	−	1.59050i	0.0682547	−	0.118221i	−0.829878	−	0.557944i	$-0.811590\pi$
$181$	0.918274	−	1.59050i	0.0682547	−	0.118221i	0.898133	+	0.439724i	$0.144924\pi$
$182$	7.11027	+	12.3153i	0.527048	+	0.912874i
$183$		0			0
$184$	−0.147957	−	0.256269i	−0.0109075	−	0.0188924i
$185$	−24.8093	−	0.125468i	−1.82401	−	0.00922461i
$186$		0			0
$187$	14.6502			1.07133
$188$	3.83844	−	6.64837i	0.279947	−	0.484882i
$189$		0			0
$190$	0.732663	−	1.26901i	0.0531529	−	0.0920636i
$191$	−8.45520	+	14.6448i	−0.611797	+	1.05966i	0.379140	+	0.925339i	$0.376220\pi$
$191$	−8.45520	+	14.6448i	−0.611797	+	1.05966i	−0.990937	+	0.134324i	$0.957114\pi$
$192$		0			0
$193$	10.3364	+	17.9031i	0.744029	+	1.28870i	0.950647	+	0.310274i	$0.100421\pi$
$193$	10.3364	+	17.9031i	0.744029	+	1.28870i	−0.206618	+	0.978422i	$0.566246\pi$
$194$	0.696052	−	1.20560i	0.0499736	−	0.0865569i
$195$		0			0
$196$	−8.74321	+	15.1437i	−0.624515	+	1.08169i
$197$	7.80217	+	13.5138i	0.555882	+	0.962816i	0.997834	+	0.0657773i	$0.0209527\pi$
$197$	7.80217	+	13.5138i	0.555882	+	0.962816i	−0.441952	+	0.897039i	$0.645714\pi$
$198$		0			0
$199$	−10.2576			−0.727144			−0.363572	−	0.931566i	$-0.618443\pi$
$199$	−10.2576			−0.727144			−0.363572	+	0.931566i	$0.618443\pi$
$200$	11.6356			0.822759
$201$		0			0
$202$	−1.38693	+	2.40224i	−0.0975843	+	0.169021i
$203$	−17.1132			−1.20111
$204$		0			0
$205$	−10.0537			−0.702182
$206$	−0.774343	−	1.34120i	−0.0539510	−	0.0934459i
$207$		0			0
$208$	−2.87378			−0.199261
$209$	−0.483879	−	0.838103i	−0.0334706	−	0.0579728i
$210$		0			0
$211$	10.6091	+	18.3755i	0.730359	+	1.26502i	0.956730	+	0.290978i	$0.0939805\pi$
$211$	10.6091	+	18.3755i	0.730359	+	1.26502i	−0.226371	+	0.974041i	$0.572686\pi$
$212$	−2.45992	−	4.26070i	−0.168948	−	0.292626i
$213$		0			0
$214$	5.19514	−	8.99825i	0.355133	−	0.615108i
$215$	16.0126	−	27.7346i	1.09205	−	1.89149i
$216$		0			0
$217$	4.84946	−	8.39951i	0.329203	−	0.570196i
$218$	−9.23262	−	15.9914i	−0.625312	−	1.08307i
$219$		0			0
$220$	5.49339	−	9.51483i	0.370364	−	0.641490i
$221$	−7.81475	−	13.5355i	−0.525677	−	0.910499i
$222$		0			0
$223$	−8.98920	+	15.5698i	−0.601962	+	1.04263i	0.390562	+	0.920577i	$0.372281\pi$
$223$	−8.98920	+	15.5698i	−0.601962	+	1.04263i	−0.992524	+	0.122052i	$0.961053\pi$
$224$	−2.47419	−	4.28542i	−0.165314	−	0.286332i
$225$		0			0
$226$	−7.99901	+	13.8547i	−0.532086	+	0.921600i
$227$	−3.04228	−	5.26939i	−0.201923	−	0.349742i	0.747225	−	0.664571i	$-0.231386\pi$
$227$	−3.04228	−	5.26939i	−0.201923	−	0.349742i	−0.949148	+	0.314830i	$0.898053\pi$
$228$		0			0
$229$	−14.9476			−0.987766			−0.493883	−	0.869528i	$-0.664423\pi$
$229$	−14.9476			−0.987766			−0.493883	+	0.869528i	$0.664423\pi$
$230$	−0.603468	−	1.04524i	−0.0397915	−	0.0689209i
$231$		0			0
$232$	1.72918	−	2.99502i	0.113526	−	0.196633i
$233$	13.7687			0.902021			0.451010	−	0.892519i	$-0.351064\pi$
$233$	13.7687			0.902021			0.451010	+	0.892519i	$0.351064\pi$
$234$		0			0
$235$	15.6557	−	27.1165i	1.02127	−	1.76889i
$236$	3.27974	−	5.68067i	0.213493	−	0.369780i
$237$		0			0
$238$	13.4563	−	23.3069i	0.872240	−	1.51076i
$239$	2.62191	−	4.54128i	0.169597	−	0.293751i	−0.768681	−	0.639632i	$-0.779087\pi$
$239$	2.62191	−	4.54128i	0.169597	−	0.293751i	0.938278	+	0.345881i	$0.112420\pi$
$240$		0			0
$241$	15.4037	+	26.6799i	0.992237	+	1.71861i	0.603817	+	0.797123i	$0.293646\pi$
$241$	15.4037	+	26.6799i	0.992237	+	1.71861i	0.388421	+	0.921482i	$0.373021\pi$
$242$	1.87195	+	3.24232i	0.120334	+	0.208424i
$243$		0			0
$244$	−2.07388	−	3.59207i	−0.132767	−	0.229959i
$245$	−35.6607	+	61.7662i	−2.27828	+	3.94609i
$246$		0			0
$247$	−0.516224	+	0.894126i	−0.0328466	+	0.0568919i
$248$	0.980010	+	1.69743i	0.0622307	+	0.107787i
$249$		0			0
$250$	27.0643			1.71170
$251$	15.4213			0.973381			0.486691	−	0.873574i	$-0.338204\pi$
$251$	15.4213			0.973381			0.486691	+	0.873574i	$0.338204\pi$
$252$		0			0
$253$	−0.797107			−0.0501137
$254$	7.60717	+	13.1760i	0.477316	+	0.826736i
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.96221	−	10.3268i	0.371912	−	0.644171i	−0.617947	−	0.786219i	$-0.712036\pi$
$257$	5.96221	−	10.3268i	0.371912	−	0.644171i	0.989860	+	0.142048i	$0.0453689\pi$
$258$		0			0
$259$	14.9179	+	26.1430i	0.926952	+	1.62444i
$260$	−11.7212			−0.726918
$261$		0			0
$262$	0.447688	−	0.775418i	0.0276582	−	0.0479055i
$263$	−15.4194	−	26.7072i	−0.950800	−	1.64683i	−0.743699	−	0.668514i	$-0.766931\pi$
$263$	−15.4194	−	26.7072i	−0.950800	−	1.64683i	−0.207101	−	0.978320i	$-0.566403\pi$
$264$		0			0
$265$	−10.0332	−	17.3780i	−0.616335	−	1.06752i
$266$	−1.77778			−0.109003
$267$		0			0
$268$	−0.566061			−0.0345777
$269$	−18.7661			−1.14419			−0.572093	−	0.820189i	$-0.693868\pi$
$269$	−18.7661			−1.14419			−0.572093	+	0.820189i	$0.693868\pi$
$270$		0			0
$271$	−1.55135	−	2.68702i	−0.0942379	−	0.163225i	0.815052	−	0.579387i	$-0.196708\pi$
$271$	−1.55135	−	2.68702i	−0.0942379	−	0.163225i	−0.909290	+	0.416162i	$0.863375\pi$
$272$	2.71933	+	4.71002i	0.164884	+	0.285587i
$273$		0			0
$274$	−3.53417	+	6.12135i	−0.213507	+	0.369805i
$275$	15.6715	−	27.1438i	0.945024	−	1.63683i
$276$		0			0
$277$	2.57324	+	4.45699i	0.154611	+	0.267795i	0.932917	−	0.360090i	$-0.117254\pi$
$277$	2.57324	+	4.45699i	0.154611	+	0.267795i	−0.778306	+	0.627885i	$0.783921\pi$
$278$	−3.83262	+	6.63828i	−0.229865	+	0.398138i
$279$		0			0
$280$	−10.0914	−	17.4788i	−0.603077	−	1.04456i
$281$	−8.01445			−0.478102			−0.239051	−	0.971007i	$-0.576836\pi$
$281$	−8.01445			−0.478102			−0.239051	+	0.971007i	$0.576836\pi$
$282$		0			0
$283$	−6.09395			−0.362248			−0.181124	−	0.983460i	$-0.557974\pi$
$283$	−6.09395			−0.362248			−0.181124	+	0.983460i	$0.557974\pi$
$284$	−5.34228	+	9.25310i	−0.317006	+	0.549070i
$285$		0			0
$286$	−3.87057	+	6.70402i	−0.228871	+	0.396417i
$287$	6.09875	+	10.5633i	0.359998	+	0.623534i
$288$		0			0
$289$	−6.28952	+	10.8938i	−0.369972	+	0.640810i
$290$	7.05274	−	12.2157i	0.414151	−	0.717331i
$291$		0			0
$292$	8.59878			0.503206
$293$	5.16113			0.301516			0.150758	−	0.988571i	$-0.451829\pi$
$293$	5.16113			0.301516			0.150758	+	0.988571i	$0.451829\pi$
$294$		0			0
$295$	13.3770	−	23.1696i	0.778837	−	1.34899i
$296$	−6.08268	−	0.0307620i	−0.353549	−	0.00178801i
$297$		0			0
$298$	1.76498	+	3.05704i	0.102243	+	0.177089i
$299$	0.425195	+	0.736460i	0.0245897	+	0.0425906i
$300$		0			0
$301$	−38.8540			−2.23951
$302$	−1.13793	−	1.97095i	−0.0654803	−	0.113415i
$303$		0			0
$304$	0.179633	−	0.311133i	0.0103026	−	0.0178447i
$305$	−8.45869	−	14.6509i	−0.484343	−	0.838907i
$306$		0			0
$307$	29.9546			1.70960			0.854799	−	0.518959i	$-0.173680\pi$
$307$	29.9546			1.70960			0.854799	+	0.518959i	$0.173680\pi$
$308$	−13.3295			−0.759519
$309$		0			0
$310$	3.99714	+	6.92325i	0.227022	+	0.393214i
$311$	3.66058	−	6.34032i	0.207573	−	0.359526i	−0.743377	−	0.668873i	$-0.766777\pi$
$311$	3.66058	−	6.34032i	0.207573	−	0.359526i	0.950949	+	0.309347i	$0.100110\pi$
$312$		0			0
$313$	−17.7450			−1.00301			−0.501504	−	0.865155i	$-0.667220\pi$
$313$	−17.7450			−1.00301			−0.501504	+	0.865155i	$0.667220\pi$
$314$	5.17802	−	8.96859i	0.292213	−	0.506127i
$315$		0			0
$316$	7.09273	+	12.2850i	0.398997	+	0.691084i
$317$	6.45120			0.362336			0.181168	−	0.983452i	$-0.442012\pi$
$317$	6.45120			0.362336			0.181168	+	0.983452i	$0.442012\pi$
$318$		0			0
$319$	−4.65791	−	8.06773i	−0.260793	−	0.451706i
$320$	4.07867			0.228005
$321$		0			0
$322$	−0.732146	+	1.26811i	−0.0408009	+	0.0706693i
$323$	1.95392			0.108719
$324$		0			0
$325$	−33.4380			−1.85481
$326$	0.937663	+	1.62408i	0.0519323	+	0.0899494i
$327$		0			0
$328$	−2.46495			−0.136104
$329$	−37.9880			−2.09435
$330$		0			0
$331$	−6.10487			−0.335554			−0.167777	−	0.985825i	$-0.553659\pi$
$331$	−6.10487			−0.335554			−0.167777	+	0.985825i	$0.553659\pi$
$332$	−12.4880			−0.685368
$333$		0			0
$334$	20.0417			1.09664
$335$	−2.30878			−0.126142
$336$		0			0
$337$	−26.4706			−1.44195			−0.720973	−	0.692963i	$-0.756305\pi$
$337$	−26.4706			−1.44195			−0.720973	+	0.692963i	$0.756305\pi$
$338$	−4.74140			−0.257898
$339$		0			0
$340$	11.0913	+	19.2106i	0.601508	+	1.04184i
$341$	5.27974			0.285914
$342$		0			0
$343$	51.8908			2.80184
$344$	3.92593	−	6.79991i	0.211672	−	0.366627i
$345$		0			0
$346$	13.9219			0.748446
$347$	−1.05120	−	1.82073i	−0.0564313	−	0.0977419i	0.836430	−	0.548074i	$-0.184639\pi$
$347$	−1.05120	−	1.82073i	−0.0564313	−	0.0977419i	−0.892861	+	0.450332i	$0.851306\pi$
$348$		0			0
$349$	14.9569			0.800624			0.400312	−	0.916379i	$-0.368902\pi$
$349$	14.9569			0.800624			0.400312	+	0.916379i	$0.368902\pi$
$350$	−28.7886	−	49.8633i	−1.53882	−	2.66531i
$351$		0			0
$352$	1.34686	−	2.33282i	0.0717877	−	0.124340i
$353$	−20.2998			−1.08045			−0.540225	−	0.841521i	$-0.681661\pi$
$353$	−20.2998			−1.08045			−0.540225	+	0.841521i	$0.681661\pi$
$354$		0			0
$355$	−21.7894	+	37.7404i	−1.15646	+	2.00305i
$356$	9.19327	+	15.9232i	0.487242	+	0.843928i
$357$		0			0
$358$	−24.6042			−1.30037
$359$	−0.967788			−0.0510779			−0.0255390	−	0.999674i	$-0.508130\pi$
$359$	−0.967788			−0.0510779			−0.0255390	+	0.999674i	$0.508130\pi$
$360$		0			0
$361$	9.43546	+	16.3427i	0.496603	+	0.860142i
$362$	0.918274	−	1.59050i	0.0482634	−	0.0835947i
$363$		0			0
$364$	7.11027	+	12.3153i	0.372679	+	0.645499i
$365$	35.0716			1.83573
$366$		0			0
$367$	2.44838	+	4.24073i	0.127805	+	0.221364i	0.922826	−	0.385218i	$-0.125874\pi$
$367$	2.44838	+	4.24073i	0.127805	+	0.221364i	−0.795021	+	0.606582i	$0.792540\pi$
$368$	−0.147957	−	0.256269i	−0.00771278	−	0.0133589i
$369$		0			0
$370$	−24.8093	−	0.125468i	−1.28977	−	0.00652278i
$371$	−12.1726	+	21.0836i	−0.631970	+	1.09460i
$372$		0			0
$373$	19.6595			1.01793			0.508965	−	0.860787i	$-0.330028\pi$
$373$	19.6595			1.01793			0.508965	+	0.860787i	$0.330028\pi$
$374$	14.6502			0.757544
$375$		0			0
$376$	3.83844	−	6.64837i	0.197952	−	0.342863i
$377$	−4.96927	+	8.60702i	−0.255930	+	0.443284i
$378$		0			0
$379$	5.06580	+	8.77422i	0.260213	+	0.450701i	0.966298	−	0.257425i	$-0.0828740\pi$
$379$	5.06580	+	8.77422i	0.260213	+	0.450701i	−0.706086	+	0.708126i	$0.749541\pi$
$380$	0.732663	−	1.26901i	0.0375848	−	0.0650988i
$381$		0			0
$382$	−8.45520	+	14.6448i	−0.432606	+	0.749295i
$383$	4.43692			0.226716			0.113358	−	0.993554i	$-0.463839\pi$
$383$	4.43692			0.226716			0.113358	+	0.993554i	$0.463839\pi$
$384$		0			0
$385$	−54.3667			−2.77078
$386$	10.3364	+	17.9031i	0.526108	+	0.911246i
$387$		0			0
$388$	0.696052	−	1.20560i	0.0353367	−	0.0612050i
$389$	0.450298	+	0.779939i	0.0228310	+	0.0395445i	0.877215	−	0.480097i	$-0.159399\pi$
$389$	0.450298	+	0.779939i	0.0228310	+	0.0395445i	−0.854384	+	0.519642i	$0.826065\pi$
$390$		0			0
$391$	0.804687	−	1.39376i	0.0406948	−	0.0704854i
$392$	−8.74321	+	15.1437i	−0.441599	+	0.764872i
$393$		0			0
$394$	7.80217	+	13.5138i	0.393068	+	0.680814i
$395$	28.9289	+	50.1064i	1.45557	+	2.52113i
$396$		0			0
$397$	−10.9614			−0.550138			−0.275069	−	0.961424i	$-0.588701\pi$
$397$	−10.9614			−0.550138			−0.275069	+	0.961424i	$0.588701\pi$
$398$	−10.2576			−0.514169
$399$		0			0
$400$	11.6356			0.581779
$401$	8.41549	+	14.5761i	0.420250	+	0.727894i	0.995964	−	0.0897573i	$-0.0286091\pi$
$401$	8.41549	+	14.5761i	0.420250	+	0.727894i	−0.575714	+	0.817651i	$0.695276\pi$
$402$		0			0
$403$	−2.81633	−	4.87803i	−0.140291	−	0.242992i
$404$	−1.38693	+	2.40224i	−0.0690025	+	0.119516i
$405$		0			0
$406$	−17.1132			−0.849315
$407$	−8.26427	+	14.1484i	−0.409645	+	0.701310i
$408$		0			0
$409$	2.97026	−	5.14465i	0.146870	−	0.254387i	−0.783199	−	0.621771i	$-0.786413\pi$
$409$	2.97026	−	5.14465i	0.146870	−	0.254387i	0.930069	+	0.367385i	$0.119747\pi$
$410$	−10.0537			−0.496518
$411$		0			0
$412$	−0.774343	−	1.34120i	−0.0381491	−	0.0660762i
$413$	−32.4587			−1.59719
$414$		0			0
$415$	−50.9345			−2.50027
$416$	−2.87378			−0.140899
$417$		0			0
$418$	−0.483879	−	0.838103i	−0.0236673	−	0.0409929i
$419$	−12.0195	+	20.8184i	−0.587191	+	1.01704i	0.407408	+	0.913246i	$0.366433\pi$
$419$	−12.0195	+	20.8184i	−0.587191	+	1.01704i	−0.994598	+	0.103798i	$0.966901\pi$
$420$		0			0
$421$	−4.13010	+	7.15355i	−0.201289	+	0.348642i	−0.948944	−	0.315445i	$-0.897846\pi$
$421$	−4.13010	+	7.15355i	−0.201289	+	0.348642i	0.747655	+	0.664087i	$0.231180\pi$
$422$	10.6091	+	18.3755i	0.516442	+	0.894503i
$423$		0			0
$424$	−2.45992	−	4.26070i	−0.119464	−	0.206918i
$425$	31.6410	+	54.8038i	1.53481	+	2.65837i
$426$		0			0
$427$	−10.2624	+	17.7749i	−0.496630	+	0.860189i
$428$	5.19514	−	8.99825i	0.251117	−	0.434947i
$429$		0			0
$430$	16.0126	−	27.7346i	0.772196	−	1.33748i
$431$	−0.940710	+	1.62936i	−0.0453124	+	0.0784834i	−0.887792	−	0.460245i	$-0.847762\pi$
$431$	−0.940710	+	1.62936i	−0.0453124	+	0.0784834i	0.842480	+	0.538728i	$0.181095\pi$
$432$		0			0
$433$	−4.97802			−0.239229			−0.119614	−	0.992820i	$-0.538166\pi$
$433$	−4.97802			−0.239229			−0.119614	+	0.992820i	$0.538166\pi$
$434$	4.84946	−	8.39951i	0.232782	−	0.403189i
$435$		0			0
$436$	−9.23262	−	15.9914i	−0.442162	−	0.765848i
$437$	−0.106312			−0.00508557
$438$		0			0
$439$	3.99894	+	6.92636i	0.190859	+	0.330577i	0.945535	−	0.325520i	$-0.105539\pi$
$439$	3.99894	+	6.92636i	0.190859	+	0.330577i	−0.754676	+	0.656097i	$0.772206\pi$
$440$	5.49339	−	9.51483i	0.261887	−	0.453602i
$441$		0			0
$442$	−7.81475	−	13.5355i	−0.371710	−	0.643820i
$443$	−10.2402	+	17.7365i	−0.486525	+	0.842685i	−0.999880	−	0.0154907i	$-0.995069\pi$
$443$	−10.2402	+	17.7365i	−0.486525	+	0.842685i	0.513355	+	0.858176i	$0.328402\pi$
$444$		0			0
$445$	37.4963	+	64.9456i	1.77750	+	3.07871i
$446$	−8.98920	+	15.5698i	−0.425651	+	0.737249i
$447$		0			0
$448$	−2.47419	−	4.28542i	−0.116894	−	0.202467i
$449$	16.2173	−	28.0891i	0.765340	−	1.32561i	−0.174726	−	0.984617i	$-0.555904\pi$
$449$	16.2173	−	28.0891i	0.765340	−	1.32561i	0.940066	−	0.340991i	$-0.110763\pi$
$450$		0			0
$451$	−3.31993	+	5.75029i	−0.156330	+	0.270771i
$452$	−7.99901	+	13.8547i	−0.376242	+	0.651670i
$453$		0			0
$454$	−3.04228	−	5.26939i	−0.142781	−	0.247305i
$455$	29.0004	+	50.2303i	1.35956	+	2.35483i
$456$		0			0
$457$	12.4242	+	21.5194i	0.581180	+	1.00663i	0.995340	+	0.0964294i	$0.0307422\pi$
$457$	12.4242	+	21.5194i	0.581180	+	1.00663i	−0.414160	+	0.910204i	$0.635924\pi$
$458$	−14.9476			−0.698456
$459$		0			0
$460$	−0.603468	−	1.04524i	−0.0281368	−	0.0487344i
$461$	−33.2803			−1.55002			−0.775010	−	0.631949i	$-0.782255\pi$
$461$	−33.2803			−1.55002			−0.775010	+	0.631949i	$0.782255\pi$
$462$		0			0
$463$	−30.2977			−1.40806			−0.704028	−	0.710172i	$-0.748617\pi$
$463$	−30.2977			−1.40806			−0.704028	+	0.710172i	$0.748617\pi$
$464$	1.72918	−	2.99502i	0.0802750	−	0.139040i
$465$		0			0
$466$	13.7687			0.637825
$467$	−0.866573			−0.0401002			−0.0200501	−	0.999799i	$-0.506383\pi$
$467$	−0.866573			−0.0401002			−0.0200501	+	0.999799i	$0.506383\pi$
$468$		0			0
$469$	1.40054	+	2.42581i	0.0646710	+	0.112013i
$470$	15.6557	−	27.1165i	0.722145	−	1.25079i
$471$		0			0
$472$	3.27974	−	5.68067i	0.150962	−	0.261474i
$473$	−10.5753	−	18.3170i	−0.486254	−	0.842217i
$474$		0			0
$475$	2.09013	−	3.62021i	0.0959017	−	0.166107i
$476$	13.4563	−	23.3069i	0.616767	−	1.06827i
$477$		0			0
$478$	2.62191	−	4.54128i	0.119923	−	0.207714i
$479$	12.2144			0.558089			0.279045	−	0.960278i	$-0.409982\pi$
$479$	12.2144			0.558089			0.279045	+	0.960278i	$0.409982\pi$
$480$		0			0
$481$	17.4803	+	0.0884032i	0.797032	+	0.00403084i
$482$	15.4037	+	26.6799i	0.701618	+	1.21524i
$483$		0			0
$484$	1.87195	+	3.24232i	0.0850887	+	0.147378i
$485$	2.83897	−	4.91724i	0.128911	−	0.223280i
$486$		0			0
$487$	−32.8770			−1.48980			−0.744899	−	0.667177i	$-0.767503\pi$
$487$	−32.8770			−1.48980			−0.744899	+	0.667177i	$0.767503\pi$
$488$	−2.07388	−	3.59207i	−0.0938803	−	0.162605i
$489$		0			0
$490$	−35.6607	+	61.7662i	−1.61099	+	2.79031i
$491$	1.47498	+	2.55474i	0.0665650	+	0.115294i	0.897387	−	0.441244i	$-0.145463\pi$
$491$	1.47498	+	2.55474i	0.0665650	+	0.115294i	−0.830822	+	0.556538i	$0.812129\pi$
$492$		0			0
$493$	18.8088			0.847106
$494$	−0.516224	+	0.894126i	−0.0232260	+	0.0402287i
$495$		0			0
$496$	0.980010	+	1.69743i	0.0440038	+	0.0762168i
$497$	52.8712			2.37160
$498$		0			0
$499$	−0.369989			−0.0165630			−0.00828150	−	0.999966i	$-0.502636\pi$
$499$	−0.369989			−0.0165630			−0.00828150	+	0.999966i	$0.502636\pi$
$500$	27.0643			1.21035
$501$		0			0
$502$	15.4213			0.688284
$503$	−10.7459	−	18.6124i	−0.479136	−	0.829888i	0.520578	−	0.853814i	$-0.325717\pi$
$503$	−10.7459	−	18.6124i	−0.479136	−	0.829888i	−0.999714	+	0.0239263i	$0.992383\pi$
$504$		0			0
$505$	−5.65685	+	9.79795i	−0.251726	+	0.436003i
$506$	−0.797107			−0.0354357
$507$		0			0
$508$	7.60717	+	13.1760i	0.337514	+	0.584591i
$509$	3.12995	−	5.42124i	0.138733	−	0.240292i	−0.788284	−	0.615311i	$-0.789030\pi$
$509$	3.12995	−	5.42124i	0.138733	−	0.240292i	0.927017	+	0.375019i	$0.122364\pi$
$510$		0			0
$511$	−21.2750	−	36.8494i	−0.941151	−	1.63012i
$512$	1.00000			0.0441942
$513$		0			0
$514$	5.96221	−	10.3268i	0.262982	−	0.455498i
$515$	−3.15829	−	5.47032i	−0.139171	−	0.241051i
$516$		0			0
$517$	−10.3396	−	17.9088i	−0.454737	−	0.787628i
$518$	14.9179	+	26.1430i	0.655454	+	1.14866i
$519$		0			0
$520$	−11.7212			−0.514009
$521$	7.69612	−	13.3301i	0.337173	−	0.584001i	−0.646727	−	0.762722i	$-0.723863\pi$
$521$	7.69612	−	13.3301i	0.337173	−	0.584001i	0.983900	+	0.178721i	$0.0571959\pi$
$522$		0			0
$523$	−14.3709	+	24.8912i	−0.628397	+	1.08842i	0.359477	+	0.933154i	$0.382955\pi$
$523$	−14.3709	+	24.8912i	−0.628397	+	1.08842i	−0.987873	+	0.155261i	$0.950378\pi$
$524$	0.447688	−	0.775418i	0.0195573	−	0.0338743i
$525$		0			0
$526$	−15.4194	−	26.7072i	−0.672317	−	1.16449i
$527$	−5.32994	+	9.23173i	−0.232176	+	0.402141i
$528$		0			0
$529$	11.4562	−	19.8428i	0.498096	−	0.862728i
$530$	−10.0332	−	17.3780i	−0.435814	−	0.754853i
$531$		0			0
$532$	−1.77778			−0.0770765
$533$	7.08372			0.306830
$534$		0			0
$535$	21.1893	−	36.7009i	0.916093	−	1.58672i
$536$	−0.566061			−0.0244501
$537$		0			0
$538$	−18.7661			−0.809062
$539$	23.5517	+	40.7928i	1.01444	+	1.75707i
$540$		0			0
$541$	−26.9707			−1.15956			−0.579781	−	0.814772i	$-0.696862\pi$
$541$	−26.9707			−1.15956			−0.579781	+	0.814772i	$0.696862\pi$
$542$	−1.55135	−	2.68702i	−0.0666362	−	0.115417i
$543$		0			0
$544$	2.71933	+	4.71002i	0.116590	+	0.201940i
$545$	−37.6568	−	65.2236i	−1.61304	−	2.79387i
$546$		0			0
$547$	4.30857	−	7.46266i	0.184221	−	0.319080i	−0.759093	−	0.650983i	$-0.774357\pi$
$547$	4.30857	−	7.46266i	0.184221	−	0.319080i	0.943314	+	0.331902i	$0.107690\pi$
$548$	−3.53417	+	6.12135i	−0.150972	+	0.261491i
$549$		0			0
$550$	15.6715	−	27.1438i	0.668233	−	1.15741i
$551$	−0.621233	−	1.07601i	−0.0264654	−	0.0458394i
$552$		0			0
$553$	35.0975	−	60.7907i	1.49250	−	2.58508i
$554$	2.57324	+	4.45699i	0.109327	+	0.189359i
$555$		0			0
$556$	−3.83262	+	6.63828i	−0.162539	+	0.281526i
$557$	−16.0140	−	27.7370i	−0.678533	−	1.17525i	−0.975423	−	0.220342i	$-0.929283\pi$
$557$	−16.0140	−	27.7370i	−0.678533	−	1.17525i	0.296890	−	0.954912i	$-0.404051\pi$
$558$		0			0
$559$	−11.2823	+	19.5414i	−0.477188	+	0.826515i
$560$	−10.0914	−	17.4788i	−0.426440	−	0.738615i
$561$		0			0
$562$	−8.01445			−0.338069
$563$	−1.61380	−	2.79518i	−0.0680134	−	0.117803i	0.830013	−	0.557744i	$-0.188333\pi$
$563$	−1.61380	−	2.79518i	−0.0680134	−	0.117803i	−0.898027	+	0.439941i	$0.854999\pi$
$564$		0			0
$565$	−32.6253	+	56.5087i	−1.37256	+	2.37734i
$566$	−6.09395			−0.256148
$567$		0			0
$568$	−5.34228	+	9.25310i	−0.224157	+	0.388251i
$569$	10.5932	−	18.3479i	0.444089	−	0.769185i	−0.553899	−	0.832584i	$-0.686861\pi$
$569$	10.5932	−	18.3479i	0.444089	−	0.769185i	0.997988	+	0.0633988i	$0.0201940\pi$
$570$		0			0
$571$	16.3465	−	28.3130i	0.684081	−	1.18486i	−0.289643	−	0.957135i	$-0.593537\pi$
$571$	16.3465	−	28.3130i	0.684081	−	1.18486i	0.973725	−	0.227729i	$-0.0731300\pi$
$572$	−3.87057	+	6.70402i	−0.161837	+	0.280309i
$573$		0			0
$574$	6.09875	+	10.5633i	0.254557	+	0.440905i
$575$	−1.72156	−	2.98183i	−0.0717941	−	0.124351i
$576$		0			0
$577$	−20.3587	−	35.2622i	−0.847542	−	1.46799i	−0.883395	−	0.468628i	$-0.844748\pi$
$577$	−20.3587	−	35.2622i	−0.847542	−	1.46799i	0.0358537	−	0.999357i	$-0.488585\pi$
$578$	−6.28952	+	10.8938i	−0.261609	+	0.453121i
$579$		0			0
$580$	7.05274	−	12.2157i	0.292849	−	0.507230i
$581$	30.8977	+	53.5163i	1.28185	+	2.22023i
$582$		0			0
$583$	−13.2526			−0.548868
$584$	8.59878			0.355820
$585$		0			0
$586$	5.16113			0.213204
$587$	−5.64417	−	9.77599i	−0.232960	−	0.403498i	0.725718	−	0.687992i	$-0.241508\pi$
$587$	−5.64417	−	9.77599i	−0.232960	−	0.403498i	−0.958678	+	0.284494i	$0.908174\pi$
$588$		0			0
$589$	0.704167			0.0290147
$590$	13.3770	−	23.1696i	0.550721	−	0.953877i
$591$		0			0
$592$	−6.08268	−	0.0307620i	−0.249997	−	0.00126431i
$593$	6.64250			0.272775			0.136387	−	0.990656i	$-0.456451\pi$
$593$	6.64250			0.272775			0.136387	+	0.990656i	$0.456451\pi$
$594$		0			0
$595$	54.8837	−	95.0614i	2.25001	−	3.89714i
$596$	1.76498	+	3.05704i	0.0722964	+	0.125221i
$597$		0			0
$598$	0.425195	+	0.736460i	0.0173875	+	0.0301161i
$599$	−33.4805			−1.36798			−0.683988	−	0.729493i	$-0.739756\pi$
$599$	−33.4805			−1.36798			−0.683988	+	0.729493i	$0.739756\pi$
$600$		0			0
$601$	15.8923			0.648262			0.324131	−	0.946012i	$-0.394928\pi$
$601$	15.8923			0.648262			0.324131	+	0.946012i	$0.394928\pi$
$602$	−38.8540			−1.58357
$603$		0			0
$604$	−1.13793	−	1.97095i	−0.0463016	−	0.0801967i
$605$	7.63508	+	13.2243i	0.310410	+	0.537646i
$606$		0			0
$607$	18.0329	−	31.2339i	0.731933	−	1.26774i	−0.224123	−	0.974561i	$-0.571952\pi$
$607$	18.0329	−	31.2339i	0.731933	−	1.26774i	0.956056	−	0.293184i	$-0.0947148\pi$
$608$	0.179633	−	0.311133i	0.00728506	−	0.0126181i
$609$		0			0
$610$	−8.45869	−	14.6509i	−0.342482	−	0.593197i
$611$	−11.0308	+	19.1059i	−0.446259	+	0.772943i
$612$		0			0
$613$	−10.5010	−	18.1882i	−0.424130	−	0.734615i	0.572208	−	0.820108i	$-0.306087\pi$
$613$	−10.5010	−	18.1882i	−0.424130	−	0.734615i	−0.996339	+	0.0854929i	$0.972754\pi$
$614$	29.9546			1.20887
$615$		0			0
$616$	−13.3295			−0.537061
$617$	17.0831	−	29.5887i	0.687738	−	1.19120i	−0.284830	−	0.958578i	$-0.591937\pi$
$617$	17.0831	−	29.5887i	0.687738	−	1.19120i	0.972568	−	0.232619i	$-0.0747294\pi$
$618$		0			0
$619$	−3.48390	+	6.03430i	−0.140030	+	0.242539i	−0.927508	−	0.373804i	$-0.878053\pi$
$619$	−3.48390	+	6.03430i	−0.140030	+	0.242539i	0.787478	+	0.616343i	$0.211387\pi$
$620$	3.99714	+	6.92325i	0.160529	+	0.278045i
$621$		0			0
$622$	3.66058	−	6.34032i	0.146776	−	0.254224i
$623$	45.4918	−	78.7940i	1.82259	−	3.15682i
$624$		0			0
$625$	52.2087			2.08835
$626$	−17.7450			−0.709234
$627$		0			0
$628$	5.17802	−	8.96859i	0.206625	−	0.357886i
$629$	−16.3959	−	28.7332i	−0.653749	−	1.14567i
$630$		0			0
$631$	21.2519	+	36.8094i	0.846025	+	1.46536i	0.884728	+	0.466108i	$0.154344\pi$
$631$	21.2519	+	36.8094i	0.846025	+	1.46536i	−0.0387024	+	0.999251i	$0.512322\pi$
$632$	7.09273	+	12.2850i	0.282134	+	0.488670i
$633$		0			0
$634$	6.45120			0.256210
$635$	31.0272	+	53.7406i	1.23127	+	2.13263i
$636$		0			0
$637$	25.1260	−	43.5196i	0.995530	−	1.72431i
$638$	−4.65791	−	8.06773i	−0.184408	−	0.319404i
$639$		0			0
$640$	4.07867			0.161224
$641$	24.0766			0.950967			0.475484	−	0.879725i	$-0.342273\pi$
$641$	24.0766			0.950967			0.475484	+	0.879725i	$0.342273\pi$
$642$		0			0
$643$	−18.6736	−	32.3437i	−0.736416	−	1.27551i	−0.954099	−	0.299491i	$-0.903183\pi$
$643$	−18.6736	−	32.3437i	−0.736416	−	1.27551i	0.217683	−	0.976019i	$-0.430150\pi$
$644$	−0.732146	+	1.26811i	−0.0288506	+	0.0499707i
$645$		0			0
$646$	1.95392			0.0768760
$647$	−8.21733	+	14.2328i	−0.323057	+	0.559551i	−0.981117	−	0.193415i	$-0.938044\pi$
$647$	−8.21733	+	14.2328i	−0.323057	+	0.559551i	0.658060	+	0.752965i	$0.271377\pi$
$648$		0			0
$649$	−8.83467	−	15.3021i	−0.346791	−	0.600660i
$650$	−33.4380			−1.31155
$651$		0			0
$652$	0.937663	+	1.62408i	0.0367217	+	0.0636039i
$653$	−1.27488			−0.0498898			−0.0249449	−	0.999689i	$-0.507941\pi$
$653$	−1.27488			−0.0498898			−0.0249449	+	0.999689i	$0.507941\pi$
$654$		0			0
$655$	1.82597	−	3.16268i	0.0713466	−	0.123576i
$656$	−2.46495			−0.0962401
$657$		0			0
$658$	−37.9880			−1.48093
$659$	7.98464	+	13.8298i	0.311037	+	0.538733i	0.978587	−	0.205833i	$-0.0659902\pi$
$659$	7.98464	+	13.8298i	0.311037	+	0.538733i	−0.667550	+	0.744565i	$0.732657\pi$
$660$		0			0
$661$	17.5395			0.682206			0.341103	−	0.940026i	$-0.389200\pi$
$661$	17.5395			0.682206			0.341103	+	0.940026i	$0.389200\pi$
$662$	−6.10487			−0.237272
$663$		0			0
$664$	−12.4880			−0.484628
$665$	−7.25098			−0.281181
$666$		0			0
$667$	−1.02337			−0.0396252
$668$	20.0417			0.775438
$669$		0			0
$670$	−2.30878			−0.0891958
$671$	−11.1729			−0.431325
$672$		0			0
$673$	3.29894	+	5.71394i	0.127165	+	0.220256i	0.922577	−	0.385813i	$-0.126079\pi$
$673$	3.29894	+	5.71394i	0.127165	+	0.220256i	−0.795412	+	0.606069i	$0.792746\pi$
$674$	−26.4706			−1.01961
$675$		0			0
$676$	−4.74140			−0.182362
$677$	−3.41586	+	5.91644i	−0.131282	+	0.227387i	−0.924171	−	0.381979i	$-0.875243\pi$
$677$	−3.41586	+	5.91644i	−0.131282	+	0.227387i	0.792889	+	0.609366i	$0.208576\pi$
$678$		0			0
$679$	−6.88866			−0.264362
$680$	11.0913	+	19.2106i	0.425330	+	0.736694i
$681$		0			0
$682$	5.27974			0.202172
$683$	−18.4475	−	31.9520i	−0.705873	−	1.22261i	−0.966376	−	0.257135i	$-0.917222\pi$
$683$	−18.4475	−	31.9520i	−0.705873	−	1.22261i	0.260502	−	0.965473i	$-0.416112\pi$
$684$		0			0
$685$	−14.4147	+	24.9670i	−0.550758	+	0.953940i
$686$	51.8908			1.98120
$687$		0			0
$688$	3.92593	−	6.79991i	0.149675	−	0.259244i
$689$	7.06926	+	12.2443i	0.269317	+	0.466471i
$690$		0			0
$691$	−46.7453			−1.77828			−0.889138	−	0.457639i	$-0.848695\pi$
$691$	−46.7453			−1.77828			−0.889138	+	0.457639i	$0.848695\pi$
$692$	13.9219			0.529231
$693$		0			0
$694$	−1.05120	−	1.82073i	−0.0399030	−	0.0691139i
$695$	−15.6320	+	27.0754i	−0.592955	+	1.02703i
$696$		0			0
$697$	−6.70301	−	11.6100i	−0.253895	−	0.439759i
$698$	14.9569			0.566127
$699$		0			0
$700$	−28.7886	−	49.8633i	−1.08811	−	1.88466i
$701$	−5.64416	−	9.77597i	−0.213177	−	0.369233i	0.739530	−	0.673123i	$-0.235048\pi$
$701$	−5.64416	−	9.77597i	−0.213177	−	0.369233i	−0.952707	+	0.303890i	$0.901714\pi$
$702$		0			0
$703$	−1.10222	+	1.88700i	−0.0415710	+	0.0711694i
$704$	1.34686	−	2.33282i	0.0507616	−	0.0879216i
$705$		0			0
$706$	−20.2998			−0.763993
$707$	13.7261			0.516224
$708$		0			0
$709$	5.62324	−	9.73975i	0.211185	−	0.365784i	−0.740900	−	0.671615i	$-0.765601\pi$
$709$	5.62324	−	9.73975i	0.211185	−	0.365784i	0.952086	+	0.305831i	$0.0989343\pi$
$710$	−21.7894	+	37.7404i	−0.817742	+	1.41637i
$711$		0			0
$712$	9.19327	+	15.9232i	0.344532	+	0.596747i
$713$	0.289999	−	0.502292i	0.0108605	−	0.0188110i
$714$		0			0
$715$	−15.7868	+	27.3435i	−0.590392	+	1.02259i
$716$	−24.6042			−0.919502
$717$		0			0
$718$	−0.967788			−0.0361175
$719$	7.44352	+	12.8926i	0.277597	+	0.480811i	0.970787	−	0.239943i	$-0.0771288\pi$
$719$	7.44352	+	12.8926i	0.277597	+	0.480811i	−0.693190	+	0.720755i	$0.743795\pi$
$720$		0			0
$721$	−3.83174	+	6.63677i	−0.142701	+	0.247166i
$722$	9.43546	+	16.3427i	0.351152	+	0.608212i
$723$		0			0
$724$	0.918274	−	1.59050i	0.0341274	−	0.0591103i
$725$	20.1200	−	34.8488i	0.747236	−	1.29425i
$726$		0			0
$727$	−12.7157	−	22.0243i	−0.471600	−	0.816835i	0.527872	−	0.849324i	$-0.322990\pi$
$727$	−12.7157	−	22.0243i	−0.471600	−	0.816835i	−0.999472	+	0.0324890i	$0.989657\pi$
$728$	7.11027	+	12.3153i	0.263524	+	0.456437i
$729$		0			0
$730$	35.0716			1.29806
$731$	42.7036			1.57945
$732$		0			0
$733$	18.6537			0.688990			0.344495	−	0.938788i	$-0.388050\pi$
$733$	18.6537			0.688990			0.344495	+	0.938788i	$0.388050\pi$
$734$	2.44838	+	4.24073i	0.0903715	+	0.156528i
$735$		0			0
$736$	−0.147957	−	0.256269i	−0.00545376	−	0.00944619i
$737$	−0.762403	+	1.32052i	−0.0280835	+	0.0486420i
$738$		0			0
$739$	5.66251			0.208299			0.104149	−	0.994562i	$-0.466788\pi$
$739$	5.66251			0.208299			0.104149	+	0.994562i	$0.466788\pi$
$740$	−24.8093	−	0.125468i	−0.912007	−	0.00461230i
$741$		0			0
$742$	−12.1726	+	21.0836i	−0.446870	+	0.774002i
$743$	−4.76308			−0.174740			−0.0873702	−	0.996176i	$-0.527846\pi$
$743$	−4.76308			−0.174740			−0.0873702	+	0.996176i	$0.527846\pi$
$744$		0			0
$745$	7.19878	+	12.4686i	0.263743	+	0.456816i
$746$	19.6595			0.719786
$747$		0			0
$748$	14.6502			0.535664
$749$	−51.4151			−1.87867
$750$		0			0
$751$	8.90826	+	15.4296i	0.325067	+	0.563033i	0.981526	−	0.191329i	$-0.0612797\pi$
$751$	8.90826	+	15.4296i	0.325067	+	0.563033i	−0.656459	+	0.754362i	$0.727946\pi$
$752$	3.83844	−	6.64837i	0.139973	−	0.242441i
$753$		0			0
$754$	−4.96927	+	8.60702i	−0.180970	+	0.313449i
$755$	−4.64123	−	8.03885i	−0.168912	−	0.292564i
$756$		0			0
$757$	1.08317	+	1.87611i	0.0393685	+	0.0681882i	0.885038	−	0.465518i	$-0.154132\pi$
$757$	1.08317	+	1.87611i	0.0393685	+	0.0681882i	−0.845670	+	0.533706i	$0.820799\pi$
$758$	5.06580	+	8.77422i	0.183998	+	0.318694i
$759$		0			0
$760$	0.732663	−	1.26901i	0.0265765	−	0.0460318i
$761$	−4.25013	+	7.36144i	−0.154067	+	0.266852i	−0.932719	−	0.360604i	$-0.882571\pi$
$761$	−4.25013	+	7.36144i	−0.154067	+	0.266852i	0.778652	+	0.627456i	$0.215904\pi$
$762$		0			0
$763$	−45.6865	+	79.1313i	−1.65396	+	2.86475i
$764$	−8.45520	+	14.6448i	−0.305899	+	0.529832i
$765$		0			0
$766$	4.43692			0.160312
$767$	−9.42523	+	16.3250i	−0.340325	+	0.589461i
$768$		0			0
$769$	−7.78195	−	13.4787i	−0.280624	−	0.486055i	0.690914	−	0.722937i	$-0.257208\pi$
$769$	−7.78195	−	13.4787i	−0.280624	−	0.486055i	−0.971539	+	0.236881i	$0.923875\pi$
$770$	−54.3667			−1.95924
$771$		0			0
$772$	10.3364	+	17.9031i	0.372014	+	0.644348i
$773$	−12.3527	+	21.3954i	−0.444294	+	0.769540i	−0.998003	−	0.0631705i	$-0.979879\pi$
$773$	−12.3527	+	21.3954i	−0.444294	+	0.769540i	0.553709	+	0.832710i	$0.313212\pi$
$774$		0			0
$775$	11.4030	+	19.7505i	0.409607	+	0.709461i
$776$	0.696052	−	1.20560i	0.0249868	−	0.0432784i
$777$		0			0
$778$	0.450298	+	0.779939i	0.0161440	+	0.0279622i
$779$	−0.442785	+	0.766927i	−0.0158644	+	0.0274780i
$780$		0			0
$781$	14.3906	+	24.9252i	0.514935	+	0.891894i
$782$	0.804687	−	1.39376i	0.0287756	−	0.0498407i
$783$		0			0
$784$	−8.74321	+	15.1437i	−0.312258	+	0.540846i
$785$	21.1194	−	36.5800i	0.753785	−	1.30559i
$786$		0			0
$787$	4.71774	+	8.17137i	0.168169	+	0.291278i	0.937776	−	0.347240i	$-0.112881\pi$
$787$	4.71774	+	8.17137i	0.168169	+	0.291278i	−0.769607	+	0.638518i	$0.779548\pi$
$788$	7.80217	+	13.5138i	0.277941	+	0.481408i
$789$		0			0
$790$	28.9289	+	50.1064i	1.02925	+	1.78271i
$791$	79.1642			2.81475
$792$		0			0
$793$	5.95988	+	10.3228i	0.211641	+	0.366574i
$794$	−10.9614			−0.389006
$795$		0			0
$796$	−10.2576			−0.363572
$797$	9.65670	−	16.7259i	0.342058	−	0.592462i	−0.642757	−	0.766070i	$-0.722209\pi$
$797$	9.65670	−	16.7259i	0.342058	−	0.592462i	0.984815	+	0.173609i	$0.0555428\pi$
$798$		0			0
$799$	41.7519			1.47708
$800$	11.6356			0.411380
$801$		0			0
$802$	8.41549	+	14.5761i	0.297161	+	0.514699i
$803$	11.5813	−	20.0595i	0.408696	−	0.707883i
$804$		0			0
$805$	−2.98618	+	5.17222i	−0.105249	+	0.182297i
$806$	−2.81633	−	4.87803i	−0.0992011	−	0.171821i
$807$		0			0
$808$	−1.38693	+	2.40224i	−0.0487921	+	0.0845105i
$809$	−4.56673	+	7.90981i	−0.160558	+	0.278094i	−0.935069	−	0.354466i	$-0.884663\pi$
$809$	−4.56673	+	7.90981i	−0.160558	+	0.278094i	0.774511	+	0.632560i	$0.217996\pi$
$810$		0			0
$811$	8.80739	−	15.2548i	0.309269	−	0.535670i	−0.668933	−	0.743322i	$-0.733249\pi$
$811$	8.80739	−	15.2548i	0.309269	−	0.535670i	0.978203	+	0.207652i	$0.0665822\pi$
$812$	−17.1132			−0.600557
$813$		0			0
$814$	−8.26427	+	14.1484i	−0.289662	+	0.495901i
$815$	3.82442	+	6.62409i	0.133964	+	0.232032i
$816$		0			0
$817$	−1.41045	−	2.44297i	−0.0493454	−	0.0854688i
$818$	2.97026	−	5.14465i	0.103853	−	0.179878i
$819$		0			0
$820$	−10.0537			−0.351091
$821$	−23.6018	−	40.8795i	−0.823709	−	1.42671i	−0.902902	−	0.429846i	$-0.858568\pi$
$821$	−23.6018	−	40.8795i	−0.823709	−	1.42671i	0.0791935	−	0.996859i	$-0.474766\pi$
$822$		0			0
$823$	2.56932	−	4.45019i	0.0895609	−	0.155124i	−0.817765	−	0.575553i	$-0.804787\pi$
$823$	2.56932	−	4.45019i	0.0895609	−	0.155124i	0.907326	+	0.420429i	$0.138120\pi$
$824$	−0.774343	−	1.34120i	−0.0269755	−	0.0467230i
$825$		0			0
$826$	−32.4587			−1.12938
$827$	12.8003	−	22.1707i	0.445110	−	0.770952i	−0.552950	−	0.833214i	$-0.686498\pi$
$827$	12.8003	−	22.1707i	0.445110	−	0.770952i	0.998060	+	0.0622618i	$0.0198314\pi$
$828$		0			0
$829$	15.7572	+	27.2923i	0.547271	+	0.947900i	0.998460	+	0.0554724i	$0.0176665\pi$
$829$	15.7572	+	27.2923i	0.547271	+	0.947900i	−0.451190	+	0.892428i	$0.649000\pi$
$830$	−50.9345			−1.76796
$831$		0			0
$832$	−2.87378			−0.0996303
$833$	−95.1027			−3.29511
$834$		0			0
$835$	81.7437			2.82886
$836$	−0.483879	−	0.838103i	−0.0167353	−	0.0289864i
$837$		0			0
$838$	−12.0195	+	20.8184i	−0.415206	+	0.719159i
$839$	−26.4795			−0.914173			−0.457087	−	0.889422i	$-0.651107\pi$
$839$	−26.4795			−0.914173			−0.457087	+	0.889422i	$0.651107\pi$
$840$		0			0
$841$	8.51990	+	14.7569i	0.293790	+	0.508859i
$842$	−4.13010	+	7.15355i	−0.142333	+	0.246527i
$843$		0			0
$844$	10.6091	+	18.3755i	0.365179	+	0.632509i
$845$	−19.3386			−0.665269
$846$		0			0
$847$	9.26312	−	16.0442i	0.318285	−	0.551285i
$848$	−2.45992	−	4.26070i	−0.0844739	−	0.146313i
$849$		0			0
$850$	31.6410	+	54.8038i	1.08528	+	1.87975i
$851$	0.892092	+	1.56335i	0.0305805	+	0.0535911i
$852$		0			0
$853$	−4.84077			−0.165745			−0.0828724	−	0.996560i	$-0.526409\pi$
$853$	−4.84077			−0.165745			−0.0828724	+	0.996560i	$0.526409\pi$
$854$	−10.2624	+	17.7749i	−0.351170	+	0.608245i
$855$		0			0
$856$	5.19514	−	8.99825i	0.177566	−	0.307554i
$857$	5.98835	−	10.3721i	0.204558	−	0.354305i	−0.745434	−	0.666580i	$-0.767758\pi$
$857$	5.98835	−	10.3721i	0.204558	−	0.354305i	0.949992	+	0.312275i	$0.101091\pi$
$858$		0			0
$859$	−4.83688	−	8.37773i	−0.165032	−	0.285844i	0.771634	−	0.636066i	$-0.219440\pi$
$859$	−4.83688	−	8.37773i	−0.165032	−	0.285844i	−0.936667	+	0.350222i	$0.886106\pi$
$860$	16.0126	−	27.7346i	0.546025	−	0.945743i
$861$		0			0
$862$	−0.940710	+	1.62936i	−0.0320407	+	0.0554961i
$863$	−10.6682	−	18.4778i	−0.363148	−	0.628991i	0.625329	−	0.780361i	$-0.284965\pi$
$863$	−10.6682	−	18.4778i	−0.363148	−	0.628991i	−0.988477	+	0.151370i	$0.951631\pi$
$864$		0			0
$865$	56.7828			1.93067
$866$	−4.97802			−0.169160
$867$		0			0
$868$	4.84946	−	8.39951i	0.164601	−	0.285098i
$869$	38.2116			1.29624
$870$		0			0
$871$	1.62673			0.0551197
$872$	−9.23262	−	15.9914i	−0.312656	−	0.541536i
$873$		0			0
$874$	−0.106312			−0.00359604
$875$	−66.9622	−	115.982i	−2.26374	−	3.92091i
$876$		0			0
$877$	−0.927137	−	1.60585i	−0.0313072	−	0.0542257i	0.849947	−	0.526868i	$-0.176634\pi$
$877$	−0.927137	−	1.60585i	−0.0313072	−	0.0542257i	−0.881254	+	0.472642i	$0.843300\pi$
$878$	3.99894	+	6.92636i	0.134958	+	0.233753i
$879$		0			0
$880$	5.49339	−	9.51483i	0.185182	−	0.320745i
$881$	−2.98102	+	5.16327i	−0.100433	+	0.173955i	−0.911863	−	0.410494i	$-0.865356\pi$
$881$	−2.98102	+	5.16327i	−0.100433	+	0.173955i	0.811430	+	0.584449i	$0.198689\pi$
$882$		0			0
$883$	9.62006	−	16.6624i	0.323741	−	0.560736i	−0.657516	−	0.753441i	$-0.728393\pi$
$883$	9.62006	−	16.6624i	0.323741	−	0.560736i	0.981257	+	0.192705i	$0.0617261\pi$
$884$	−7.81475	−	13.5355i	−0.262839	−	0.455250i
$885$		0			0
$886$	−10.2402	+	17.7365i	−0.344025	+	0.595869i
$887$	−21.7165	−	37.6140i	−0.729167	−	1.26295i	−0.957236	−	0.289309i	$-0.906574\pi$
$887$	−21.7165	−	37.6140i	−0.729167	−	1.26295i	0.228068	−	0.973645i	$-0.426759\pi$
$888$		0			0
$889$	37.6431	−	65.1998i	1.26251	−	2.18673i
$890$	37.4963	+	64.9456i	1.25688	+	2.17698i
$891$		0			0
$892$	−8.98920	+	15.5698i	−0.300981	+	0.521314i
$893$	−1.37902	−	2.38853i	−0.0461470	−	0.0799290i
$894$		0			0
$895$	−100.352			−3.35441
$896$	−2.47419	−	4.28542i	−0.0826568	−	0.143166i
$897$		0			0
$898$	16.2173	−	28.0891i	0.541177	−	0.937347i
$899$	6.77844			0.226074
$900$		0			0
$901$	13.3787	−	23.1725i	0.445708	−	0.771988i
$902$	−3.31993	+	5.75029i	−0.110542	+	0.191464i
$903$		0			0
$904$	−7.99901	+	13.8547i	−0.266043	+	0.460800i
$905$	3.74534	−	6.48712i	0.124499	−	0.215639i
$906$		0			0
$907$	−15.2999	−	26.5002i	−0.508024	−	0.879924i	−0.999957	−	0.00929062i	$-0.997043\pi$
$907$	−15.2999	−	26.5002i	−0.508024	−	0.879924i	0.491933	−	0.870633i	$-0.336291\pi$
$908$	−3.04228	−	5.26939i	−0.100962	−	0.174871i
$909$		0			0
$910$	29.0004	+	50.2303i	0.961356	+	1.66512i
$911$	−1.87114	+	3.24090i	−0.0619935	+	0.107376i	−0.895356	−	0.445350i	$-0.853079\pi$
$911$	−1.87114	+	3.24090i	−0.0619935	+	0.107376i	0.833363	+	0.552726i	$0.186412\pi$
$912$		0			0
$913$	−16.8195	+	29.1323i	−0.556646	+	0.964139i
$914$	12.4242	+	21.5194i	0.410956	+	0.711798i
$915$		0			0
$916$	−14.9476			−0.493883
$917$	−4.43065			−0.146313
$918$		0			0
$919$	−22.1894			−0.731961			−0.365980	−	0.930623i	$-0.619266\pi$
$919$	−22.1894			−0.731961			−0.365980	+	0.930623i	$0.619266\pi$
$920$	−0.603468	−	1.04524i	−0.0198957	−	0.0344604i
$921$		0			0
$922$	−33.2803			−1.09603
$923$	15.3525	−	26.5914i	0.505334	−	0.875265i
$924$		0			0
$925$	−70.7755	−	0.357934i	−2.32708	−	0.0117688i
$926$	−30.2977			−0.995646
$927$		0			0
$928$	1.72918	−	2.99502i	0.0567630	−	0.0983164i
$929$	13.7314	+	23.7836i	0.450514	+	0.780313i	0.998418	−	0.0562281i	$-0.0179074\pi$
$929$	13.7314	+	23.7836i	0.450514	+	0.780313i	−0.547904	+	0.836541i	$0.684574\pi$
$930$		0			0
$931$	3.14113	+	5.44060i	0.102946	+	0.178308i
$932$	13.7687			0.451010
$933$		0			0
$934$	−0.866573			−0.0283551
$935$	59.7534			1.95414
$936$		0			0
$937$	19.8980	+	34.4643i	0.650039	+	1.12590i	0.983113	+	0.183000i	$0.0585808\pi$
$937$	19.8980	+	34.4643i	0.650039	+	1.12590i	−0.333074	+	0.942901i	$0.608086\pi$
$938$	1.40054	+	2.42581i	0.0457293	+	0.0792054i
$939$		0			0
$940$	15.6557	−	27.1165i	0.510633	−	0.884443i
$941$	−13.7060	+	23.7395i	−0.446803	+	0.773886i	−0.998176	−	0.0603731i	$-0.980771\pi$
$941$	−13.7060	+	23.7395i	−0.446803	+	0.773886i	0.551373	+	0.834259i	$0.314104\pi$
$942$		0			0
$943$	0.364706	+	0.631690i	0.0118765	+	0.0205706i
$944$	3.27974	−	5.68067i	0.106746	−	0.184890i
$945$		0			0
$946$	−10.5753	−	18.3170i	−0.343834	−	0.595538i
$947$	41.0644			1.33441			0.667206	−	0.744873i	$-0.267490\pi$
$947$	41.0644			1.33441			0.667206	+	0.744873i	$0.267490\pi$
$948$		0			0
$949$	−24.7110			−0.802153
$950$	2.09013	−	3.62021i	0.0678127	−	0.117455i
$951$		0			0
$952$	13.4563	−	23.3069i	0.436120	−	0.755382i
$953$	−25.2544	−	43.7419i	−0.818070	−	1.41694i	−0.907102	−	0.420911i	$-0.861711\pi$
$953$	−25.2544	−	43.7419i	−0.818070	−	1.41694i	0.0890318	−	0.996029i	$-0.471623\pi$
$954$		0			0
$955$	−34.4860	+	59.7315i	−1.11594	+	1.93287i
$956$	2.62191	−	4.54128i	0.0847987	−	0.146876i
$957$		0			0
$958$	12.2144			0.394629
$959$	34.9768			1.12946
$960$		0			0
$961$	13.5792	−	23.5198i	0.438037	−	0.758703i
$962$	17.4803	+	0.0884032i	0.563587	+	0.00285023i
$963$		0			0
$964$	15.4037	+	26.6799i	0.496119	+	0.859303i
$965$	42.1587	+	73.0210i	1.35714	+	2.35063i
$966$		0			0
$967$	−1.91874			−0.0617026			−0.0308513	−	0.999524i	$-0.509822\pi$
$967$	−1.91874			−0.0617026			−0.0308513	+	0.999524i	$0.509822\pi$
$968$	1.87195	+	3.24232i	0.0601668	+	0.104212i
$969$		0			0
$970$	2.83897	−	4.91724i	0.0911538	−	0.157883i
$971$	−15.2072	−	26.3397i	−0.488024	−	0.845282i	0.511881	−	0.859056i	$-0.328949\pi$
$971$	−15.2072	−	26.3397i	−0.488024	−	0.845282i	−0.999905	+	0.0137742i	$0.995615\pi$
$972$		0			0
$973$	37.9304			1.21599
$974$	−32.8770			−1.05345
$975$		0			0
$976$	−2.07388	−	3.59207i	−0.0663834	−	0.114979i
$977$	−19.2141	+	33.2799i	−0.614715	+	1.06472i	0.375719	+	0.926733i	$0.377396\pi$
$977$	−19.2141	+	33.2799i	−0.614715	+	1.06472i	−0.990434	+	0.137984i	$0.955938\pi$
$978$		0			0
$979$	49.5281			1.58292
$980$	−35.6607	+	61.7662i	−1.13914	+	1.97305i
$981$		0			0
$982$	1.47498	+	2.55474i	0.0470686	+	0.0815252i
$983$	26.4505			0.843641			0.421820	−	0.906679i	$-0.361391\pi$
$983$	26.4505			0.843641			0.421820	+	0.906679i	$0.361391\pi$
$984$		0			0
$985$	31.8225	+	55.1182i	1.01395	+	1.75621i
$986$	18.8088			0.598994
$987$		0			0
$988$	−0.516224	+	0.894126i	−0.0164233	+	0.0284460i
$989$	−2.32347			−0.0738822
$990$		0			0
$991$	15.7162			0.499243			0.249621	−	0.968344i	$-0.419694\pi$
$991$	15.7162			0.499243			0.249621	+	0.968344i	$0.419694\pi$
$992$	0.980010	+	1.69743i	0.0311154	+	0.0538934i
$993$		0			0
$994$	52.8712			1.67697
$995$	−41.8375			−1.32634
$996$		0			0
$997$	18.6072			0.589296			0.294648	−	0.955606i	$-0.404798\pi$
$997$	18.6072			0.589296			0.294648	+	0.955606i	$0.404798\pi$
$998$	−0.369989			−0.0117118
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.h.b.1099.17		36
3.2	odd	2		666.2.h.b.655.3	yes	36
9.4	even	3		1998.2.g.b.1765.2		36
9.5	odd	6		666.2.g.b.211.11	✓	36
37.10	even	3		1998.2.g.b.343.2		36
111.47	odd	6		666.2.g.b.565.11	yes	36
333.121	even	3	inner	1998.2.h.b.1009.17		36
333.158	odd	6		666.2.h.b.121.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.g.b.211.11	✓	36	9.5	odd	6
666.2.g.b.565.11	yes	36	111.47	odd	6
666.2.h.b.121.3	yes	36	333.158	odd	6
666.2.h.b.655.3	yes	36	3.2	odd	2
1998.2.g.b.343.2		36	37.10	even	3
1998.2.g.b.1765.2		36	9.4	even	3
1998.2.h.b.1009.17		36	333.121	even	3	inner
1998.2.h.b.1099.17		36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +4.07867 q^{5} +(-2.47419 - 4.28542i) q^{7} +1.00000 q^{8} +4.07867 q^{10} +(1.34686 - 2.33282i) q^{11} -2.87378 q^{13} +(-2.47419 - 4.28542i) q^{14} +1.00000 q^{16} +(2.71933 + 4.71002i) q^{17} +(0.179633 - 0.311133i) q^{19} +4.07867 q^{20} +(1.34686 - 2.33282i) q^{22} +(-0.147957 - 0.256269i) q^{23} +11.6356 q^{25} -2.87378 q^{26} +(-2.47419 - 4.28542i) q^{28} +(1.72918 - 2.99502i) q^{29} +(0.980010 + 1.69743i) q^{31} +1.00000 q^{32} +(2.71933 + 4.71002i) q^{34} +(-10.0914 - 17.4788i) q^{35} +(-6.08268 - 0.0307620i) q^{37} +(0.179633 - 0.311133i) q^{38} +4.07867 q^{40} -2.46495 q^{41} +(3.92593 - 6.79991i) q^{43} +(1.34686 - 2.33282i) q^{44} +(-0.147957 - 0.256269i) q^{46} +(3.83844 - 6.64837i) q^{47} +(-8.74321 + 15.1437i) q^{49} +11.6356 q^{50} -2.87378 q^{52} +(-2.45992 - 4.26070i) q^{53} +(5.49339 - 9.51483i) q^{55} +(-2.47419 - 4.28542i) q^{56} +(1.72918 - 2.99502i) q^{58} +(3.27974 - 5.68067i) q^{59} +(-2.07388 - 3.59207i) q^{61} +(0.980010 + 1.69743i) q^{62} +1.00000 q^{64} -11.7212 q^{65} -0.566061 q^{67} +(2.71933 + 4.71002i) q^{68} +(-10.0914 - 17.4788i) q^{70} +(-5.34228 + 9.25310i) q^{71} +8.59878 q^{73} +(-6.08268 - 0.0307620i) q^{74} +(0.179633 - 0.311133i) q^{76} -13.3295 q^{77} +(7.09273 + 12.2850i) q^{79} +4.07867 q^{80} -2.46495 q^{82} -12.4880 q^{83} +(11.0913 + 19.2106i) q^{85} +(3.92593 - 6.79991i) q^{86} +(1.34686 - 2.33282i) q^{88} +(9.19327 + 15.9232i) q^{89} +(7.11027 + 12.3153i) q^{91} +(-0.147957 - 0.256269i) q^{92} +(3.83844 - 6.64837i) q^{94} +(0.732663 - 1.26901i) q^{95} +(0.696052 - 1.20560i) q^{97} +(-8.74321 + 15.1437i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{2} + 36 q^{4} + 8 q^{5} + 4 q^{7} + 36 q^{8} + 8 q^{10} - 3 q^{11} - 2 q^{13} + 4 q^{14} + 36 q^{16} - 3 q^{17} + 9 q^{19} + 8 q^{20} - 3 q^{22} - 11 q^{23} + 44 q^{25} - 2 q^{26} + 4 q^{28}+ \cdots - 12 q^{98}+O(q^{100}) \) 36 * q + 36 * q^2 + 36 * q^4 + 8 * q^5 + 4 * q^7 + 36 * q^8 + 8 * q^10 - 3 * q^11 - 2 * q^13 + 4 * q^14 + 36 * q^16 - 3 * q^17 + 9 * q^19 + 8 * q^20 - 3 * q^22 - 11 * q^23 + 44 * q^25 - 2 * q^26 + 4 * q^28 + 12 * q^29 + 16 * q^31 + 36 * q^32 - 3 * q^34 - 3 * q^35 + 8 * q^37 + 9 * q^38 + 8 * q^40 - 12 * q^41 + 4 * q^43 - 3 * q^44 - 11 * q^46 + 5 * q^47 - 12 * q^49 + 44 * q^50 - 2 * q^52 - 8 * q^53 + 9 * q^55 + 4 * q^56 + 12 * q^58 + 12 * q^59 - 15 * q^61 + 16 * q^62 + 36 * q^64 - 52 * q^65 + 28 * q^67 - 3 * q^68 - 3 * q^70 + 22 * q^73 + 8 * q^74 + 9 * q^76 + 50 * q^77 + 16 * q^79 + 8 * q^80 - 12 * q^82 + 15 * q^85 + 4 * q^86 - 3 * q^88 - 3 * q^89 + 37 * q^91 - 11 * q^92 + 5 * q^94 - 3 * q^95 + 11 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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