LMFDB - Embedded newform 1998.2.t.a.397.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(307,1998)] 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("1998.307"); 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, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1998 = 2 \cdot 3^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1998.t (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			397.21
Character	$\chi$	$=$	1998.397
Dual form			1998.2.t.a.307.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.57279 - 2.06275i) q^{5} -2.48600 q^{7} -1.00000i q^{8} -4.12550 q^{10} +(0.302670 - 0.524240i) q^{11} +(2.47892 + 1.43120i) q^{13} +(-2.15294 + 1.24300i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.47905 - 3.16333i) q^{17} +(-2.07794 + 1.19970i) q^{19} +(-3.57279 + 2.06275i) q^{20} -0.605341i q^{22} +(-3.33371 + 1.92472i) q^{23} +(6.00988 + 10.4094i) q^{25} +2.86241 q^{26} +(-1.24300 + 2.15294i) q^{28} +(8.47236 + 4.89152i) q^{29} +(6.23125 - 3.59761i) q^{31} +(-0.866025 - 0.500000i) q^{32} -6.32666 q^{34} +(8.88196 + 5.12800i) q^{35} +(-5.55330 + 2.48211i) q^{37} +(-1.19970 + 2.07794i) q^{38} +(-2.06275 + 3.57279i) q^{40} +(0.906242 - 1.56966i) q^{41} +(4.05787 + 2.34281i) q^{43} +(-0.302670 - 0.524240i) q^{44} +(-1.92472 + 3.33371i) q^{46} +(-0.873232 + 1.51248i) q^{47} -0.819791 q^{49} +(10.4094 + 6.00988i) q^{50} +(2.47892 - 1.43120i) q^{52} +(-1.48820 + 2.57764i) q^{53} +(-2.16275 + 1.24867i) q^{55} +2.48600i q^{56} +9.78303 q^{58} +9.12268i q^{59} +4.04781i q^{61} +(3.59761 - 6.23125i) q^{62} -1.00000 q^{64} +(-5.90443 - 10.2268i) q^{65} +(-0.575513 + 0.996818i) q^{67} +(-5.47905 + 3.16333i) q^{68} +10.2560 q^{70} +(-3.34971 - 5.80188i) q^{71} +1.65116 q^{73} +(-3.56824 + 4.92622i) q^{74} +2.39940i q^{76} +(-0.752439 + 1.30326i) q^{77} -2.21202i q^{79} +4.12550i q^{80} -1.81248i q^{82} +(8.26306 + 14.3120i) q^{83} +(13.0503 + 22.6038i) q^{85} +4.68563 q^{86} +(-0.524240 - 0.302670i) q^{88} +(-8.11389 - 4.68456i) q^{89} +(-6.16260 - 3.55798i) q^{91} +3.84944i q^{92} +1.74646i q^{94} +9.89872 q^{95} +(1.47331 + 0.850618i) q^{97} +(-0.709960 + 0.409896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) $ 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Character values

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

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.57279	−	2.06275i	−1.59780	−	0.922490i	−0.991910	−	0.126941i	$-0.959484\pi$
$5$	−3.57279	−	2.06275i	−1.59780	−	0.922490i	−0.605889	−	0.795549i	$-0.707183\pi$
$6$		0			0
$7$	−2.48600			−0.939621			−0.469810	−	0.882767i	$-0.655678\pi$
$7$	−2.48600			−0.939621			−0.469810	+	0.882767i	$0.655678\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−4.12550			−1.30460
$11$	0.302670	−	0.524240i	0.0912585	−	0.158064i	−0.816782	−	0.576946i	$-0.804244\pi$
$11$	0.302670	−	0.524240i	0.0912585	−	0.158064i	0.908041	+	0.418881i	$0.137578\pi$
$12$		0			0
$13$	2.47892	+	1.43120i	0.687528	+	0.396945i	0.802685	−	0.596403i	$-0.203404\pi$
$13$	2.47892	+	1.43120i	0.687528	+	0.396945i	−0.115157	+	0.993347i	$0.536737\pi$
$14$	−2.15294	+	1.24300i	−0.575398	+	0.332206i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.47905	−	3.16333i	−1.32886	−	0.767220i	−0.343740	−	0.939065i	$-0.611694\pi$
$17$	−5.47905	−	3.16333i	−1.32886	−	0.767220i	−0.985124	+	0.171844i	$0.945027\pi$
$18$		0			0
$19$	−2.07794	+	1.19970i	−0.476712	+	0.275230i	−0.719045	−	0.694963i	$-0.755421\pi$
$19$	−2.07794	+	1.19970i	−0.476712	+	0.275230i	0.242333	+	0.970193i	$0.422087\pi$
$20$	−3.57279	+	2.06275i	−0.798900	+	0.461245i
$21$		0			0
$22$		−	0.605341i		−	0.129059i
$23$	−3.33371	+	1.92472i	−0.695127	+	0.401332i	−0.805530	−	0.592555i	$-0.798119\pi$
$23$	−3.33371	+	1.92472i	−0.695127	+	0.401332i	0.110403	+	0.993887i	$0.464786\pi$
$24$		0			0
$25$	6.00988	+	10.4094i	1.20198	+	2.08188i
$26$	2.86241			0.561364
$27$		0			0
$28$	−1.24300	+	2.15294i	−0.234905	+	0.406868i
$29$	8.47236	+	4.89152i	1.57328	+	0.908332i	0.995764	+	0.0919506i	$0.0293102\pi$
$29$	8.47236	+	4.89152i	1.57328	+	0.908332i	0.577513	+	0.816381i	$0.304023\pi$
$30$		0			0
$31$	6.23125	−	3.59761i	1.11917	−	0.646151i	0.177978	−	0.984034i	$-0.443044\pi$
$31$	6.23125	−	3.59761i	1.11917	−	0.646151i	0.941188	+	0.337884i	$0.109711\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−6.32666			−1.08501
$35$	8.88196	+	5.12800i	1.50133	+	0.866791i
$36$		0			0
$37$	−5.55330	+	2.48211i	−0.912957	+	0.408056i
$37$	−5.55330	+	2.48211i	−0.912957	+	0.408056i
$38$	−1.19970	+	2.07794i	−0.194617	+	0.337086i
$39$		0			0
$40$	−2.06275	+	3.57279i	−0.326149	+	0.564907i
$41$	0.906242	−	1.56966i	0.141531	−	0.245139i	−0.786542	−	0.617537i	$-0.788131\pi$
$41$	0.906242	−	1.56966i	0.141531	−	0.245139i	0.928073	+	0.372397i	$0.121464\pi$
$42$		0			0
$43$	4.05787	+	2.34281i	0.618820	+	0.357276i	0.776409	−	0.630229i	$-0.217039\pi$
$43$	4.05787	+	2.34281i	0.618820	+	0.357276i	−0.157589	+	0.987505i	$0.550372\pi$
$44$	−0.302670	−	0.524240i	−0.0456293	−	0.0790322i
$45$		0			0
$46$	−1.92472	+	3.33371i	−0.283784	+	0.491529i
$47$	−0.873232	+	1.51248i	−0.127374	+	0.220618i	−0.922658	−	0.385618i	$-0.873988\pi$
$47$	−0.873232	+	1.51248i	−0.127374	+	0.220618i	0.795284	+	0.606236i	$0.207321\pi$
$48$		0			0
$49$	−0.819791			−0.117113
$50$	10.4094	+	6.00988i	1.47211	+	0.849925i
$51$		0			0
$52$	2.47892	−	1.43120i	0.343764	−	0.198472i
$53$	−1.48820	+	2.57764i	−0.204420	+	0.354066i	−0.949948	−	0.312409i	$-0.898864\pi$
$53$	−1.48820	+	2.57764i	−0.204420	+	0.354066i	0.745528	+	0.666475i	$0.232197\pi$
$54$		0			0
$55$	−2.16275	+	1.24867i	−0.291626	+	0.168370i
$56$			2.48600i			0.332206i
$57$		0			0
$58$	9.78303			1.28458
$59$			9.12268i			1.18767i	0.804586	+	0.593836i	$0.202387\pi$
$59$			9.12268i			1.18767i	−0.804586	+	0.593836i	$0.797613\pi$
$60$		0			0
$61$			4.04781i			0.518269i	0.965841	+	0.259135i	$0.0834374\pi$
$61$			4.04781i			0.518269i	−0.965841	+	0.259135i	$0.916563\pi$
$62$	3.59761	−	6.23125i	0.456898	−	0.791370i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.90443	−	10.2268i	−0.732355	−	1.26848i
$66$		0			0
$67$	−0.575513	+	0.996818i	−0.0703101	+	0.121781i	−0.899037	−	0.437872i	$-0.855732\pi$
$67$	−0.575513	+	0.996818i	−0.0703101	+	0.121781i	0.828727	+	0.559653i	$0.189066\pi$
$68$	−5.47905	+	3.16333i	−0.664432	+	0.383610i
$69$		0			0
$70$	10.2560			1.22583
$71$	−3.34971	−	5.80188i	−0.397538	−	0.688556i	0.595884	−	0.803071i	$-0.296802\pi$
$71$	−3.34971	−	5.80188i	−0.397538	−	0.688556i	−0.993422	+	0.114515i	$0.963469\pi$
$72$		0			0
$73$	1.65116			0.193254			0.0966268	−	0.995321i	$-0.469195\pi$
$73$	1.65116			0.193254			0.0966268	+	0.995321i	$0.469195\pi$
$74$	−3.56824	+	4.92622i	−0.414800	+	0.572661i
$75$		0			0
$76$			2.39940i			0.275230i
$77$	−0.752439	+	1.30326i	−0.0857484	+	0.148521i
$78$		0			0
$79$		−	2.21202i		−	0.248871i	−0.992228	−	0.124436i	$-0.960288\pi$
$79$		−	2.21202i		−	0.248871i	0.992228	−	0.124436i	$-0.0397120\pi$
$80$			4.12550i			0.461245i
$81$		0			0
$82$		−	1.81248i		−	0.200155i
$83$	8.26306	+	14.3120i	0.906989	+	1.57095i	0.818225	+	0.574898i	$0.194958\pi$
$83$	8.26306	+	14.3120i	0.906989	+	1.57095i	0.0887633	+	0.996053i	$0.471709\pi$
$84$		0			0
$85$	13.0503	+	22.6038i	1.41551	+	2.45173i
$86$	4.68563			0.505264
$87$		0			0
$88$	−0.524240	−	0.302670i	−0.0558842	−	0.0322648i
$89$	−8.11389	−	4.68456i	−0.860071	−	0.496562i	0.00396519	−	0.999992i	$-0.498738\pi$
$89$	−8.11389	−	4.68456i	−0.860071	−	0.496562i	−0.864036	+	0.503430i	$0.832071\pi$
$90$		0			0
$91$	−6.16260	−	3.55798i	−0.646016	−	0.372977i
$92$			3.84944i			0.401332i
$93$		0			0
$94$			1.74646i			0.180134i
$95$	9.89872			1.01559
$96$		0			0
$97$	1.47331	+	0.850618i	0.149592	+	0.0863672i	0.572928	−	0.819606i	$-0.305808\pi$
$97$	1.47331	+	0.850618i	0.149592	+	0.0863672i	−0.423336	+	0.905973i	$0.639141\pi$
$98$	−0.709960	+	0.409896i	−0.0717168	+	0.0414057i
$99$		0			0
$100$	12.0198			1.20198
$101$	6.03643	−	10.4554i	0.600647	−	1.04035i	−0.392076	−	0.919933i	$-0.628243\pi$
$101$	6.03643	−	10.4554i	0.600647	−	1.04035i	0.992723	−	0.120418i	$-0.0384235\pi$
$102$		0			0
$103$	−13.9924	+	8.07850i	−1.37871	+	0.795998i	−0.992004	−	0.126205i	$-0.959720\pi$
$103$	−13.9924	+	8.07850i	−1.37871	+	0.795998i	−0.386705	+	0.922203i	$0.626387\pi$
$104$	1.43120	−	2.47892i	0.140341	−	0.243078i
$105$		0			0
$106$			2.97640i			0.289094i
$107$	6.78135	+	11.7456i	0.655578	+	1.13549i	0.981749	+	0.190183i	$0.0609081\pi$
$107$	6.78135	+	11.7456i	0.655578	+	1.13549i	−0.326171	+	0.945311i	$0.605759\pi$
$108$		0			0
$109$	−5.09721	−	2.94287i	−0.488224	−	0.281876i	0.235613	−	0.971847i	$-0.424290\pi$
$109$	−5.09721	−	2.94287i	−0.488224	−	0.281876i	−0.723837	+	0.689971i	$0.757623\pi$
$110$	−1.24867	+	2.16275i	−0.119056	+	0.206211i
$111$		0			0
$112$	1.24300	+	2.15294i	0.117453	+	0.203434i
$113$			20.8920i			1.96535i	0.185325	+	0.982677i	$0.440666\pi$
$113$			20.8920i			1.96535i	−0.185325	+	0.982677i	$0.559334\pi$
$114$		0			0
$115$	15.8809			1.48090
$116$	8.47236	−	4.89152i	0.786638	−	0.454166i
$117$		0			0
$118$	4.56134	+	7.90047i	0.419905	+	0.727298i
$119$	13.6209	+	7.86405i	1.24863	+	0.720896i
$120$		0			0
$121$	5.31678	+	9.20894i	0.483344	+	0.837176i
$122$	2.02391	+	3.50551i	0.183236	+	0.317374i
$123$		0			0
$124$		−	7.19523i		−	0.646151i
$125$		−	28.9600i		−	2.59026i
$126$		0			0
$127$	1.95417	−	3.38472i	0.173404	−	0.300345i	−0.766204	−	0.642598i	$-0.777857\pi$
$127$	1.95417	−	3.38472i	0.173404	−	0.300345i	0.939608	+	0.342253i	$0.111190\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−10.2268	−	5.90443i	−0.896948	−	0.517853i
$131$		−	16.4259i		−	1.43514i	−0.696487	−	0.717570i	$-0.745254\pi$
$131$		−	16.4259i		−	1.43514i	0.696487	−	0.717570i	$-0.254746\pi$
$132$		0			0
$133$	5.16577	−	2.98246i	0.447929	−	0.258612i
$134$			1.15103i			0.0994335i
$135$		0			0
$136$	−3.16333	+	5.47905i	−0.271253	+	0.469825i
$137$	−5.96292	+	10.3281i	−0.509447	+	0.882388i	0.490493	+	0.871445i	$0.336817\pi$
$137$	−5.96292	+	10.3281i	−0.509447	+	0.882388i	−0.999940	+	0.0109431i	$0.996517\pi$
$138$		0			0
$139$	−7.40028			−0.627684			−0.313842	−	0.949475i	$-0.601616\pi$
$139$	−7.40028			−0.627684			−0.313842	+	0.949475i	$0.601616\pi$
$140$	8.88196	−	5.12800i	0.750663	−	0.433395i
$141$		0			0
$142$	−5.80188	−	3.34971i	−0.486883	−	0.281102i
$143$	1.50059	−	0.866366i	0.125486	−	0.0724492i
$144$		0			0
$145$	−20.1800	−	34.9527i	−1.67585	−	2.90266i
$146$	1.42995	−	0.825580i	0.118343	−	0.0683255i
$147$		0			0
$148$	−0.627079	+	6.05035i	−0.0515456	+	0.497336i
$149$	−10.1249	−	17.5368i	−0.829463	−	1.43667i	−0.898460	−	0.439055i	$-0.855313\pi$
$149$	−10.1249	−	17.5368i	−0.829463	−	1.43667i	0.0689968	−	0.997617i	$-0.478020\pi$
$150$		0			0
$151$	−10.2770			−0.836329			−0.418165	−	0.908371i	$-0.637326\pi$
$151$	−10.2770			−0.836329			−0.418165	+	0.908371i	$0.637326\pi$
$152$	1.19970	+	2.07794i	0.0973085	+	0.168543i
$153$		0			0
$154$			1.50488i			0.121267i
$155$	−29.6839			−2.38427
$156$		0			0
$157$	−14.0756			−1.12336			−0.561678	−	0.827356i	$-0.689844\pi$
$157$	−14.0756			−1.12336			−0.561678	+	0.827356i	$0.689844\pi$
$158$	−1.10601	−	1.91566i	−0.0879892	−	0.152402i
$159$		0			0
$160$	2.06275	+	3.57279i	0.163075	+	0.282454i
$161$	8.28762	−	4.78486i	0.653156	−	0.377100i
$162$		0			0
$163$	−14.1012	−	8.14132i	−1.10449	−	0.637678i	−0.167093	−	0.985941i	$-0.553438\pi$
$163$	−14.1012	−	8.14132i	−1.10449	−	0.637678i	−0.937397	+	0.348264i	$0.886771\pi$
$164$	−0.906242	−	1.56966i	−0.0707656	−	0.122570i
$165$		0			0
$166$	14.3120	+	8.26306i	1.11083	+	0.641338i
$167$	7.22703	+	4.17253i	0.559244	+	0.322880i	0.752842	−	0.658201i	$-0.228682\pi$
$167$	7.22703	+	4.17253i	0.559244	+	0.322880i	−0.193598	+	0.981081i	$0.562016\pi$
$168$		0			0
$169$	−2.40331	−	4.16266i	−0.184870	−	0.320204i
$170$	22.6038	+	13.0503i	1.73363	+	1.00091i
$171$		0			0
$172$	4.05787	−	2.34281i	0.309410	−	0.178638i
$173$	−4.29582	−	7.44059i	−0.326605	−	0.565697i	0.655231	−	0.755429i	$-0.272571\pi$
$173$	−4.29582	−	7.44059i	−0.326605	−	0.565697i	−0.981836	+	0.189732i	$0.939238\pi$
$174$		0			0
$175$	−14.9406	−	25.8778i	−1.12940	−	1.95618i
$176$	−0.605341			−0.0456293
$177$		0			0
$178$	−9.36912			−0.702245
$179$			19.5696i			1.46270i	0.682003	+	0.731349i	$0.261109\pi$
$179$			19.5696i			1.46270i	−0.682003	+	0.731349i	$0.738891\pi$
$180$		0			0
$181$	−11.3299	−	19.6239i	−0.842143	−	1.45863i	−0.888080	−	0.459689i	$-0.847961\pi$
$181$	−11.3299	−	19.6239i	−0.842143	−	1.45863i	0.0459372	−	0.998944i	$-0.485373\pi$
$182$	−7.11595			−0.527470
$183$		0			0
$184$	1.92472	+	3.33371i	0.141892	+	0.245765i
$185$	24.9607	+	2.58702i	1.83515	+	0.190201i
$186$		0			0
$187$	−3.31669	+	1.91489i	−0.242540	+	0.140031i
$188$	0.873232	+	1.51248i	0.0636870	+	0.110309i
$189$		0			0
$190$	8.57255	−	4.94936i	0.621918	−	0.359064i
$191$	6.29116	+	3.63220i	0.455212	+	0.262817i	0.710029	−	0.704172i	$-0.248682\pi$
$191$	6.29116	+	3.63220i	0.455212	+	0.262817i	−0.254817	+	0.966989i	$0.582015\pi$
$192$		0			0
$193$	−0.268129	+	0.154804i	−0.0193003	+	0.0111431i	−0.509619	−	0.860400i	$-0.670214\pi$
$193$	−0.268129	+	0.154804i	−0.0193003	+	0.0111431i	0.490319	+	0.871543i	$0.336880\pi$
$194$	1.70124			0.122142
$195$		0			0
$196$	−0.409896	+	0.709960i	−0.0292783	+	0.0507114i
$197$	−7.41930	+	12.8506i	−0.528604	+	0.915568i	0.470840	+	0.882219i	$0.343951\pi$
$197$	−7.41930	+	12.8506i	−0.528604	+	0.915568i	−0.999444	+	0.0333497i	$0.989382\pi$
$198$		0			0
$199$			16.7753i			1.18917i	0.804032	+	0.594586i	$0.202684\pi$
$199$			16.7753i			1.18917i	−0.804032	+	0.594586i	$0.797316\pi$
$200$	10.4094	−	6.00988i	0.736057	−	0.424963i
$201$		0			0
$202$		−	12.0729i		−	0.849443i
$203$	−21.0623	−	12.1603i	−1.47828	−	0.853487i
$204$		0			0
$205$	−6.47562	+	3.73870i	−0.452277	+	0.261122i
$206$	−8.07850	+	13.9924i	−0.562856	+	0.974895i
$207$		0			0
$208$		−	2.86241i		−	0.198472i
$209$			1.45245i			0.100468i
$210$		0			0
$211$	1.45399	+	2.51838i	0.100097	+	0.173373i	0.911724	−	0.410803i	$-0.134751\pi$
$211$	1.45399	+	2.51838i	0.100097	+	0.173373i	−0.811628	+	0.584175i	$0.801418\pi$
$212$	1.48820	+	2.57764i	0.102210	+	0.177033i
$213$		0			0
$214$	11.7456	+	6.78135i	0.802915	+	0.463563i
$215$	−9.66528	−	16.7408i	−0.659167	−	1.14171i
$216$		0			0
$217$	−15.4909	+	8.94368i	−1.05159	+	0.607137i
$218$	−5.88575			−0.398633
$219$		0			0
$220$			2.49733i			0.168370i
$221$	−9.05474	−	15.6833i	−0.609088	−	1.05497i
$222$		0			0
$223$	−12.5979	+	21.8203i	−0.843621	+	1.46119i	0.0431922	+	0.999067i	$0.486247\pi$
$223$	−12.5979	+	21.8203i	−0.843621	+	1.46119i	−0.886813	+	0.462128i	$0.847086\pi$
$224$	2.15294	+	1.24300i	0.143849	+	0.0830515i
$225$		0			0
$226$	10.4460	+	18.0930i	0.694858	+	1.20353i
$227$		−	13.2781i		−	0.881296i	−0.897680	−	0.440648i	$-0.854749\pi$
$227$		−	13.2781i		−	0.881296i	0.897680	−	0.440648i	$-0.145251\pi$
$228$		0			0
$229$	−3.45629	+	5.98648i	−0.228398	+	0.395598i	−0.957334	−	0.288985i	$-0.906682\pi$
$229$	−3.45629	+	5.98648i	−0.228398	+	0.395598i	0.728935	+	0.684583i	$0.240016\pi$
$230$	13.7532	−	7.94043i	0.906862	−	0.523577i
$231$		0			0
$232$	4.89152	−	8.47236i	0.321144	−	0.556237i
$233$	24.9882			1.63703			0.818515	−	0.574486i	$-0.194798\pi$
$233$	24.9882			1.63703			0.818515	+	0.574486i	$0.194798\pi$
$234$		0			0
$235$	6.23975	−	3.60252i	0.407036	−	0.235002i
$236$	7.90047	+	4.56134i	0.514277	+	0.296918i
$237$		0			0
$238$	15.7281			1.01950
$239$		−	3.78856i		−	0.245061i	−0.992465	−	0.122531i	$-0.960899\pi$
$239$		−	3.78856i		−	0.245061i	0.992465	−	0.122531i	$-0.0391010\pi$
$240$		0			0
$241$			5.75575i			0.370760i	0.982667	+	0.185380i	$0.0593517\pi$
$241$			5.75575i			0.370760i	−0.982667	+	0.185380i	$0.940648\pi$
$242$	9.20894	+	5.31678i	0.591973	+	0.341776i
$243$		0			0
$244$	3.50551	+	2.02391i	0.224417	+	0.129567i
$245$	2.92894	+	1.69102i	0.187123	+	0.108036i
$246$		0			0
$247$	−6.86806			−0.437004
$248$	−3.59761	−	6.23125i	−0.228449	−	0.395685i
$249$		0			0
$250$	−14.4800	−	25.0801i	−0.915796	−	1.58621i
$251$		−	7.00459i		−	0.442126i	−0.975260	−	0.221063i	$-0.929047\pi$
$251$		−	7.00459i		−	0.442126i	0.975260	−	0.221063i	$-0.0709526\pi$
$252$		0			0
$253$			2.33022i			0.146500i
$254$		−	3.90834i		−	0.245231i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	7.38730i		−	0.460807i	−0.973095	−	0.230403i	$-0.925995\pi$
$257$		−	7.38730i		−	0.460807i	0.973095	−	0.230403i	$-0.0740046\pi$
$258$		0			0
$259$	13.8055	−	6.17053i	0.857833	−	0.383418i
$260$	−11.8089			−0.732355
$261$		0			0
$262$	−8.21296	−	14.2253i	−0.507398	−	0.878840i
$263$	26.4999			1.63405			0.817026	−	0.576601i	$-0.195621\pi$
$263$	26.4999			1.63405			0.817026	+	0.576601i	$0.195621\pi$
$264$		0			0
$265$	10.6340	−	6.13957i	0.653244	−	0.377151i
$266$	2.98246	−	5.16577i	0.182866	−	0.316733i
$267$		0			0
$268$	0.575513	+	0.996818i	0.0351550	+	0.0608903i
$269$	−12.5852			−0.767335			−0.383667	−	0.923471i	$-0.625339\pi$
$269$	−12.5852			−0.767335			−0.383667	+	0.923471i	$0.625339\pi$
$270$		0			0
$271$	−0.170960	+	0.296111i	−0.0103851	+	0.0179875i	−0.871171	−	0.490979i	$-0.836639\pi$
$271$	−0.170960	+	0.296111i	−0.0103851	+	0.0179875i	0.860786	+	0.508967i	$0.169972\pi$
$272$			6.32666i			0.383610i
$273$		0			0
$274$			11.9258i			0.720467i
$275$	7.27605			0.438762
$276$		0			0
$277$		−	0.995407i		−	0.0598082i	−0.999553	−	0.0299041i	$-0.990480\pi$
$277$		−	0.995407i		−	0.0598082i	0.999553	−	0.0299041i	$-0.00952019\pi$
$278$	−6.40883	+	3.70014i	−0.384376	+	0.221920i
$279$		0			0
$280$	5.12800	−	8.88196i	0.306457	−	0.530799i
$281$	−15.1475	+	8.74542i	−0.903625	+	0.521708i	−0.878375	−	0.477973i	$-0.841372\pi$
$281$	−15.1475	+	8.74542i	−0.903625	+	0.521708i	−0.0252505	+	0.999681i	$0.508038\pi$
$282$		0			0
$283$	−17.5361	−	10.1245i	−1.04241	−	0.601837i	−0.121897	−	0.992543i	$-0.538898\pi$
$283$	−17.5361	−	10.1245i	−1.04241	−	0.601837i	−0.920516	+	0.390706i	$0.872231\pi$
$284$	−6.69943			−0.397538
$285$		0			0
$286$	0.866366	−	1.50059i	0.0512293	−	0.0887317i
$287$	−2.25292	+	3.90217i	−0.132986	+	0.230338i
$288$		0			0
$289$	11.5133	+	19.9416i	0.677254	+	1.17304i
$290$	−34.9527	−	20.1800i	−2.05249	−	1.18501i
$291$		0			0
$292$	0.825580	−	1.42995i	0.0483134	−	0.0836813i
$293$	−5.40082	+	9.35450i	−0.315519	+	0.546496i	−0.979548	−	0.201212i	$-0.935512\pi$
$293$	−5.40082	+	9.35450i	−0.315519	+	0.546496i	0.664028	+	0.747707i	$0.268845\pi$
$294$		0			0
$295$	18.8178	−	32.5934i	1.09562	−	1.89766i
$296$	2.48211	+	5.55330i	0.144270	+	0.322779i
$297$		0			0
$298$	−17.5368	−	10.1249i	−1.01588	−	0.586519i
$299$	−11.0187			−0.637226
$300$		0			0
$301$	−10.0879	−	5.82424i	−0.581456	−	0.335704i
$302$	−8.90013	+	5.13849i	−0.512145	+	0.295687i
$303$		0			0
$304$	2.07794	+	1.19970i	0.119178	+	0.0688075i
$305$	8.34963	−	14.4620i	0.478098	−	0.828091i
$306$		0			0
$307$	8.74549			0.499131			0.249566	−	0.968358i	$-0.419712\pi$
$307$	8.74549			0.499131			0.249566	+	0.968358i	$0.419712\pi$
$308$	0.752439	+	1.30326i	0.0428742	+	0.0742603i
$309$		0			0
$310$	−25.7070	+	14.8420i	−1.46006	+	0.842967i
$311$		−	10.5913i		−	0.600579i	−0.953848	−	0.300289i	$-0.902917\pi$
$311$		−	10.5913i		−	0.600579i	0.953848	−	0.300289i	$-0.0970833\pi$
$312$		0			0
$313$	−3.19799	+	1.84636i	−0.180761	+	0.104362i	−0.587650	−	0.809115i	$-0.699947\pi$
$313$	−3.19799	+	1.84636i	−0.180761	+	0.104362i	0.406889	+	0.913478i	$0.366614\pi$
$314$	−12.1898	+	7.03781i	−0.687913	+	0.397167i
$315$		0			0
$316$	−1.91566	−	1.10601i	−0.107764	−	0.0622178i
$317$	−0.630529	−	1.09211i	−0.0354140	−	0.0613389i	0.847775	−	0.530356i	$-0.177942\pi$
$317$	−0.630529	−	1.09211i	−0.0354140	−	0.0613389i	−0.883189	+	0.469017i	$0.844608\pi$
$318$		0			0
$319$	5.12866	−	2.96103i	0.287150	−	0.165786i
$320$	3.57279	+	2.06275i	0.199725	+	0.115311i
$321$		0			0
$322$	4.78486	−	8.28762i	0.266650	−	0.461851i
$323$	15.1802			0.844648
$324$		0			0
$325$			34.4055i			1.90847i
$326$	−16.2826			−0.901812
$327$		0			0
$328$	−1.56966	−	0.906242i	−0.0866698	−	0.0500389i
$329$	2.17086	−	3.76003i	0.119683	−	0.207297i
$330$		0			0
$331$	7.48480	−	4.32135i	0.411402	−	0.237523i	−0.279990	−	0.960003i	$-0.590331\pi$
$331$	7.48480	−	4.32135i	0.411402	−	0.237523i	0.691392	+	0.722480i	$0.256998\pi$
$332$	16.5261			0.906989
$333$		0			0
$334$	8.34505			0.456621
$335$	4.11237	−	2.37428i	0.224683	−	0.129721i
$336$		0			0
$337$	1.92654	−	3.33687i	0.104946	−	0.181771i	−0.808770	−	0.588124i	$-0.799867\pi$
$337$	1.92654	−	3.33687i	0.104946	−	0.181771i	0.913716	+	0.406353i	$0.133200\pi$
$338$	−4.16266	−	2.40331i	−0.226419	−	0.130723i
$339$		0			0
$340$	26.1006			1.41551
$341$		−	4.35556i		−	0.235867i
$342$		0			0
$343$	19.4400			1.04966
$344$	2.34281	−	4.05787i	0.126316	−	0.218786i
$345$		0			0
$346$	−7.44059	−	4.29582i	−0.400008	−	0.230945i
$347$	−20.7963	+	12.0067i	−1.11640	+	0.644555i	−0.940480	−	0.339849i	$-0.889624\pi$
$347$	−20.7963	+	12.0067i	−1.11640	+	0.644555i	−0.175922	+	0.984404i	$0.556291\pi$
$348$		0			0
$349$	−13.8212	−	23.9390i	−0.739830	−	1.28142i	−0.952571	−	0.304315i	$-0.901572\pi$
$349$	−13.8212	−	23.9390i	−0.739830	−	1.28142i	0.212741	−	0.977109i	$-0.431761\pi$
$350$	−25.8778	−	14.9406i	−1.38323	−	0.798607i
$351$		0			0
$352$	−0.524240	+	0.302670i	−0.0279421	+	0.0161324i
$353$	−7.41334	+	4.28009i	−0.394572	+	0.227806i	−0.684139	−	0.729351i	$-0.739822\pi$
$353$	−7.41334	+	4.28009i	−0.394572	+	0.227806i	0.289567	+	0.957158i	$0.406489\pi$
$354$		0			0
$355$			27.6385i			1.46690i
$356$	−8.11389	+	4.68456i	−0.430035	+	0.248281i
$357$		0			0
$358$	9.78479	+	16.9478i	0.517142	+	0.895716i
$359$	−20.0102			−1.05610			−0.528048	−	0.849215i	$-0.677076\pi$
$359$	−20.0102			−1.05610			−0.528048	+	0.849215i	$0.677076\pi$
$360$		0			0
$361$	−6.62144	+	11.4687i	−0.348497	+	0.603614i
$362$	−19.6239	−	11.3299i	−1.03141	−	0.595485i
$363$		0			0
$364$	−6.16260	+	3.55798i	−0.323008	+	0.186489i
$365$	−5.89924	−	3.40593i	−0.308780	−	0.178274i
$366$		0			0
$367$	25.2744			1.31931			0.659657	−	0.751567i	$-0.270702\pi$
$367$	25.2744			1.31931			0.659657	+	0.751567i	$0.270702\pi$
$368$	3.33371	+	1.92472i	0.173782	+	0.100333i
$369$		0			0
$370$	22.9101	−	10.2399i	1.19104	−	0.532349i
$371$	3.69967	−	6.40802i	0.192077	−	0.332688i
$372$		0			0
$373$	6.12686	−	10.6120i	0.317237	−	0.549470i	−0.662674	−	0.748908i	$-0.730578\pi$
$373$	6.12686	−	10.6120i	0.317237	−	0.549470i	0.979910	+	0.199438i	$0.0639117\pi$
$374$	−1.91489	+	3.31669i	−0.0990167	+	0.171502i
$375$		0			0
$376$	1.51248	+	0.873232i	0.0780003	+	0.0450335i
$377$	14.0015	+	24.2513i	0.721115	+	1.24901i
$378$		0			0
$379$	15.4180	−	26.7048i	0.791970	−	1.37173i	−0.132776	−	0.991146i	$-0.542389\pi$
$379$	15.4180	−	26.7048i	0.791970	−	1.37173i	0.924745	−	0.380586i	$-0.124278\pi$
$380$	4.94936	−	8.57255i	0.253897	−	0.439762i
$381$		0			0
$382$	7.26440			0.371679
$383$	−13.3006	−	7.67909i	−0.679627	−	0.392383i	0.120087	−	0.992763i	$-0.461683\pi$
$383$	−13.3006	−	7.67909i	−0.679627	−	0.392383i	−0.799715	+	0.600380i	$0.795016\pi$
$384$		0			0
$385$	5.37661	−	3.10419i	0.274018	−	0.158204i
$386$	−0.154804	+	0.268129i	−0.00787933	+	0.0136474i
$387$		0			0
$388$	1.47331	−	0.850618i	0.0747962	−	0.0431836i
$389$			5.07594i			0.257360i	0.991686	+	0.128680i	$0.0410741\pi$
$389$			5.07594i			0.257360i	−0.991686	+	0.128680i	$0.958926\pi$
$390$		0			0
$391$	24.3541			1.23164
$392$			0.819791i			0.0414057i
$393$		0			0
$394$			14.8386i			0.747558i
$395$	−4.56284	+	7.90306i	−0.229581	+	0.397646i
$396$		0			0
$397$	36.0842			1.81101			0.905507	−	0.424331i	$-0.139491\pi$
$397$	36.0842			1.81101			0.905507	+	0.424331i	$0.139491\pi$
$398$	8.38767	+	14.5279i	0.420436	+	0.728216i
$399$		0			0
$400$	6.00988	−	10.4094i	0.300494	−	0.520471i
$401$	−26.6967	+	15.4133i	−1.33317	+	0.769705i	−0.985784	−	0.168018i	$-0.946263\pi$
$401$	−26.6967	+	15.4133i	−1.33317	+	0.769705i	−0.347384	+	0.937723i	$0.612930\pi$
$402$		0			0
$403$	20.5957			1.02594
$404$	−6.03643	−	10.4554i	−0.300323	−	0.520175i
$405$		0			0
$406$	−24.3206			−1.20701
$407$	−0.379597	+	3.66252i	−0.0188159	+	0.181545i
$408$		0			0
$409$			24.1680i			1.19503i	0.801857	+	0.597515i	$0.203845\pi$
$409$			24.1680i			1.19503i	−0.801857	+	0.597515i	$0.796155\pi$
$410$	−3.73870	+	6.47562i	−0.184641	+	0.319808i
$411$		0			0
$412$			16.1570i			0.795998i
$413$		−	22.6790i		−	1.11596i
$414$		0			0
$415$		−	68.1785i		−	3.34675i
$416$	−1.43120	−	2.47892i	−0.0701705	−	0.121539i
$417$		0			0
$418$	0.726227	+	1.25786i	0.0355209	+	0.0615240i
$419$	32.4909			1.58728			0.793642	−	0.608386i	$-0.208183\pi$
$419$	32.4909			1.58728			0.793642	+	0.608386i	$0.208183\pi$
$420$		0			0
$421$	4.23360	+	2.44427i	0.206333	+	0.119126i	0.599606	−	0.800295i	$-0.295324\pi$
$421$	4.23360	+	2.44427i	0.206333	+	0.119126i	−0.393273	+	0.919422i	$0.628657\pi$
$422$	2.51838	+	1.45399i	0.122593	+	0.0707791i
$423$		0			0
$424$	2.57764	+	1.48820i	0.125181	+	0.0722734i
$425$		−	76.0449i		−	3.68872i
$426$		0			0
$427$		−	10.0629i		−	0.486977i
$428$	13.5627			0.655578
$429$		0			0
$430$	−16.7408	−	9.66528i	−0.807311	−	0.466101i
$431$	−3.95310	+	2.28233i	−0.190414	+	0.109936i	−0.592176	−	0.805808i	$-0.701731\pi$
$431$	−3.95310	+	2.28233i	−0.190414	+	0.109936i	0.401762	+	0.915744i	$0.368398\pi$
$432$		0			0
$433$	−20.1711			−0.969362			−0.484681	−	0.874691i	$-0.661064\pi$
$433$	−20.1711			−0.969362			−0.484681	+	0.874691i	$0.661064\pi$
$434$	−8.94368	+	15.4909i	−0.429310	+	0.743587i
$435$		0			0
$436$	−5.09721	+	2.94287i	−0.244112	+	0.140938i
$437$	4.61817	−	7.99891i	0.220917	−	0.382640i
$438$		0			0
$439$			24.6561i			1.17677i	0.808581	+	0.588385i	$0.200236\pi$
$439$			24.6561i			1.17677i	−0.808581	+	0.588385i	$0.799764\pi$
$440$	1.24867	+	2.16275i	0.0595278	+	0.103105i
$441$		0			0
$442$	−15.6833	−	9.05474i	−0.745977	−	0.430690i
$443$	−15.6754	+	27.1505i	−0.744759	+	1.28996i	0.205549	+	0.978647i	$0.434102\pi$
$443$	−15.6754	+	27.1505i	−0.744759	+	1.28996i	−0.950307	+	0.311313i	$0.899231\pi$
$444$		0			0
$445$	19.3261	+	33.4739i	0.916147	+	1.58681i
$446$			25.1959i			1.19306i
$447$		0			0
$448$	2.48600			0.117453
$449$	−33.1427	+	19.1350i	−1.56410	+	0.903035i	−0.567267	+	0.823534i	$0.691999\pi$
$449$	−33.1427	+	19.1350i	−1.56410	+	0.903035i	−0.996835	+	0.0795010i	$0.974667\pi$
$450$		0			0
$451$	−0.548585	−	0.950178i	−0.0258319	−	0.0447421i
$452$	18.0930	+	10.4460i	0.851024	+	0.491339i
$453$		0			0
$454$	−6.63903	−	11.4991i	−0.311585	−	0.539681i
$455$	14.6784	+	25.4238i	0.688136	+	1.19189i
$456$		0			0
$457$		−	3.25163i		−	0.152105i	−0.997104	−	0.0760525i	$-0.975768\pi$
$457$		−	3.25163i		−	0.152105i	0.997104	−	0.0760525i	$-0.0242317\pi$
$458$			6.91259i			0.323004i
$459$		0			0
$460$	7.94043	−	13.7532i	0.370225	−	0.641248i
$461$	2.06701	−	1.19339i	0.0962703	−	0.0555817i	−0.451092	−	0.892478i	$-0.648965\pi$
$461$	2.06701	−	1.19339i	0.0962703	−	0.0555817i	0.547362	+	0.836896i	$0.315632\pi$
$462$		0			0
$463$	4.38802	+	2.53343i	0.203929	+	0.117738i	0.598487	−	0.801133i	$-0.295769\pi$
$463$	4.38802	+	2.53343i	0.203929	+	0.117738i	−0.394558	+	0.918871i	$0.629102\pi$
$464$		−	9.78303i		−	0.454166i
$465$		0			0
$466$	21.6404	−	12.4941i	1.00247	−	0.578777i
$467$			11.0299i			0.510405i	0.966888	+	0.255203i	$0.0821422\pi$
$467$			11.0299i			0.510405i	−0.966888	+	0.255203i	$0.917858\pi$
$468$		0			0
$469$	1.43073	−	2.47809i	0.0660648	−	0.114428i
$470$	3.60252	−	6.23975i	0.166172	−	0.287818i
$471$		0			0
$472$	9.12268			0.419905
$473$	2.45640	−	1.41820i	0.112945	−	0.0652089i
$474$		0			0
$475$	−24.9763	−	14.4201i	−1.14599	−	0.661639i
$476$	13.6209	−	7.86405i	0.624314	−	0.360448i
$477$		0			0
$478$	−1.89428	−	3.28098i	−0.0866422	−	0.150069i
$479$	24.5137	−	14.1530i	1.12006	−	0.646667i	0.178644	−	0.983914i	$-0.442829\pi$
$479$	24.5137	−	14.1530i	1.12006	−	0.646667i	0.941416	+	0.337247i	$0.109496\pi$
$480$		0			0
$481$	−17.3186	−	1.79496i	−0.789659	−	0.0818430i
$482$	2.87787	+	4.98462i	0.131084	+	0.227043i
$483$		0			0
$484$	10.6336			0.483344
$485$	−3.50923	−	6.07816i	−0.159346	−	0.275995i
$486$		0			0
$487$			28.7296i			1.30186i	0.759137	+	0.650930i	$0.225621\pi$
$487$			28.7296i			1.30186i	−0.759137	+	0.650930i	$0.774379\pi$
$488$	4.04781			0.183236
$489$		0			0
$490$	3.38205			0.152785
$491$	−4.23594	−	7.33687i	−0.191166	−	0.331108i	0.754471	−	0.656333i	$-0.227893\pi$
$491$	−4.23594	−	7.33687i	−0.191166	−	0.331108i	−0.945637	+	0.325225i	$0.894560\pi$
$492$		0			0
$493$	−30.9470	−	53.6017i	−1.39378	−	2.41410i
$494$	−5.94791	+	3.43403i	−0.267609	+	0.154504i
$495$		0			0
$496$	−6.23125	−	3.59761i	−0.279791	−	0.161538i
$497$	8.32740	+	14.4235i	0.373535	+	0.646981i
$498$		0			0
$499$	1.14612	+	0.661710i	0.0513072	+	0.0296222i	0.525434	−	0.850834i	$-0.323903\pi$
$499$	1.14612	+	0.661710i	0.0513072	+	0.0296222i	−0.474127	+	0.880456i	$0.657236\pi$
$500$	−25.0801	−	14.4800i	−1.12162	−	0.647566i
$501$		0			0
$502$	−3.50230	−	6.06615i	−0.156315	−	0.270746i
$503$	5.97983	+	3.45246i	0.266628	+	0.153937i	0.627354	−	0.778734i	$-0.284138\pi$
$503$	5.97983	+	3.45246i	0.266628	+	0.153937i	−0.360727	+	0.932672i	$0.617471\pi$
$504$		0			0
$505$	−43.1337	+	24.9033i	−1.91943	+	1.10818i
$506$	1.16511	+	2.01803i	0.0517955	+	0.0897125i
$507$		0			0
$508$	−1.95417	−	3.38472i	−0.0867022	−	0.150173i
$509$	−17.1039			−0.758117			−0.379058	−	0.925373i	$-0.623752\pi$
$509$	−17.1039			−0.758117			−0.379058	+	0.925373i	$0.623752\pi$
$510$		0			0
$511$	−4.10479			−0.181585
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−3.69365	−	6.39759i	−0.162920	−	0.282185i
$515$	66.6557			2.93720
$516$		0			0
$517$	0.528603	+	0.915567i	0.0232479	+	0.0402666i
$518$	8.87066	−	12.2466i	0.389755	−	0.538084i
$519$		0			0
$520$	−10.2268	+	5.90443i	−0.448474	+	0.258927i
$521$	−4.87121	−	8.43719i	−0.213412	−	0.369640i	0.739368	−	0.673301i	$-0.235124\pi$
$521$	−4.87121	−	8.43719i	−0.213412	−	0.369640i	−0.952780	+	0.303661i	$0.901791\pi$
$522$		0			0
$523$	−32.4156	+	18.7152i	−1.41744	+	0.818357i	−0.996073	−	0.0885347i	$-0.971782\pi$
$523$	−32.4156	+	18.7152i	−1.41744	+	0.818357i	−0.421363	+	0.906892i	$0.638448\pi$
$524$	−14.2253	−	8.21296i	−0.621434	−	0.358785i
$525$		0			0
$526$	22.9496	−	13.2499i	1.00065	−	0.577725i
$527$	−45.5218			−1.98296
$528$		0			0
$529$	−4.09091	+	7.08566i	−0.177865	+	0.308072i
$530$	6.13957	−	10.6340i	0.266686	−	0.461914i
$531$		0			0
$532$		−	5.96491i		−	0.258612i
$533$	4.49300	−	2.59404i	0.194613	−	0.112360i
$534$		0			0
$535$		−	55.9529i		−	2.41906i
$536$	0.996818	+	0.575513i	0.0430560	+	0.0248584i
$537$		0			0
$538$	−10.8991	+	6.29261i	−0.469895	+	0.271294i
$539$	−0.248126	+	0.429768i	−0.0106876	+	0.0185114i
$540$		0			0
$541$			34.2078i			1.47071i	0.677683	+	0.735355i	$0.262984\pi$
$541$			34.2078i			1.47071i	−0.677683	+	0.735355i	$0.737016\pi$
$542$			0.341920i			0.0146867i
$543$		0			0
$544$	3.16333	+	5.47905i	0.135627	+	0.234912i
$545$	12.1408	+	21.0285i	0.520056	+	0.900764i
$546$		0			0
$547$	14.8414	+	8.56867i	0.634571	+	0.366370i	0.782520	−	0.622625i	$-0.213934\pi$
$547$	14.8414	+	8.56867i	0.634571	+	0.366370i	−0.147949	+	0.988995i	$0.547267\pi$
$548$	5.96292	+	10.3281i	0.254724	+	0.441194i
$549$		0			0
$550$	6.30124	−	3.63802i	0.268686	−	0.155126i
$551$	−23.4734			−1.00000
$552$		0			0
$553$			5.49908i			0.233844i
$554$	−0.497703	−	0.862047i	−0.0211454	−	0.0366249i
$555$		0			0
$556$	−3.70014	+	6.40883i	−0.156921	+	0.271795i
$557$	−1.53311	−	0.885143i	−0.0649601	−	0.0375047i	0.467168	−	0.884168i	$-0.345274\pi$
$557$	−1.53311	−	0.885143i	−0.0649601	−	0.0375047i	−0.532128	+	0.846664i	$0.678608\pi$
$558$		0			0
$559$	6.70609	+	11.6153i	0.283637	+	0.491274i
$560$		−	10.2560i		−	0.433395i
$561$		0			0
$562$	−8.74542	+	15.1475i	−0.368903	+	0.638959i
$563$	8.77097	−	5.06392i	0.369652	−	0.213419i	−0.303654	−	0.952782i	$-0.598207\pi$
$563$	8.77097	−	5.06392i	0.369652	−	0.213419i	0.673307	+	0.739363i	$0.264873\pi$
$564$		0			0
$565$	43.0950	−	74.6427i	1.81302	−	3.14024i
$566$	−20.2489			−0.851126
$567$		0			0
$568$	−5.80188	+	3.34971i	−0.243441	+	0.140551i
$569$	24.7799	+	14.3067i	1.03883	+	0.599768i	0.919501	−	0.393087i	$-0.128593\pi$
$569$	24.7799	+	14.3067i	1.03883	+	0.599768i	0.119327	+	0.992855i	$0.461926\pi$
$570$		0			0
$571$	28.7818			1.20448			0.602241	−	0.798315i	$-0.294275\pi$
$571$	28.7818			1.20448			0.602241	+	0.798315i	$0.294275\pi$
$572$		−	1.73273i		−	0.0724492i
$573$		0			0
$574$			4.50584i			0.188070i
$575$	−40.0704	−	23.1347i	−1.67105	−	0.964782i
$576$		0			0
$577$	18.2753	+	10.5513i	0.760812	+	0.439255i	0.829587	−	0.558377i	$-0.188576\pi$
$577$	18.2753	+	10.5513i	0.760812	+	0.439255i	−0.0687750	+	0.997632i	$0.521909\pi$
$578$	19.9416	+	11.5133i	0.829463	+	0.478891i
$579$		0			0
$580$	−40.3599			−1.67585
$581$	−20.5420	−	35.5798i	−0.852225	−	1.47610i
$582$		0			0
$583$	0.900868	+	1.56035i	0.0373101	+	0.0646231i
$584$		−	1.65116i		−	0.0683255i
$585$		0			0
$586$			10.8016i			0.446212i
$587$		−	1.42564i		−	0.0588425i	−0.999567	−	0.0294212i	$-0.990634\pi$
$587$		−	1.42564i		−	0.0588425i	0.999567	−	0.0294212i	$-0.00936643\pi$
$588$		0			0
$589$	−8.63211	+	14.9513i	−0.355680	+	0.616056i
$590$		−	37.6356i		−	1.54943i
$591$		0			0
$592$	4.92622	+	3.56824i	0.202466	+	0.146654i
$593$	−35.9950			−1.47814			−0.739069	−	0.673630i	$-0.764734\pi$
$593$	−35.9950			−1.47814			−0.739069	+	0.673630i	$0.764734\pi$
$594$		0			0
$595$	−32.4431	−	56.1932i	−1.33004	−	2.30369i
$596$	−20.2498			−0.829463
$597$		0			0
$598$	−9.54245	+	5.50933i	−0.390220	+	0.225293i
$599$	−5.03565	+	8.72200i	−0.205751	+	0.356371i	−0.950372	−	0.311117i	$-0.899297\pi$
$599$	−5.03565	+	8.72200i	−0.205751	+	0.356371i	0.744621	+	0.667488i	$0.232630\pi$
$600$		0			0
$601$	−2.33730	−	4.04833i	−0.0953406	−	0.165135i	0.814410	−	0.580290i	$-0.197061\pi$
$601$	−2.33730	−	4.04833i	−0.0953406	−	0.165135i	−0.909751	+	0.415155i	$0.863727\pi$
$602$	−11.6485			−0.474757
$603$		0			0
$604$	−5.13849	+	8.90013i	−0.209082	+	0.362141i
$605$		−	43.8688i		−	1.78352i
$606$		0			0
$607$		−	16.8691i		−	0.684695i	−0.939573	−	0.342347i	$-0.888778\pi$
$607$		−	16.8691i		−	0.684695i	0.939573	−	0.342347i	$-0.111222\pi$
$608$	2.39940			0.0973085
$609$		0			0
$610$		−	16.6993i		−	0.676133i
$611$	−4.32934	+	2.49955i	−0.175146	+	0.101121i
$612$		0			0
$613$	−1.50842	+	2.61266i	−0.0609244	+	0.105524i	−0.894879	−	0.446309i	$-0.852738\pi$
$613$	−1.50842	+	2.61266i	−0.0609244	+	0.105524i	0.833954	+	0.551833i	$0.186072\pi$
$614$	7.57381	−	4.37274i	0.305654	−	0.176470i
$615$		0			0
$616$	1.30326	+	0.752439i	0.0525100	+	0.0303166i
$617$	−0.449061			−0.0180785			−0.00903925	−	0.999959i	$-0.502877\pi$
$617$	−0.449061			−0.0180785			−0.00903925	+	0.999959i	$0.502877\pi$
$618$		0			0
$619$	−5.72174	+	9.91034i	−0.229976	+	0.398330i	−0.957801	−	0.287433i	$-0.907198\pi$
$619$	−5.72174	+	9.91034i	−0.229976	+	0.398330i	0.727825	+	0.685763i	$0.240531\pi$
$620$	−14.8420	+	25.7070i	−0.596068	+	1.03242i
$621$		0			0
$622$	−5.29566	−	9.17236i	−0.212337	−	0.367778i
$623$	20.1712	+	11.6458i	0.808140	+	0.466580i
$624$		0			0
$625$	−29.6879	+	51.4209i	−1.18752	+	2.05684i
$626$	−1.84636	+	3.19799i	−0.0737954	+	0.127817i
$627$		0			0
$628$	−7.03781	+	12.1898i	−0.280839	+	0.486428i
$629$	38.2785	+	3.96732i	1.52626	+	0.158187i
$630$		0			0
$631$	2.21908	+	1.28118i	0.0883400	+	0.0510031i	0.543519	−	0.839397i	$-0.317091\pi$
$631$	2.21908	+	1.28118i	0.0883400	+	0.0510031i	−0.455179	+	0.890400i	$0.650425\pi$
$632$	−2.21202			−0.0879892
$633$		0			0
$634$	−1.09211	−	0.630529i	−0.0433732	−	0.0250415i
$635$	−13.9637	+	8.06192i	−0.554131	+	0.319928i
$636$		0			0
$637$	−2.03219	−	1.17329i	−0.0805185	−	0.0464874i
$638$	2.96103	−	5.12866i	0.117228	−	0.203046i
$639$		0			0
$640$	4.12550			0.163075
$641$	10.1296	+	17.5449i	0.400094	+	0.692983i	0.993737	−	0.111746i	$-0.0356442\pi$
$641$	10.1296	+	17.5449i	0.400094	+	0.692983i	−0.593643	+	0.804728i	$0.702311\pi$
$642$		0			0
$643$	24.6651	−	14.2404i	0.972698	−	0.561588i	0.0726405	−	0.997358i	$-0.476857\pi$
$643$	24.6651	−	14.2404i	0.972698	−	0.561588i	0.900058	+	0.435771i	$0.143524\pi$
$644$		−	9.56972i		−	0.377100i
$645$		0			0
$646$	13.1464	−	7.59009i	0.517239	−	0.298628i
$647$	14.3995	−	8.31354i	0.566102	−	0.326839i	−0.189489	−	0.981883i	$-0.560683\pi$
$647$	14.3995	−	8.31354i	0.566102	−	0.326839i	0.755591	+	0.655044i	$0.227350\pi$
$648$		0			0
$649$	4.78248	+	2.76116i	0.187729	+	0.108385i
$650$	17.2027	+	29.7960i	0.674746	+	1.16870i
$651$		0			0
$652$	−14.1012	+	8.14132i	−0.552245	+	0.318839i
$653$	−28.7228	−	16.5831i	−1.12401	−	0.648948i	−0.181589	−	0.983374i	$-0.558124\pi$
$653$	−28.7228	−	16.5831i	−1.12401	−	0.648948i	−0.942422	+	0.334426i	$0.891457\pi$
$654$		0			0
$655$	−33.8826	+	58.6864i	−1.32390	+	2.29307i
$656$	−1.81248			−0.0707656
$657$		0			0
$658$		−	4.34171i		−	0.169258i
$659$	18.7987			0.732294			0.366147	−	0.930557i	$-0.380677\pi$
$659$	18.7987			0.732294			0.366147	+	0.930557i	$0.380677\pi$
$660$		0			0
$661$	−10.5279	−	6.07830i	−0.409488	−	0.236418i	0.281081	−	0.959684i	$-0.409307\pi$
$661$	−10.5279	−	6.07830i	−0.409488	−	0.236418i	−0.690570	+	0.723266i	$0.742640\pi$
$662$	4.32135	−	7.48480i	0.167954	−	0.290905i
$663$		0			0
$664$	14.3120	−	8.26306i	0.555415	−	0.320669i
$665$	−24.6083			−0.954267
$666$		0			0
$667$	−37.6592			−1.45817
$668$	7.22703	−	4.17253i	0.279622	−	0.161440i
$669$		0			0
$670$	2.37428	−	4.11237i	0.0917264	−	0.158875i
$671$	2.12203	+	1.22515i	0.0819200	+	0.0472965i
$672$		0			0
$673$	15.4933			0.597222			0.298611	−	0.954375i	$-0.403477\pi$
$673$	15.4933			0.597222			0.298611	+	0.954375i	$0.403477\pi$
$674$		−	3.85309i		−	0.148415i
$675$		0			0
$676$	−4.80662			−0.184870
$677$	−17.3613	+	30.0707i	−0.667249	+	1.15571i	0.311421	+	0.950272i	$0.399195\pi$
$677$	−17.3613	+	30.0707i	−0.667249	+	1.15571i	−0.978670	+	0.205437i	$0.934138\pi$
$678$		0			0
$679$	−3.66266	−	2.11464i	−0.140560	−	0.0811524i
$680$	22.6038	−	13.0503i	0.866817	−	0.500457i
$681$		0			0
$682$	−2.17778	−	3.77203i	−0.0833916	−	0.144438i
$683$	−36.3425	−	20.9823i	−1.39061	−	0.802867i	−0.397224	−	0.917722i	$-0.630026\pi$
$683$	−36.3425	−	20.9823i	−1.39061	−	0.802867i	−0.993382	+	0.114855i	$0.963360\pi$
$684$		0			0
$685$	42.6085	−	24.6001i	1.62799	−	0.939920i
$686$	16.8356	−	9.72001i	0.642784	−	0.371112i
$687$		0			0
$688$		−	4.68563i		−	0.178638i
$689$	−7.37825	+	4.25984i	−0.281089	+	0.162287i
$690$		0			0
$691$	4.67543	+	8.09809i	0.177862	+	0.308066i	0.941148	−	0.337995i	$-0.109749\pi$
$691$	4.67543	+	8.09809i	0.177862	+	0.308066i	−0.763286	+	0.646061i	$0.776415\pi$
$692$	−8.59165			−0.326605
$693$		0			0
$694$	−12.0067	+	20.7963i	−0.455769	+	0.789415i
$695$	26.4396	+	15.2649i	1.00291	+	0.579032i
$696$		0			0
$697$	−9.93069	+	5.73349i	−0.376152	+	0.217171i
$698$	−23.9390	−	13.8212i	−0.906103	−	0.523139i
$699$		0			0
$700$	−29.8811			−1.12940
$701$	0.124833	+	0.0720722i	0.00471486	+	0.00272213i	0.502356	−	0.864661i	$-0.332467\pi$
$701$	0.124833	+	0.0720722i	0.00471486	+	0.00272213i	−0.497641	+	0.867383i	$0.665800\pi$
$702$		0			0
$703$	8.56164	−	11.8200i	0.322908	−	0.445799i
$704$	−0.302670	+	0.524240i	−0.0114073	+	0.0197581i
$705$		0			0
$706$	−4.28009	+	7.41334i	−0.161083	+	0.279005i
$707$	−15.0066	+	25.9921i	−0.564380	+	0.977535i
$708$		0			0
$709$	−24.2810	−	14.0186i	−0.911891	−	0.526480i	−0.0308516	−	0.999524i	$-0.509822\pi$
$709$	−24.2810	−	14.0186i	−0.911891	−	0.526480i	−0.881039	+	0.473044i	$0.843155\pi$
$710$	13.8193	+	23.9356i	0.518627	+	0.898289i
$711$		0			0
$712$	−4.68456	+	8.11389i	−0.175561	+	0.304081i
$713$	−13.8488	+	23.9868i	−0.518642	+	0.898314i
$714$		0			0
$715$	−7.14839			−0.267335
$716$	16.9478	+	9.78479i	0.633367	+	0.365675i
$717$		0			0
$718$	−17.3293	+	10.0051i	−0.646724	+	0.373386i
$719$	20.1693	−	34.9342i	0.752187	−	1.30283i	−0.194573	−	0.980888i	$-0.562332\pi$
$719$	20.1693	−	34.9342i	0.752187	−	1.30283i	0.946760	−	0.321939i	$-0.104335\pi$
$720$		0			0
$721$	34.7851	−	20.0832i	1.29546	−	0.747936i
$722$			13.2429i			0.492849i
$723$		0			0
$724$	−22.6597			−0.842143
$725$			117.590i			4.36717i
$726$		0			0
$727$		−	29.2365i		−	1.08432i	−0.840275	−	0.542160i	$-0.817607\pi$
$727$		−	29.2365i		−	1.08432i	0.840275	−	0.542160i	$-0.182393\pi$
$728$	−3.55798	+	6.16260i	−0.131867	+	0.228401i
$729$		0			0
$730$	−6.81186			−0.252118
$731$	−14.8222	−	25.6728i	−0.548219	−	0.949542i
$732$		0			0
$733$	12.3469	−	21.3855i	0.456044	−	0.789892i	−0.542703	−	0.839924i	$-0.682599\pi$
$733$	12.3469	−	21.3855i	0.456044	−	0.789892i	0.998748	+	0.0500327i	$0.0159326\pi$
$734$	21.8883	−	12.6372i	0.807912	−	0.466448i
$735$		0			0
$736$	3.84944			0.141892
$737$	0.348381	+	0.603414i	0.0128328	+	0.0222270i
$738$		0			0
$739$	51.9399			1.91064			0.955319	−	0.295576i	$-0.0955116\pi$
$739$	51.9399			1.91064			0.955319	+	0.295576i	$0.0955116\pi$
$740$	14.7208	−	20.3231i	0.541147	−	0.747093i
$741$		0			0
$742$		−	7.39934i		−	0.271638i
$743$	14.7936	−	25.6233i	0.542726	−	0.940028i	−0.456021	−	0.889969i	$-0.650726\pi$
$743$	14.7936	−	25.6233i	0.542726	−	0.940028i	0.998746	−	0.0500592i	$-0.0159410\pi$
$744$		0			0
$745$			83.5405i			3.06069i
$746$		−	12.2537i		−	0.448640i
$747$		0			0
$748$			3.82978i			0.140031i
$749$	−16.8584	−	29.1997i	−0.615994	−	1.06693i
$750$		0			0
$751$	5.43236	+	9.40913i	0.198230	+	0.343344i	0.947955	−	0.318406i	$-0.103147\pi$
$751$	5.43236	+	9.40913i	0.198230	+	0.343344i	−0.749725	+	0.661750i	$0.769814\pi$
$752$	1.74646			0.0636870
$753$		0			0
$754$	24.2513	+	14.0015i	0.883182	+	0.509905i
$755$	36.7175	+	21.1989i	1.33629	+	0.771505i
$756$		0			0
$757$	−25.6528	−	14.8107i	−0.932368	−	0.538303i	−0.0448084	−	0.998996i	$-0.514268\pi$
$757$	−25.6528	−	14.8107i	−0.932368	−	0.538303i	−0.887560	+	0.460693i	$0.847601\pi$
$758$		−	30.8360i		−	1.12001i
$759$		0			0
$760$		−	9.89872i		−	0.359064i
$761$	52.4236			1.90035			0.950176	−	0.311714i	$-0.100903\pi$
$761$	52.4236			1.90035			0.950176	+	0.311714i	$0.100903\pi$
$762$		0			0
$763$	12.6717	+	7.31599i	0.458745	+	0.264857i
$764$	6.29116	−	3.63220i	0.227606	−	0.131408i
$765$		0			0
$766$	−15.3582			−0.554913
$767$	−13.0564	+	22.6144i	−0.471440	+	0.816558i
$768$		0			0
$769$	10.8810	−	6.28216i	0.392379	−	0.226540i	−0.290811	−	0.956780i	$-0.593925\pi$
$769$	10.8810	−	6.28216i	0.392379	−	0.226540i	0.683191	+	0.730240i	$0.260592\pi$
$770$	3.10419	−	5.37661i	0.111867	−	0.193760i
$771$		0			0
$772$			0.309608i			0.0111431i
$773$	−17.3339	−	30.0232i	−0.623457	−	1.07986i	−0.988837	−	0.149000i	$-0.952394\pi$
$773$	−17.3339	−	30.0232i	−0.623457	−	1.07986i	0.365381	−	0.930858i	$-0.380939\pi$
$774$		0			0
$775$	74.8981	+	43.2425i	2.69042	+	1.55331i
$776$	0.850618	−	1.47331i	0.0305354	−	0.0528889i
$777$		0			0
$778$	2.53797	+	4.39589i	0.0909907	+	0.157600i
$779$			4.34887i			0.155815i
$780$		0			0
$781$	−4.05544			−0.145115
$782$	21.0913	−	12.1770i	0.754222	−	0.435450i
$783$		0			0
$784$	0.409896	+	0.709960i	0.0146391	+	0.0253557i
$785$	50.2892	+	29.0345i	1.79490	+	1.03629i
$786$		0			0
$787$	10.3612	+	17.9462i	0.369338	+	0.639713i	0.989462	−	0.144791i	$-0.0462510\pi$
$787$	10.3612	+	17.9462i	0.369338	+	0.639713i	−0.620124	+	0.784504i	$0.712918\pi$
$788$	7.41930	+	12.8506i	0.264302	+	0.457784i
$789$		0			0
$790$			9.12567i			0.324677i
$791$		−	51.9376i		−	1.84669i
$792$		0			0
$793$	−5.79325	+	10.0342i	−0.205724	+	0.356325i
$794$	31.2498	−	18.0421i	1.10902	−	0.640290i
$795$		0			0
$796$	14.5279	+	8.38767i	0.514927	+	0.297293i
$797$			52.0326i			1.84309i	0.388274	+	0.921544i	$0.373071\pi$
$797$			52.0326i			1.84309i	−0.388274	+	0.921544i	$0.626929\pi$
$798$		0			0
$799$	9.56896	−	5.52464i	0.338525	−	0.195448i
$800$		−	12.0198i		−	0.424963i
$801$		0			0
$802$	−15.4133	+	26.6967i	−0.544264	+	0.942692i
$803$	0.499757	−	0.865604i	0.0176360	−	0.0305465i
$804$		0			0
$805$	−39.4799			−1.39148
$806$	17.8364	−	10.2978i	0.628260	−	0.362726i
$807$		0			0
$808$	−10.4554	−	6.03643i	−0.367820	−	0.212361i
$809$	−30.9772	+	17.8847i	−1.08910	+	0.628792i	−0.933337	−	0.359003i	$-0.883117\pi$
$809$	−30.9772	+	17.8847i	−1.08910	+	0.628792i	−0.155763	+	0.987794i	$0.549784\pi$
$810$		0			0
$811$	13.6185	+	23.5880i	0.478212	+	0.828287i	0.999688	−	0.0249787i	$-0.00795179\pi$
$811$	13.6185	+	23.5880i	0.478212	+	0.828287i	−0.521476	+	0.853266i	$0.674618\pi$
$812$	−21.0623	+	12.1603i	−0.739142	+	0.426744i
$813$		0			0
$814$	1.50252	+	3.36164i	0.0526634	+	0.117825i
$815$	33.5870	+	58.1744i	1.17650	+	2.03776i
$816$		0			0
$817$	−11.2427			−0.393332
$818$	12.0840	+	20.9301i	0.422507	+	0.731804i
$819$		0			0
$820$			7.47741i			0.261122i
$821$	−37.8405			−1.32064			−0.660321	−	0.750983i	$-0.729580\pi$
$821$	−37.8405			−1.32064			−0.660321	+	0.750983i	$0.729580\pi$
$822$		0			0
$823$	25.4542			0.887279			0.443640	−	0.896205i	$-0.353687\pi$
$823$	25.4542			0.887279			0.443640	+	0.896205i	$0.353687\pi$
$824$	8.07850	+	13.9924i	0.281428	+	0.487447i
$825$		0			0
$826$	−11.3395	−	19.6406i	−0.394552	−	0.683384i
$827$	−37.0494	+	21.3905i	−1.28833	+	0.743820i	−0.978357	−	0.206923i	$-0.933655\pi$
$827$	−37.0494	+	21.3905i	−1.28833	+	0.743820i	−0.309978	+	0.950744i	$0.600322\pi$
$828$		0			0
$829$	−32.3114	−	18.6550i	−1.12222	−	0.647915i	−0.180254	−	0.983620i	$-0.557692\pi$
$829$	−32.3114	−	18.6550i	−1.12222	−	0.647915i	−0.941967	+	0.335705i	$0.891025\pi$
$830$	−34.0893	−	59.0443i	−1.18326	−	2.04946i
$831$		0			0
$832$	−2.47892	−	1.43120i	−0.0859410	−	0.0496181i
$833$	4.49167	+	2.59327i	0.155627	+	0.0898515i
$834$		0			0
$835$	−17.2138	−	29.8151i	−0.595707	−	1.03179i
$836$	1.25786	+	0.726227i	0.0435041	+	0.0251171i
$837$		0			0
$838$	28.1379	−	16.2454i	0.972008	−	0.561189i
$839$	−26.9506	−	46.6798i	−0.930437	−	1.61156i	−0.782574	−	0.622557i	$-0.786094\pi$
$839$	−26.9506	−	46.6798i	−0.930437	−	1.61156i	−0.147863	−	0.989008i	$-0.547240\pi$
$840$		0			0
$841$	33.3539	+	57.7706i	1.15013	+	1.99209i
$842$	4.88854			0.168470
$843$		0			0
$844$	2.90798			0.100097
$845$			19.8297i			0.682163i
$846$		0			0
$847$	−13.2175	−	22.8934i	−0.454160	−	0.786628i
$848$	2.97640			0.102210
$849$		0			0
$850$	−38.0225	−	65.8568i	−1.30416	−	2.25887i
$851$	13.7357	−	18.9632i	0.470855	−	0.650050i
$852$		0			0
$853$	6.35746	−	3.67048i	0.217675	−	0.125675i	−0.387198	−	0.921997i	$-0.626557\pi$
$853$	6.35746	−	3.67048i	0.217675	−	0.125675i	0.604873	+	0.796322i	$0.293224\pi$
$854$	−5.03144	−	8.71471i	−0.172172	−	0.298211i
$855$		0			0
$856$	11.7456	−	6.78135i	0.401458	−	0.231782i
$857$	14.7608	+	8.52218i	0.504221	+	0.291112i	0.730455	−	0.682961i	$-0.239308\pi$
$857$	14.7608	+	8.52218i	0.504221	+	0.291112i	−0.226234	+	0.974073i	$0.572641\pi$
$858$		0			0
$859$	−11.2707	+	6.50714i	−0.384551	+	0.222021i	−0.679797	−	0.733401i	$-0.737932\pi$
$859$	−11.2707	+	6.50714i	−0.384551	+	0.222021i	0.295245	+	0.955421i	$0.404599\pi$
$860$	−19.3306			−0.659167
$861$		0			0
$862$	−2.28233	+	3.95310i	−0.0777363	+	0.134643i
$863$	23.6154	−	40.9031i	0.803879	−	1.39236i	−0.113167	−	0.993576i	$-0.536099\pi$
$863$	23.6154	−	40.9031i	0.803879	−	1.39236i	0.917046	−	0.398783i	$-0.130567\pi$
$864$		0			0
$865$			35.4449i			1.20516i
$866$	−17.4687	+	10.0856i	−0.593611	+	0.342721i
$867$		0			0
$868$			17.8874i			0.607137i
$869$	−1.15963	−	0.669511i	−0.0393377	−	0.0227116i
$870$		0			0
$871$	−2.85330	+	1.64735i	−0.0966803	+	0.0558184i
$872$	−2.94287	+	5.09721i	−0.0996583	+	0.172613i
$873$		0			0
$874$		−	9.23634i		−	0.312424i
$875$			71.9947i			2.43386i
$876$		0			0
$877$	−16.6836	−	28.8969i	−0.563366	−	0.975779i	−0.997200	−	0.0747860i	$-0.976173\pi$
$877$	−16.6836	−	28.8969i	−0.563366	−	0.975779i	0.433833	−	0.900993i	$-0.357161\pi$
$878$	12.3280	+	21.3528i	0.416051	+	0.720622i
$879$		0			0
$880$	2.16275	+	1.24867i	0.0729064	+	0.0420925i
$881$	4.32602	+	7.49288i	0.145747	+	0.252441i	0.929651	−	0.368440i	$-0.120108\pi$
$881$	4.32602	+	7.49288i	0.145747	+	0.252441i	−0.783904	+	0.620882i	$0.786775\pi$
$882$		0			0
$883$	−1.30842	+	0.755415i	−0.0440318	+	0.0254217i	−0.521854	−	0.853035i	$-0.674760\pi$
$883$	−1.30842	+	0.755415i	−0.0440318	+	0.0254217i	0.477823	+	0.878456i	$0.341426\pi$
$884$	−18.1095			−0.609088
$885$		0			0
$886$			31.3507i			1.05325i
$887$	0.0315682	+	0.0546777i	0.00105996	+	0.00183590i	0.866555	−	0.499082i	$-0.166329\pi$
$887$	0.0315682	+	0.0546777i	0.00105996	+	0.00183590i	−0.865495	+	0.500918i	$0.832996\pi$
$888$		0			0
$889$	−4.85807	+	8.41442i	−0.162934	+	0.282210i
$890$	33.4739	+	19.3261i	1.12205	+	0.647814i
$891$		0			0
$892$	12.5979	+	21.8203i	0.421811	+	0.730597i
$893$		−	4.19046i		−	0.140229i
$894$		0			0
$895$	40.3672	−	69.9180i	1.34933	−	2.33710i
$896$	2.15294	−	1.24300i	0.0719247	−	0.0415258i
$897$		0			0
$898$	−19.1350	+	33.1427i	−0.638542	+	1.10599i
$899$	70.3912			2.34768
$900$		0			0
$901$	16.3078	−	9.41534i	0.543293	−	0.313670i
$902$	−0.950178	−	0.548585i	−0.0316375	−	0.0182659i
$903$		0			0
$904$	20.8920			0.694858
$905$			93.4828i			3.10747i
$906$		0			0
$907$		−	3.32728i		−	0.110481i	−0.998473	−	0.0552403i	$-0.982408\pi$
$907$		−	3.32728i		−	0.110481i	0.998473	−	0.0552403i	$-0.0175925\pi$
$908$	−11.4991	−	6.63903i	−0.381612	−	0.220324i
$909$		0			0
$910$	25.4238	+	14.6784i	0.842791	+	0.486585i
$911$	−18.5335	−	10.7003i	−0.614043	−	0.354518i	0.160503	−	0.987035i	$-0.448688\pi$
$911$	−18.5335	−	10.7003i	−0.614043	−	0.354518i	−0.774546	+	0.632518i	$0.782022\pi$
$912$		0			0
$913$	10.0039			0.331082
$914$	−1.62582	−	2.81600i	−0.0537772	−	0.0931449i
$915$		0			0
$916$	3.45629	+	5.98648i	0.114199	+	0.197799i
$917$			40.8349i			1.34849i
$918$		0			0
$919$			15.8634i			0.523286i	0.965165	+	0.261643i	$0.0842643\pi$
$919$			15.8634i			0.523286i	−0.965165	+	0.261643i	$0.915736\pi$
$920$		−	15.8809i		−	0.523577i
$921$		0			0
$922$	1.19339	−	2.06701i	0.0393022	−	0.0680734i
$923$		−	19.1765i		−	0.631202i
$924$		0			0
$925$	−59.2120	−	42.8894i	−1.94688	−	1.41020i
$926$	5.06685			0.166507
$927$		0			0
$928$	−4.89152	−	8.47236i	−0.160572	−	0.278119i
$929$	−53.9091			−1.76870			−0.884351	−	0.466823i	$-0.845398\pi$
$929$	−53.9091			−1.76870			−0.884351	+	0.466823i	$0.845398\pi$
$930$		0			0
$931$	1.70348	−	0.983503i	0.0558292	−	0.0322330i
$932$	12.4941	−	21.6404i	0.409257	−	0.708854i
$933$		0			0
$934$	5.51497	+	9.55222i	0.180455	+	0.312558i
$935$	15.7998			0.516708
$936$		0			0
$937$	−16.6169	+	28.7812i	−0.542849	+	0.940242i	0.455890	+	0.890036i	$0.349321\pi$
$937$	−16.6169	+	28.7812i	−0.542849	+	0.940242i	−0.998739	+	0.0502059i	$0.984012\pi$
$938$		−	2.86145i		−	0.0934298i
$939$		0			0
$940$		−	7.20504i		−	0.235002i
$941$	12.8333			0.418354			0.209177	−	0.977878i	$-0.432921\pi$
$941$	12.8333			0.418354			0.209177	+	0.977878i	$0.432921\pi$
$942$		0			0
$943$			6.97705i			0.227204i
$944$	7.90047	−	4.56134i	0.257139	−	0.148459i
$945$		0			0
$946$	1.41820	−	2.45640i	0.0461097	−	0.0798643i
$947$	37.8981	−	21.8805i	1.23152	−	0.711020i	0.264175	−	0.964475i	$-0.414900\pi$
$947$	37.8981	−	21.8805i	1.23152	−	0.711020i	0.967347	+	0.253455i	$0.0815670\pi$
$948$		0			0
$949$	4.09309	+	2.36315i	0.132867	+	0.0767110i
$950$	−28.8402			−0.935700
$951$		0			0
$952$	7.86405	−	13.6209i	0.254875	−	0.441457i
$953$	−23.1853	+	40.1581i	−0.751045	+	1.30085i	0.196272	+	0.980550i	$0.437117\pi$
$953$	−23.1853	+	40.1581i	−0.751045	+	1.30085i	−0.947317	+	0.320299i	$0.896217\pi$
$954$		0			0
$955$	−14.9847	−	25.9542i	−0.484892	−	0.839857i
$956$	−3.28098	−	1.89428i	−0.106115	−	0.0612653i
$957$		0			0
$958$	14.1530	−	24.5137i	0.457263	−	0.792002i
$959$	14.8238	−	25.6757i	0.478687	−	0.829110i
$960$		0			0
$961$	10.3857	−	17.9885i	0.335021	−	0.580274i
$962$	−15.8958	+	7.10481i	−0.512501	+	0.229068i
$963$		0			0
$964$	4.98462	+	2.87787i	0.160544	+	0.0926901i
$965$	1.27729			0.0411174
$966$		0			0
$967$	−13.6711	−	7.89300i	−0.439632	−	0.253822i	0.263809	−	0.964575i	$-0.415021\pi$
$967$	−13.6711	−	7.89300i	−0.439632	−	0.253822i	−0.703442	+	0.710753i	$0.748354\pi$
$968$	9.20894	−	5.31678i	0.295986	−	0.170888i
$969$		0			0
$970$	−6.07816	−	3.50923i	−0.195158	−	0.112674i
$971$	16.9504	−	29.3589i	0.543963	−	0.942172i	−0.454708	−	0.890640i	$-0.650256\pi$
$971$	16.9504	−	29.3589i	0.543963	−	0.942172i	0.998671	−	0.0515314i	$-0.0164102\pi$
$972$		0			0
$973$	18.3971			0.589784
$974$	14.3648	+	24.8805i	0.460277	+	0.797224i
$975$		0			0
$976$	3.50551	−	2.02391i	0.112209	−	0.0647837i
$977$			34.0650i			1.08984i	0.838490	+	0.544918i	$0.183439\pi$
$977$			34.0650i			1.08984i	−0.838490	+	0.544918i	$0.816561\pi$
$978$		0			0
$979$	−4.91167	+	2.83575i	−0.156978	+	0.0906311i
$980$	2.92894	−	1.69102i	0.0935616	−	0.0540178i
$981$		0			0
$982$	−7.33687	−	4.23594i	−0.234129	−	0.135174i
$983$	−6.49712	−	11.2533i	−0.207226	−	0.358926i	0.743614	−	0.668610i	$-0.233110\pi$
$983$	−6.49712	−	11.2533i	−0.207226	−	0.358926i	−0.950840	+	0.309684i	$0.899777\pi$
$984$		0			0
$985$	53.0152	−	30.6083i	1.68921	−	0.975263i
$986$	−53.6017	−	30.9470i	−1.70703	−	0.985552i
$987$		0			0
$988$	−3.43403	+	5.94791i	−0.109251	+	0.189228i
$989$	−18.0370			−0.573545
$990$		0			0
$991$		−	36.1067i		−	1.14697i	−0.819217	−	0.573483i	$-0.805592\pi$
$991$		−	36.1067i		−	1.14697i	0.819217	−	0.573483i	$-0.194408\pi$
$992$	−7.19523			−0.228449
$993$		0			0
$994$	14.4235	+	8.32740i	0.457485	+	0.264129i
$995$	34.6033	−	59.9348i	1.09700	−	1.90006i
$996$		0			0
$997$	−40.9489	+	23.6418i	−1.29686	+	0.748745i	−0.979861	−	0.199680i	$-0.936010\pi$
$997$	−40.9489	+	23.6418i	−1.29686	+	0.748745i	−0.317003	+	0.948425i	$0.602676\pi$
$998$	1.32342			0.0418921
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.t.a.397.21		76
3.2	odd	2		666.2.t.a.619.14	yes	76
9.4	even	3		1998.2.k.a.1063.21		76
9.5	odd	6		666.2.k.a.175.2	✓	76
37.11	even	6		1998.2.k.a.1639.18		76
111.11	odd	6		666.2.k.a.529.21	yes	76
333.85	even	6	inner	1998.2.t.a.307.21		76
333.122	odd	6		666.2.t.a.85.14	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.2	✓	76	9.5	odd	6
666.2.k.a.529.21	yes	76	111.11	odd	6
666.2.t.a.85.14	yes	76	333.122	odd	6
666.2.t.a.619.14	yes	76	3.2	odd	2
1998.2.k.a.1063.21		76	9.4	even	3
1998.2.k.a.1639.18		76	37.11	even	6
1998.2.t.a.307.21		76	333.85	even	6	inner
1998.2.t.a.397.21		76	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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.57279 - 2.06275i) q^{5} -2.48600 q^{7} -1.00000i q^{8} -4.12550 q^{10} +(0.302670 - 0.524240i) q^{11} +(2.47892 + 1.43120i) q^{13} +(-2.15294 + 1.24300i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.47905 - 3.16333i) q^{17} +(-2.07794 + 1.19970i) q^{19} +(-3.57279 + 2.06275i) q^{20} -0.605341i q^{22} +(-3.33371 + 1.92472i) q^{23} +(6.00988 + 10.4094i) q^{25} +2.86241 q^{26} +(-1.24300 + 2.15294i) q^{28} +(8.47236 + 4.89152i) q^{29} +(6.23125 - 3.59761i) q^{31} +(-0.866025 - 0.500000i) q^{32} -6.32666 q^{34} +(8.88196 + 5.12800i) q^{35} +(-5.55330 + 2.48211i) q^{37} +(-1.19970 + 2.07794i) q^{38} +(-2.06275 + 3.57279i) q^{40} +(0.906242 - 1.56966i) q^{41} +(4.05787 + 2.34281i) q^{43} +(-0.302670 - 0.524240i) q^{44} +(-1.92472 + 3.33371i) q^{46} +(-0.873232 + 1.51248i) q^{47} -0.819791 q^{49} +(10.4094 + 6.00988i) q^{50} +(2.47892 - 1.43120i) q^{52} +(-1.48820 + 2.57764i) q^{53} +(-2.16275 + 1.24867i) q^{55} +2.48600i q^{56} +9.78303 q^{58} +9.12268i q^{59} +4.04781i q^{61} +(3.59761 - 6.23125i) q^{62} -1.00000 q^{64} +(-5.90443 - 10.2268i) q^{65} +(-0.575513 + 0.996818i) q^{67} +(-5.47905 + 3.16333i) q^{68} +10.2560 q^{70} +(-3.34971 - 5.80188i) q^{71} +1.65116 q^{73} +(-3.56824 + 4.92622i) q^{74} +2.39940i q^{76} +(-0.752439 + 1.30326i) q^{77} -2.21202i q^{79} +4.12550i q^{80} -1.81248i q^{82} +(8.26306 + 14.3120i) q^{83} +(13.0503 + 22.6038i) q^{85} +4.68563 q^{86} +(-0.524240 - 0.302670i) q^{88} +(-8.11389 - 4.68456i) q^{89} +(-6.16260 - 3.55798i) q^{91} +3.84944i q^{92} +1.74646i q^{94} +9.89872 q^{95} +(1.47331 + 0.850618i) q^{97} +(-0.709960 + 0.409896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) \) 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more