LMFDB - Embedded newform 2970.2.t.a.791.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2970,2,Mod(791,2970)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2970, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2970.791"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2970.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7155694003$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 990)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			791.5
Character	$\chi$	$=$	2970.791
Dual form			2970.2.t.a.2771.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.700188 + 0.404254i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(3.25169 + 0.653075i) q^{11} +(-1.59171 + 0.918976i) q^{13} +(-0.700188 + 0.404254i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.50173 q^{17} +1.87055i q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.19142 + 2.48951i) q^{22} +(4.50121 - 2.59877i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.83795i q^{26} -0.808507i q^{28} +(-0.0530153 + 0.0918253i) q^{29} +(-3.25998 - 5.64645i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.25087 + 5.63067i) q^{34} -0.808507 q^{35} -4.15951 q^{37} +(-1.61995 - 0.935276i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-1.74087 - 3.01528i) q^{41} +(-1.09708 - 0.633401i) q^{43} +(-1.06027 - 3.14258i) q^{44} +5.19755i q^{46} +(4.05652 + 2.34204i) q^{47} +(-3.17316 - 5.49607i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.59171 + 0.918976i) q^{52} -11.0936i q^{53} +(-3.14258 + 1.06027i) q^{55} +(0.700188 + 0.404254i) q^{56} +(-0.0530153 - 0.0918253i) q^{58} +(1.38435 - 0.799257i) q^{59} +(10.7598 + 6.21219i) q^{61} +6.51996 q^{62} +1.00000 q^{64} +(0.918976 - 1.59171i) q^{65} +(-0.221611 - 0.383842i) q^{67} +(-3.25087 - 5.63067i) q^{68} +(0.404254 - 0.700188i) q^{70} +8.87630i q^{71} +14.6450i q^{73} +(2.07976 - 3.60224i) q^{74} +(1.61995 - 0.935276i) q^{76} +(2.01279 + 1.77178i) q^{77} +(10.8062 + 6.23895i) q^{79} -1.00000i q^{80} +3.48175 q^{82} +(-5.77334 + 9.99972i) q^{83} +(-5.63067 + 3.25087i) q^{85} +(1.09708 - 0.633401i) q^{86} +(3.25169 + 0.653075i) q^{88} +7.20794i q^{89} -1.48600 q^{91} +(-4.50121 - 2.59877i) q^{92} +(-4.05652 + 2.34204i) q^{94} +(-0.935276 - 1.61995i) q^{95} +(5.63450 - 9.75924i) q^{97} +6.34632 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2970\mathbb{Z}\right)^\times$.

$n$	$541$	$1541$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	0.700188	+	0.404254i	0.264646	+	0.152793i	0.626452	−	0.779460i	$-0.284506\pi$
$7$	0.700188	+	0.404254i	0.264646	+	0.152793i	−0.361806	+	0.932253i	$0.617840\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	3.25169	+	0.653075i	0.980422	+	0.196910i
$11$	3.25169	+	0.653075i	0.980422	+	0.196910i
$12$		0			0
$13$	−1.59171	+	0.918976i	−0.441462	+	0.254878i	−0.704218	−	0.709984i	$-0.748702\pi$
$13$	−1.59171	+	0.918976i	−0.441462	+	0.254878i	0.262756	+	0.964862i	$0.415369\pi$
$14$	−0.700188	+	0.404254i	−0.187133	+	0.108041i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.50173			1.57690			0.788451	−	0.615098i	$-0.210883\pi$
$17$	6.50173			1.57690			0.788451	+	0.615098i	$0.210883\pi$
$18$		0			0
$19$			1.87055i			0.429134i	0.976709	+	0.214567i	$0.0688340\pi$
$19$			1.87055i			0.429134i	−0.976709	+	0.214567i	$0.931166\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	−2.19142	+	2.48951i	−0.467213	+	0.530765i
$23$	4.50121	−	2.59877i	0.938567	−	0.541882i	0.0490560	−	0.998796i	$-0.484379\pi$
$23$	4.50121	−	2.59877i	0.938567	−	0.541882i	0.889511	+	0.456914i	$0.151045\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	1.83795i		−	0.360452i
$27$		0			0
$28$		−	0.808507i		−	0.152793i
$29$	−0.0530153	+	0.0918253i	−0.00984470	+	0.0170515i	−0.870906	−	0.491450i	$-0.836467\pi$
$29$	−0.0530153	+	0.0918253i	−0.00984470	+	0.0170515i	0.861061	+	0.508502i	$0.169800\pi$
$30$		0			0
$31$	−3.25998	−	5.64645i	−0.585510	−	1.01413i	−0.994812	−	0.101733i	$-0.967561\pi$
$31$	−3.25998	−	5.64645i	−0.585510	−	1.01413i	0.409302	−	0.912399i	$-0.365772\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.25087	+	5.63067i	−0.557519	+	0.965651i
$35$	−0.808507			−0.136663
$36$		0			0
$37$	−4.15951			−0.683820			−0.341910	−	0.939733i	$-0.611074\pi$
$37$	−4.15951			−0.683820			−0.341910	+	0.939733i	$0.611074\pi$
$38$	−1.61995	−	0.935276i	−0.262790	−	0.151722i
$39$		0			0
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	−1.74087	−	3.01528i	−0.271879	−	0.470908i	0.697464	−	0.716620i	$-0.254312\pi$
$41$	−1.74087	−	3.01528i	−0.271879	−	0.470908i	−0.969343	+	0.245712i	$0.920978\pi$
$42$		0			0
$43$	−1.09708	−	0.633401i	−0.167304	−	0.0965928i	0.414010	−	0.910272i	$-0.364128\pi$
$43$	−1.09708	−	0.633401i	−0.167304	−	0.0965928i	−0.581314	+	0.813679i	$0.697461\pi$
$44$	−1.06027	−	3.14258i	−0.159841	−	0.473762i
$45$		0			0
$46$			5.19755i			0.766336i
$47$	4.05652	+	2.34204i	0.591705	+	0.341621i	0.765771	−	0.643113i	$-0.222357\pi$
$47$	4.05652	+	2.34204i	0.591705	+	0.341621i	−0.174066	+	0.984734i	$0.555691\pi$
$48$		0			0
$49$	−3.17316	−	5.49607i	−0.453308	−	0.785153i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	1.59171	+	0.918976i	0.220731	+	0.127439i
$53$		−	11.0936i		−	1.52382i	−0.647682	−	0.761911i	$-0.724261\pi$
$53$		−	11.0936i		−	1.52382i	0.647682	−	0.761911i	$-0.275739\pi$
$54$		0			0
$55$	−3.14258	+	1.06027i	−0.423746	+	0.142966i
$56$	0.700188	+	0.404254i	0.0935665	+	0.0540207i
$57$		0			0
$58$	−0.0530153	−	0.0918253i	−0.00696125	−	0.0120572i
$59$	1.38435	−	0.799257i	0.180228	−	0.104054i	−0.407172	−	0.913351i	$-0.633485\pi$
$59$	1.38435	−	0.799257i	0.180228	−	0.104054i	0.587400	+	0.809297i	$0.300152\pi$
$60$		0			0
$61$	10.7598	+	6.21219i	1.37766	+	0.795390i	0.991877	−	0.127201i	$-0.0405994\pi$
$61$	10.7598	+	6.21219i	1.37766	+	0.795390i	0.385779	+	0.922591i	$0.373933\pi$
$62$	6.51996			0.828036
$63$		0			0
$64$	1.00000			0.125000
$65$	0.918976	−	1.59171i	0.113985	−	0.197428i
$66$		0			0
$67$	−0.221611	−	0.383842i	−0.0270741	−	0.0468937i	0.852171	−	0.523264i	$-0.175286\pi$
$67$	−0.221611	−	0.383842i	−0.0270741	−	0.0468937i	−0.879245	+	0.476370i	$0.841952\pi$
$68$	−3.25087	−	5.63067i	−0.394225	−	0.682819i
$69$		0			0
$70$	0.404254	−	0.700188i	0.0483175	−	0.0836884i
$71$			8.87630i			1.05342i	0.850044	+	0.526711i	$0.176575\pi$
$71$			8.87630i			1.05342i	−0.850044	+	0.526711i	$0.823425\pi$
$72$		0			0
$73$			14.6450i			1.71407i	0.515262	+	0.857033i	$0.327695\pi$
$73$			14.6450i			1.71407i	−0.515262	+	0.857033i	$0.672305\pi$
$74$	2.07976	−	3.60224i	0.241767	−	0.418752i
$75$		0			0
$76$	1.61995	−	0.935276i	0.185820	−	0.107283i
$77$	2.01279	+	1.77178i	0.229378	+	0.201913i
$78$		0			0
$79$	10.8062	+	6.23895i	1.21579	+	0.701937i	0.964015	−	0.265848i	$-0.0856521\pi$
$79$	10.8062	+	6.23895i	1.21579	+	0.701937i	0.251776	+	0.967786i	$0.418985\pi$
$80$		−	1.00000i		−	0.111803i
$81$		0			0
$82$	3.48175			0.384495
$83$	−5.77334	+	9.99972i	−0.633707	+	1.09761i	0.353081	+	0.935593i	$0.385134\pi$
$83$	−5.77334	+	9.99972i	−0.633707	+	1.09761i	−0.986788	+	0.162019i	$0.948199\pi$
$84$		0			0
$85$	−5.63067	+	3.25087i	−0.610732	+	0.352606i
$86$	1.09708	−	0.633401i	0.118302	−	0.0683014i
$87$		0			0
$88$	3.25169	+	0.653075i	0.346631	+	0.0696180i
$89$			7.20794i			0.764040i	0.924154	+	0.382020i	$0.124771\pi$
$89$			7.20794i			0.764040i	−0.924154	+	0.382020i	$0.875229\pi$
$90$		0			0
$91$	−1.48600			−0.155775
$92$	−4.50121	−	2.59877i	−0.469283	−	0.270941i
$93$		0			0
$94$	−4.05652	+	2.34204i	−0.418399	+	0.241563i
$95$	−0.935276	−	1.61995i	−0.0959573	−	0.166203i
$96$		0			0
$97$	5.63450	−	9.75924i	0.572097	−	0.990901i	−0.424253	−	0.905543i	$-0.639463\pi$
$97$	5.63450	−	9.75924i	0.572097	−	0.990901i	0.996350	−	0.0853575i	$-0.0272032\pi$
$98$	6.34632			0.641075
$99$		0			0
$100$	−1.00000			−0.100000
$101$	5.71591	−	9.90025i	0.568755	−	0.985112i	−0.427935	−	0.903810i	$-0.640759\pi$
$101$	5.71591	−	9.90025i	0.568755	−	0.985112i	0.996689	−	0.0813024i	$-0.0259080\pi$
$102$		0			0
$103$	−6.50932	−	11.2745i	−0.641382	−	1.11091i	−0.985124	−	0.171842i	$-0.945028\pi$
$103$	−6.50932	−	11.2745i	−0.641382	−	1.11091i	0.343742	−	0.939064i	$-0.388305\pi$
$104$	−1.59171	+	0.918976i	−0.156080	+	0.0901130i
$105$		0			0
$106$	9.60733	+	5.54680i	0.933147	+	0.538753i
$107$	19.5145			1.88654			0.943268	−	0.332032i	$-0.107734\pi$
$107$	19.5145			1.88654			0.943268	+	0.332032i	$0.107734\pi$
$108$		0			0
$109$		−	3.12788i		−	0.299596i	−0.988717	−	0.149798i	$-0.952138\pi$
$109$		−	3.12788i		−	0.299596i	0.988717	−	0.149798i	$-0.0478624\pi$
$110$	0.653075	−	3.25169i	0.0622683	−	0.310037i
$111$		0			0
$112$	−0.700188	+	0.404254i	−0.0661615	+	0.0381984i
$113$	0.700012	−	0.404152i	0.0658516	−	0.0380194i	−0.466713	−	0.884409i	$-0.654562\pi$
$113$	0.700012	−	0.404152i	0.0658516	−	0.0380194i	0.532564	+	0.846390i	$0.321228\pi$
$114$		0			0
$115$	−2.59877	+	4.50121i	−0.242337	+	0.419740i
$116$	0.106031			0.00984470
$117$		0			0
$118$			1.59851i			0.147155i
$119$	4.55243	+	2.62835i	0.417321	+	0.240940i
$120$		0			0
$121$	10.1470	+	4.24720i	0.922453	+	0.386109i
$122$	−10.7598	+	6.21219i	−0.974150	+	0.562426i
$123$		0			0
$124$	−3.25998	+	5.64645i	−0.292755	+	0.507066i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	21.3573i		−	1.89516i	−0.319523	−	0.947579i	$-0.603523\pi$
$127$		−	21.3573i		−	1.89516i	0.319523	−	0.947579i	$-0.396477\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	0.918976	+	1.59171i	0.0805995	+	0.139603i
$131$	3.08156	+	5.33742i	0.269237	+	0.466332i	0.968665	−	0.248371i	$-0.0798952\pi$
$131$	3.08156	+	5.33742i	0.269237	+	0.466332i	−0.699428	+	0.714703i	$0.746562\pi$
$132$		0			0
$133$	−0.756177	+	1.30974i	−0.0655689	+	0.113569i
$134$	0.443222			0.0382886
$135$		0			0
$136$	6.50173			0.557519
$137$	8.74723	+	5.05022i	0.747326	+	0.431469i	0.824727	−	0.565531i	$-0.191329\pi$
$137$	8.74723	+	5.05022i	0.747326	+	0.431469i	−0.0774007	+	0.997000i	$0.524662\pi$
$138$		0			0
$139$	−10.7266	+	6.19303i	−0.909821	+	0.525286i	−0.880374	−	0.474281i	$-0.842708\pi$
$139$	−10.7266	+	6.19303i	−0.909821	+	0.525286i	−0.0294478	+	0.999566i	$0.509375\pi$
$140$	0.404254	+	0.700188i	0.0341657	+	0.0591767i
$141$		0			0
$142$	−7.68710	−	4.43815i	−0.645087	−	0.372441i
$143$	−5.77592	+	1.94872i	−0.483007	+	0.162960i
$144$		0			0
$145$		−	0.106031i		−	0.00880537i
$146$	−12.6829	−	7.32249i	−1.04965	−	0.606014i
$147$		0			0
$148$	2.07976	+	3.60224i	0.170955	+	0.296103i
$149$	10.3389	+	17.9074i	0.846992	+	1.46703i	0.883880	+	0.467714i	$0.154922\pi$
$149$	10.3389	+	17.9074i	0.846992	+	1.46703i	−0.0368876	+	0.999319i	$0.511744\pi$
$150$		0			0
$151$	17.5811	+	10.1504i	1.43073	+	0.826031i	0.997176	−	0.0750981i	$-0.0239270\pi$
$151$	17.5811	+	10.1504i	1.43073	+	0.826031i	0.433551	+	0.901129i	$0.357260\pi$
$152$			1.87055i			0.151722i
$153$		0			0
$154$	−2.54080	+	0.857232i	−0.204744	+	0.0690778i
$155$	5.64645	+	3.25998i	0.453534	+	0.261848i
$156$		0			0
$157$	1.07419	+	1.86056i	0.0857301	+	0.148489i	0.905702	−	0.423915i	$-0.139344\pi$
$157$	1.07419	+	1.86056i	0.0857301	+	0.148489i	−0.819972	+	0.572404i	$0.806011\pi$
$158$	−10.8062	+	6.23895i	−0.859694	+	0.496345i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	4.20225			0.331184
$162$		0			0
$163$	−11.8388			−0.927287			−0.463643	−	0.886022i	$-0.653458\pi$
$163$	−11.8388			−0.927287			−0.463643	+	0.886022i	$0.653458\pi$
$164$	−1.74087	+	3.01528i	−0.135939	+	0.235454i
$165$		0			0
$166$	−5.77334	−	9.99972i	−0.448098	−	0.776129i
$167$	11.4316	+	19.8001i	0.884604	+	1.53218i	0.846167	+	0.532918i	$0.178905\pi$
$167$	11.4316	+	19.8001i	0.884604	+	1.53218i	0.0384373	+	0.999261i	$0.487762\pi$
$168$		0			0
$169$	−4.81097	+	8.33284i	−0.370074	+	0.640987i
$170$		−	6.50173i		−	0.498660i
$171$		0			0
$172$			1.26680i			0.0965928i
$173$	2.53267	−	4.38671i	0.192555	−	0.333515i	−0.753541	−	0.657401i	$-0.771656\pi$
$173$	2.53267	−	4.38671i	0.192555	−	0.333515i	0.946096	+	0.323886i	$0.104989\pi$
$174$		0			0
$175$	0.700188	−	0.404254i	0.0529292	−	0.0305587i
$176$	−2.19142	+	2.48951i	−0.165185	+	0.187654i
$177$		0			0
$178$	−6.24226	−	3.60397i	−0.467877	−	0.270129i
$179$		−	0.683164i		−	0.0510621i	−0.999674	−	0.0255310i	$-0.991872\pi$
$179$		−	0.683164i		−	0.0510621i	0.999674	−	0.0255310i	$-0.00812767\pi$
$180$		0			0
$181$	−9.74615			−0.724425			−0.362213	−	0.932095i	$-0.617979\pi$
$181$	−9.74615			−0.724425			−0.362213	+	0.932095i	$0.617979\pi$
$182$	0.742999	−	1.28691i	0.0550747	−	0.0953922i
$183$		0			0
$184$	4.50121	−	2.59877i	0.331833	−	0.191584i
$185$	3.60224	−	2.07976i	0.264842	−	0.152907i
$186$		0			0
$187$	21.1416	+	4.24612i	1.54603	+	0.310507i
$188$		−	4.68407i		−	0.341621i
$189$		0			0
$190$	1.87055			0.135704
$191$	5.09125	+	2.93944i	0.368390	+	0.212690i	0.672755	−	0.739865i	$-0.265111\pi$
$191$	5.09125	+	2.93944i	0.368390	+	0.212690i	−0.304365	+	0.952556i	$0.598444\pi$
$192$		0			0
$193$	−1.52540	+	0.880691i	−0.109801	+	0.0633935i	−0.553895	−	0.832587i	$-0.686859\pi$
$193$	−1.52540	+	0.880691i	−0.109801	+	0.0633935i	0.444094	+	0.895980i	$0.353526\pi$
$194$	5.63450	+	9.75924i	0.404534	+	0.700673i
$195$		0			0
$196$	−3.17316	+	5.49607i	−0.226654	+	0.392577i
$197$	−2.26771			−0.161568			−0.0807839	−	0.996732i	$-0.525742\pi$
$197$	−2.26771			−0.161568			−0.0807839	+	0.996732i	$0.525742\pi$
$198$		0			0
$199$	23.0129			1.63134			0.815669	−	0.578519i	$-0.196369\pi$
$199$	23.0129			1.63134			0.815669	+	0.578519i	$0.196369\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	5.71591	+	9.90025i	0.402170	+	0.696579i
$203$	−0.0742414	+	0.0428633i	−0.00521072	+	0.00300841i
$204$		0			0
$205$	3.01528	+	1.74087i	0.210596	+	0.121588i
$206$	13.0186			0.907051
$207$		0			0
$208$		−	1.83795i		−	0.127439i
$209$	−1.22161	+	6.08246i	−0.0845006	+	0.420732i
$210$		0			0
$211$	−6.07694	+	3.50852i	−0.418354	+	0.241537i	−0.694373	−	0.719616i	$-0.744318\pi$
$211$	−6.07694	+	3.50852i	−0.418354	+	0.241537i	0.276019	+	0.961152i	$0.410985\pi$
$212$	−9.60733	+	5.54680i	−0.659834	+	0.380956i
$213$		0			0
$214$	−9.75724	+	16.9000i	−0.666991	+	1.15526i
$215$	1.26680			0.0863952
$216$		0			0
$217$		−	5.27143i		−	0.357848i
$218$	2.70882	+	1.56394i	0.183465	+	0.105923i
$219$		0			0
$220$	2.48951	+	2.19142i	0.167843	+	0.147746i
$221$	−10.3489	+	5.97494i	−0.696142	+	0.401918i
$222$		0			0
$223$	8.66329	−	15.0053i	0.580136	−	1.00483i	−0.415326	−	0.909673i	$-0.636333\pi$
$223$	8.66329	−	15.0053i	0.580136	−	1.00483i	0.995463	−	0.0951533i	$-0.0303341\pi$
$224$		−	0.808507i		−	0.0540207i
$225$		0			0
$226$			0.808304i			0.0537676i
$227$	−3.93984	+	6.82400i	−0.261496	+	0.452925i	−0.966640	−	0.256140i	$-0.917549\pi$
$227$	−3.93984	+	6.82400i	−0.261496	+	0.452925i	0.705144	+	0.709065i	$0.250883\pi$
$228$		0			0
$229$	3.92425	+	6.79701i	0.259322	+	0.449159i	0.966060	−	0.258316i	$-0.0831676\pi$
$229$	3.92425	+	6.79701i	0.259322	+	0.449159i	−0.706739	+	0.707475i	$0.749834\pi$
$230$	−2.59877	−	4.50121i	−0.171358	−	0.296801i
$231$		0			0
$232$	−0.0530153	+	0.0918253i	−0.00348063	+	0.00602862i
$233$	6.38805			0.418495			0.209247	−	0.977863i	$-0.432899\pi$
$233$	6.38805			0.418495			0.209247	+	0.977863i	$0.432899\pi$
$234$		0			0
$235$	−4.68407			−0.305555
$236$	−1.38435	−	0.799257i	−0.0901138	−	0.0520272i
$237$		0			0
$238$	−4.55243	+	2.62835i	−0.295090	+	0.170371i
$239$	−7.14471	−	12.3750i	−0.462153	−	0.800472i	0.536915	−	0.843636i	$-0.319590\pi$
$239$	−7.14471	−	12.3750i	−0.462153	−	0.800472i	−0.999068	+	0.0431641i	$0.986256\pi$
$240$		0			0
$241$	−5.57754	−	3.22019i	−0.359281	−	0.207431i	0.309484	−	0.950905i	$-0.399844\pi$
$241$	−5.57754	−	3.22019i	−0.359281	−	0.207431i	−0.668765	+	0.743474i	$0.733177\pi$
$242$	−8.75167	+	6.66395i	−0.562579	+	0.428375i
$243$		0			0
$244$		−	12.4244i		−	0.795390i
$245$	5.49607	+	3.17316i	0.351131	+	0.202726i
$246$		0			0
$247$	−1.71899	−	2.97738i	−0.109377	−	0.189446i
$248$	−3.25998	−	5.64645i	−0.207009	−	0.358550i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$		−	3.07565i		−	0.194134i	−0.995278	−	0.0970668i	$-0.969054\pi$
$251$		−	3.07565i		−	0.194134i	0.995278	−	0.0970668i	$-0.0309460\pi$
$252$		0			0
$253$	16.3337	−	5.51078i	1.02689	−	0.346460i
$254$	18.4960	+	10.6787i	1.16054	+	0.670039i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.2896	−	7.09539i	0.766603	−	0.442598i	−0.0650588	−	0.997881i	$-0.520723\pi$
$257$	12.2896	−	7.09539i	0.766603	−	0.442598i	0.831661	+	0.555283i	$0.187390\pi$
$258$		0			0
$259$	−2.91244	−	1.68150i	−0.180970	−	0.104483i
$260$	−1.83795			−0.113985
$261$		0			0
$262$	−6.16312			−0.380759
$263$	13.1025	−	22.6943i	0.807938	−	1.39939i	−0.106352	−	0.994329i	$-0.533917\pi$
$263$	13.1025	−	22.6943i	0.807938	−	1.39939i	0.914290	−	0.405061i	$-0.132750\pi$
$264$		0			0
$265$	5.54680	+	9.60733i	0.340737	+	0.590174i
$266$	−0.756177	−	1.30974i	−0.0463642	−	0.0803051i
$267$		0			0
$268$	−0.221611	+	0.383842i	−0.0135371	+	0.0234469i
$269$			6.72917i			0.410285i	0.978732	+	0.205142i	$0.0657658\pi$
$269$			6.72917i			0.410285i	−0.978732	+	0.205142i	$0.934234\pi$
$270$		0			0
$271$			11.8647i			0.720730i	0.932811	+	0.360365i	$0.117348\pi$
$271$			11.8647i			0.720730i	−0.932811	+	0.360365i	$0.882652\pi$
$272$	−3.25087	+	5.63067i	−0.197113	+	0.341409i
$273$		0			0
$274$	−8.74723	+	5.05022i	−0.528440	+	0.305095i
$275$	2.19142	−	2.48951i	0.132148	−	0.150123i
$276$		0			0
$277$	−5.70227	−	3.29221i	−0.342616	−	0.197810i	0.318812	−	0.947818i	$-0.396716\pi$
$277$	−5.70227	−	3.29221i	−0.342616	−	0.197810i	−0.661428	+	0.750008i	$0.730049\pi$
$278$		−	12.3861i		−	0.742866i
$279$		0			0
$280$	−0.808507			−0.0483175
$281$	−12.5438	+	21.7265i	−0.748302	+	1.29610i	0.200334	+	0.979728i	$0.435797\pi$
$281$	−12.5438	+	21.7265i	−0.748302	+	1.29610i	−0.948636	+	0.316369i	$0.897536\pi$
$282$		0			0
$283$	−18.9030	+	10.9137i	−1.12367	+	0.648751i	−0.942335	−	0.334671i	$-0.891375\pi$
$283$	−18.9030	+	10.9137i	−1.12367	+	0.648751i	−0.181334	+	0.983421i	$0.558042\pi$
$284$	7.68710	−	4.43815i	0.456145	−	0.263356i
$285$		0			0
$286$	1.20032	−	5.97645i	0.0709765	−	0.353395i
$287$		−	2.81502i		−	0.166165i
$288$		0			0
$289$	25.2725			1.48662
$290$	0.0918253	+	0.0530153i	0.00539216	+	0.00311317i
$291$		0			0
$292$	12.6829	−	7.32249i	0.742212	−	0.428516i
$293$	−5.87689	−	10.1791i	−0.343331	−	0.594667i	0.641718	−	0.766941i	$-0.278222\pi$
$293$	−5.87689	−	10.1791i	−0.343331	−	0.594667i	−0.985049	+	0.172274i	$0.944889\pi$
$294$		0			0
$295$	−0.799257	+	1.38435i	−0.0465346	+	0.0806002i
$296$	−4.15951			−0.241767
$297$		0			0
$298$	−20.6777			−1.19783
$299$	−4.77642	+	8.27301i	−0.276228	+	0.478440i
$300$		0			0
$301$	−0.512110	−	0.887000i	−0.0295175	−	0.0511258i
$302$	−17.5811	+	10.1504i	−1.01168	+	0.584092i
$303$		0			0
$304$	−1.61995	−	0.935276i	−0.0929102	−	0.0536417i
$305$	−12.4244			−0.711418
$306$		0			0
$307$		−	4.46253i		−	0.254690i	−0.991858	−	0.127345i	$-0.959354\pi$
$307$		−	4.46253i		−	0.254690i	0.991858	−	0.127345i	$-0.0406456\pi$
$308$	0.528016	−	2.62902i	0.0300865	−	0.149802i
$309$		0			0
$310$	−5.64645	+	3.25998i	−0.320697	+	0.185154i
$311$	−7.44194	+	4.29660i	−0.421993	+	0.243638i	−0.695930	−	0.718110i	$-0.745008\pi$
$311$	−7.44194	+	4.29660i	−0.421993	+	0.243638i	0.273936	+	0.961748i	$0.411674\pi$
$312$		0			0
$313$	−1.02823	+	1.78094i	−0.0581189	+	0.100665i	−0.893621	−	0.448822i	$-0.851844\pi$
$313$	−1.02823	+	1.78094i	−0.0581189	+	0.100665i	0.835502	+	0.549487i	$0.185177\pi$
$314$	−2.14839			−0.121241
$315$		0			0
$316$		−	12.4779i		−	0.701937i
$317$	−3.40370	−	1.96513i	−0.191171	−	0.110373i	0.401360	−	0.915920i	$-0.368538\pi$
$317$	−3.40370	−	1.96513i	−0.191171	−	0.110373i	−0.592531	+	0.805548i	$0.701871\pi$
$318$		0			0
$319$	−0.232358	+	0.263964i	−0.0130096	+	0.0147792i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	−2.10113	+	3.63926i	−0.117091	+	0.202808i
$323$			12.1618i			0.676702i
$324$		0			0
$325$			1.83795i			0.101951i
$326$	5.91940	−	10.2527i	0.327845	−	0.567845i
$327$		0			0
$328$	−1.74087	−	3.01528i	−0.0961237	−	0.166491i
$329$	1.89355	+	3.27973i	0.104395	+	0.180817i
$330$		0			0
$331$	−7.61257	+	13.1854i	−0.418424	+	0.724732i	−0.995781	−	0.0917596i	$-0.970751\pi$
$331$	−7.61257	+	13.1854i	−0.418424	+	0.724732i	0.577357	+	0.816492i	$0.304084\pi$
$332$	11.5467			0.633707
$333$		0			0
$334$	−22.8632			−1.25102
$335$	0.383842	+	0.221611i	0.0209715	+	0.0121079i
$336$		0			0
$337$	−5.77401	+	3.33363i	−0.314530	+	0.181594i	−0.648952	−	0.760829i	$-0.724792\pi$
$337$	−5.77401	+	3.33363i	−0.314530	+	0.181594i	0.334422	+	0.942424i	$0.391459\pi$
$338$	−4.81097	−	8.33284i	−0.261682	−	0.453247i
$339$		0			0
$340$	5.63067	+	3.25087i	0.305366	+	0.176303i
$341$	−6.91289	−	20.4895i	−0.374354	−	1.10957i
$342$		0			0
$343$		−	10.7906i		−	0.582637i
$344$	−1.09708	−	0.633401i	−0.0591508	−	0.0341507i
$345$		0			0
$346$	2.53267	+	4.38671i	0.136157	+	0.235831i
$347$	3.74402	+	6.48484i	0.200990	+	0.348124i	0.948848	−	0.315735i	$-0.102251\pi$
$347$	3.74402	+	6.48484i	0.200990	+	0.348124i	−0.747858	+	0.663859i	$0.768918\pi$
$348$		0			0
$349$	13.6389	+	7.87442i	0.730073	+	0.421508i	0.818449	−	0.574579i	$-0.194834\pi$
$349$	13.6389	+	7.87442i	0.730073	+	0.421508i	−0.0883758	+	0.996087i	$0.528168\pi$
$350$			0.808507i			0.0432165i
$351$		0			0
$352$	−1.06027	−	3.14258i	−0.0565124	−	0.167500i
$353$	−14.8221	−	8.55757i	−0.788903	−	0.455473i	0.0506732	−	0.998715i	$-0.483863\pi$
$353$	−14.8221	−	8.55757i	−0.788903	−	0.455473i	−0.839576	+	0.543242i	$0.817197\pi$
$354$		0			0
$355$	−4.43815	−	7.68710i	−0.235552	−	0.407989i
$356$	6.24226	−	3.60397i	0.330839	−	0.191010i
$357$		0			0
$358$	0.591638	+	0.341582i	0.0312690	+	0.0180532i
$359$	10.8139			0.570738			0.285369	−	0.958418i	$-0.407884\pi$
$359$	10.8139			0.570738			0.285369	+	0.958418i	$0.407884\pi$
$360$		0			0
$361$	15.5010			0.815844
$362$	4.87307	−	8.44041i	0.256123	−	0.443618i
$363$		0			0
$364$	0.742999	+	1.28691i	0.0389437	+	0.0674525i
$365$	−7.32249	−	12.6829i	−0.383277	−	0.663855i
$366$		0			0
$367$	−0.210501	+	0.364599i	−0.0109881	+	0.0190319i	−0.871467	−	0.490454i	$-0.836831\pi$
$367$	−0.210501	+	0.364599i	−0.0109881	+	0.0190319i	0.860479	+	0.509486i	$0.170164\pi$
$368$			5.19755i			0.270941i
$369$		0			0
$370$			4.15951i			0.216243i
$371$	4.48462	−	7.76760i	0.232830	−	0.403274i
$372$		0			0
$373$	−26.9995	+	15.5882i	−1.39798	+	0.807125i	−0.994181	−	0.107721i	$-0.965645\pi$
$373$	−26.9995	+	15.5882i	−1.39798	+	0.807125i	−0.403801	+	0.914847i	$0.632311\pi$
$374$	−14.2481	+	16.1861i	−0.736750	+	0.836965i
$375$		0			0
$376$	4.05652	+	2.34204i	0.209199	+	0.120781i
$377$		−	0.194879i		−	0.0100368i
$378$		0			0
$379$	−13.7409			−0.705820			−0.352910	−	0.935657i	$-0.614808\pi$
$379$	−13.7409			−0.705820			−0.352910	+	0.935657i	$0.614808\pi$
$380$	−0.935276	+	1.61995i	−0.0479786	+	0.0831014i
$381$		0			0
$382$	−5.09125	+	2.93944i	−0.260491	+	0.150395i
$383$	8.00915	−	4.62409i	0.409248	−	0.236280i	−0.281218	−	0.959644i	$-0.590739\pi$
$383$	8.00915	−	4.62409i	0.409248	−	0.236280i	0.690467	+	0.723364i	$0.257405\pi$
$384$		0			0
$385$	−2.62902	−	0.528016i	−0.133987	−	0.0269102i
$386$		−	1.76138i		−	0.0896520i
$387$		0			0
$388$	−11.2690			−0.572097
$389$	−4.41058	−	2.54645i	−0.223625	−	0.129110i	0.384003	−	0.923332i	$-0.374545\pi$
$389$	−4.41058	−	2.54645i	−0.223625	−	0.129110i	−0.607628	+	0.794222i	$0.707879\pi$
$390$		0			0
$391$	29.2657	−	16.8965i	1.48003	−	0.854494i
$392$	−3.17316	−	5.49607i	−0.160269	−	0.277594i
$393$		0			0
$394$	1.13386	−	1.96390i	0.0571228	−	0.0989396i
$395$	−12.4779			−0.627832
$396$		0			0
$397$	18.0972			0.908273			0.454137	−	0.890932i	$-0.349948\pi$
$397$	18.0972			0.908273			0.454137	+	0.890932i	$0.349948\pi$
$398$	−11.5064	+	19.9297i	−0.576765	+	0.998987i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	6.36615	−	3.67550i	0.317910	−	0.183546i	−0.332550	−	0.943085i	$-0.607909\pi$
$401$	6.36615	−	3.67550i	0.317910	−	0.183546i	0.650461	+	0.759540i	$0.274576\pi$
$402$		0			0
$403$	10.3779	+	5.99169i	0.516960	+	0.298467i
$404$	−11.4318			−0.568755
$405$		0			0
$406$		−	0.0857266i		−	0.00425454i
$407$	−13.5255	−	2.71647i	−0.670432	−	0.134651i
$408$		0			0
$409$	−7.31309	+	4.22222i	−0.361609	+	0.208775i	−0.669786	−	0.742554i	$-0.733614\pi$
$409$	−7.31309	+	4.22222i	−0.361609	+	0.208775i	0.308177	+	0.951329i	$0.400281\pi$
$410$	−3.01528	+	1.74087i	−0.148914	+	0.0859756i
$411$		0			0
$412$	−6.50932	+	11.2745i	−0.320691	+	0.555453i
$413$	1.29241			0.0635954
$414$		0			0
$415$		−	11.5467i		−	0.566804i
$416$	1.59171	+	0.918976i	0.0780402	+	0.0450565i
$417$		0			0
$418$	−4.65676	−	4.09917i	−0.227769	−	0.200497i
$419$	−25.9408	+	14.9769i	−1.26729	+	0.731672i	−0.974475	−	0.224496i	$-0.927926\pi$
$419$	−25.9408	+	14.9769i	−1.26729	+	0.731672i	−0.292818	+	0.956168i	$0.594593\pi$
$420$		0			0
$421$	4.82963	−	8.36516i	0.235382	−	0.407693i	−0.724002	−	0.689798i	$-0.757699\pi$
$421$	4.82963	−	8.36516i	0.235382	−	0.407693i	0.959384	+	0.282105i	$0.0910326\pi$
$422$		−	7.01704i		−	0.341584i
$423$		0			0
$424$		−	11.0936i		−	0.538753i
$425$	3.25087	−	5.63067i	0.157690	−	0.273127i
$426$		0			0
$427$	5.02260	+	8.69940i	0.243061	+	0.420994i
$428$	−9.75724	−	16.9000i	−0.471634	−	0.816894i
$429$		0			0
$430$	−0.633401	+	1.09708i	−0.0305453	+	0.0529061i
$431$	7.43225			0.357999			0.178999	−	0.983849i	$-0.442714\pi$
$431$	7.43225			0.357999			0.178999	+	0.983849i	$0.442714\pi$
$432$		0			0
$433$	38.6060			1.85529			0.927644	−	0.373466i	$-0.121831\pi$
$433$	38.6060			1.85529			0.927644	+	0.373466i	$0.121831\pi$
$434$	4.56519	+	2.63572i	0.219136	+	0.126518i
$435$		0			0
$436$	−2.70882	+	1.56394i	−0.129729	+	0.0748991i
$437$	4.86114	+	8.41974i	0.232540	+	0.402771i
$438$		0			0
$439$	−30.8607	−	17.8174i	−1.47290	−	0.850380i	−0.473367	−	0.880865i	$-0.656961\pi$
$439$	−30.8607	−	17.8174i	−1.47290	−	0.850380i	−0.999535	+	0.0304850i	$0.990295\pi$
$440$	−3.14258	+	1.06027i	−0.149817	+	0.0505462i
$441$		0			0
$442$		−	11.9499i		−	0.568398i
$443$	−19.2694	−	11.1252i	−0.915517	−	0.528574i	−0.0333149	−	0.999445i	$-0.510606\pi$
$443$	−19.2694	−	11.1252i	−0.915517	−	0.528574i	−0.882202	+	0.470871i	$0.843940\pi$
$444$		0			0
$445$	−3.60397	−	6.24226i	−0.170844	−	0.295911i
$446$	8.66329	+	15.0053i	0.410218	+	0.710519i
$447$		0			0
$448$	0.700188	+	0.404254i	0.0330808	+	0.0190992i
$449$			24.9351i			1.17676i	0.808585	+	0.588379i	$0.200234\pi$
$449$			24.9351i			1.17676i	−0.808585	+	0.588379i	$0.799766\pi$
$450$		0			0
$451$	−3.69158	−	10.9417i	−0.173830	−	0.515224i
$452$	−0.700012	−	0.404152i	−0.0329258	−	0.0190097i
$453$		0			0
$454$	−3.93984	−	6.82400i	−0.184906	−	0.320266i
$455$	1.28691	−	0.742999i	0.0603314	−	0.0348323i
$456$		0			0
$457$	3.35432	+	1.93662i	0.156909	+	0.0905912i	0.576398	−	0.817169i	$-0.304458\pi$
$457$	3.35432	+	1.93662i	0.156909	+	0.0905912i	−0.419490	+	0.907760i	$0.637791\pi$
$458$	−7.84851			−0.366737
$459$		0			0
$460$	5.19755			0.242337
$461$	4.36386	−	7.55843i	0.203245	−	0.352031i	−0.746327	−	0.665580i	$-0.768184\pi$
$461$	4.36386	−	7.55843i	0.203245	−	0.352031i	0.949572	+	0.313548i	$0.101518\pi$
$462$		0			0
$463$	−15.2101	−	26.3447i	−0.706873	−	1.22434i	−0.966011	−	0.258500i	$-0.916772\pi$
$463$	−15.2101	−	26.3447i	−0.706873	−	1.22434i	0.259138	−	0.965840i	$-0.416562\pi$
$464$	−0.0530153	−	0.0918253i	−0.00246118	−	0.00426288i
$465$		0			0
$466$	−3.19402	+	5.53221i	−0.147960	+	0.256275i
$467$			14.3264i			0.662946i	0.943465	+	0.331473i	$0.107546\pi$
$467$			14.3264i			0.662946i	−0.943465	+	0.331473i	$0.892454\pi$
$468$		0			0
$469$		−	0.358348i		−	0.0165470i
$470$	2.34204	−	4.05652i	0.108030	−	0.187114i
$471$		0			0
$472$	1.38435	−	0.799257i	0.0637201	−	0.0367888i
$473$	−3.15372	−	2.77610i	−0.145008	−	0.127645i
$474$		0			0
$475$	1.61995	+	0.935276i	0.0743282	+	0.0429134i
$476$		−	5.25670i		−	0.240940i
$477$		0			0
$478$	14.2894			0.653583
$479$	−4.21713	+	7.30428i	−0.192686	+	0.333741i	−0.946139	−	0.323760i	$-0.895053\pi$
$479$	−4.21713	+	7.30428i	−0.192686	+	0.333741i	0.753454	+	0.657501i	$0.228386\pi$
$480$		0			0
$481$	6.62075	−	3.82249i	0.301880	−	0.174291i
$482$	5.57754	−	3.22019i	0.254050	−	0.146676i
$483$		0			0
$484$	−1.39531	−	10.9111i	−0.0634233	−	0.495961i
$485$			11.2690i			0.511699i
$486$		0			0
$487$	8.04981			0.364772			0.182386	−	0.983227i	$-0.441618\pi$
$487$	8.04981			0.364772			0.182386	+	0.983227i	$0.441618\pi$
$488$	10.7598	+	6.21219i	0.487075	+	0.281213i
$489$		0			0
$490$	−5.49607	+	3.17316i	−0.248287	+	0.143349i
$491$	0.370909	+	0.642433i	0.0167389	+	0.0289926i	0.874274	−	0.485434i	$-0.161338\pi$
$491$	0.370909	+	0.642433i	0.0167389	+	0.0289926i	−0.857535	+	0.514426i	$0.828005\pi$
$492$		0			0
$493$	−0.344692	+	0.597023i	−0.0155241	+	0.0268886i
$494$	3.43798			0.154682
$495$		0			0
$496$	6.51996			0.292755
$497$	−3.58827	+	6.21507i	−0.160956	+	0.278784i
$498$		0			0
$499$	2.80828	+	4.86409i	0.125716	+	0.217747i	0.922013	−	0.387160i	$-0.126544\pi$
$499$	2.80828	+	4.86409i	0.125716	+	0.217747i	−0.796297	+	0.604906i	$0.793211\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$		0			0
$502$	2.66359	+	1.53783i	0.118882	+	0.0686366i
$503$	−28.1297			−1.25424			−0.627121	−	0.778922i	$-0.715767\pi$
$503$	−28.1297			−1.25424			−0.627121	+	0.778922i	$0.715767\pi$
$504$		0			0
$505$			11.4318i			0.508710i
$506$	−3.39439	+	16.9008i	−0.150899	+	0.751333i
$507$		0			0
$508$	−18.4960	+	10.6787i	−0.820627	+	0.473789i
$509$	36.2515	−	20.9298i	1.60682	−	0.927698i	0.616745	−	0.787163i	$-0.288451\pi$
$509$	36.2515	−	20.9298i	1.60682	−	0.927698i	0.990076	−	0.140535i	$-0.0448824\pi$
$510$		0			0
$511$	−5.92029	+	10.2542i	−0.261898	+	0.453621i
$512$	1.00000			0.0441942
$513$		0			0
$514$			14.1908i			0.625928i
$515$	11.2745	+	6.50932i	0.496812	+	0.286835i
$516$		0			0
$517$	11.6610	+	10.2648i	0.512852	+	0.451445i
$518$	2.91244	−	1.68150i	0.127965	−	0.0738808i
$519$		0			0
$520$	0.918976	−	1.59171i	0.0402998	−	0.0698013i
$521$			42.0815i			1.84362i	0.387638	+	0.921812i	$0.373291\pi$
$521$			42.0815i			1.84362i	−0.387638	+	0.921812i	$0.626709\pi$
$522$		0			0
$523$			9.18729i			0.401732i	0.979619	+	0.200866i	$0.0643756\pi$
$523$			9.18729i			0.401732i	−0.979619	+	0.200866i	$0.935624\pi$
$524$	3.08156	−	5.33742i	0.134619	−	0.233166i
$525$		0			0
$526$	13.1025	+	22.6943i	0.571298	+	0.989518i
$527$	−21.1955	−	36.7117i	−0.923291	−	1.59919i
$528$		0			0
$529$	2.00725	−	3.47665i	0.0872716	−	0.151159i
$530$	−11.0936			−0.481875
$531$		0			0
$532$	1.51235			0.0655689
$533$	5.54194	+	3.19964i	0.240048	+	0.138592i
$534$		0			0
$535$	−16.9000	+	9.75724i	−0.730652	+	0.421842i
$536$	−0.221611	−	0.383842i	−0.00957214	−	0.0165794i
$537$		0			0
$538$	−5.82763	−	3.36459i	−0.251247	−	0.145058i
$539$	−6.72878	−	19.9438i	−0.289829	−	0.859042i
$540$		0			0
$541$		−	8.40554i		−	0.361382i	−0.983540	−	0.180691i	$-0.942167\pi$
$541$		−	8.40554i		−	0.361382i	0.983540	−	0.180691i	$-0.0578335\pi$
$542$	−10.2751	−	5.93236i	−0.441355	−	0.254817i
$543$		0			0
$544$	−3.25087	−	5.63067i	−0.139380	−	0.241413i
$545$	1.56394	+	2.70882i	0.0669918	+	0.116033i
$546$		0			0
$547$	−0.617106	−	0.356286i	−0.0263855	−	0.0152337i	0.486749	−	0.873542i	$-0.338183\pi$
$547$	−0.617106	−	0.356286i	−0.0263855	−	0.0152337i	−0.513135	+	0.858308i	$0.671516\pi$
$548$		−	10.1004i		−	0.431469i
$549$		0			0
$550$	1.06027	+	3.14258i	0.0452099	+	0.134000i
$551$	−0.171764	−	0.0991679i	−0.00731739	−	0.00422470i
$552$		0			0
$553$	5.04424	+	8.73688i	0.214503	+	0.371530i
$554$	5.70227	−	3.29221i	0.242266	−	0.139872i
$555$		0			0
$556$	10.7266	+	6.19303i	0.454911	+	0.262643i
$557$	−3.99124			−0.169114			−0.0845571	−	0.996419i	$-0.526948\pi$
$557$	−3.99124			−0.169114			−0.0845571	+	0.996419i	$0.526948\pi$
$558$		0			0
$559$	2.32832			0.0984776
$560$	0.404254	−	0.700188i	0.0170828	−	0.0295883i
$561$		0			0
$562$	−12.5438	−	21.7265i	−0.529129	−	0.916479i
$563$	−23.4366	−	40.5933i	−0.987734	−	1.71081i	−0.629094	−	0.777329i	$-0.716574\pi$
$563$	−23.4366	−	40.5933i	−0.987734	−	1.71081i	−0.358639	−	0.933476i	$-0.616759\pi$
$564$		0			0
$565$	−0.404152	+	0.700012i	−0.0170028	+	0.0294497i
$566$		−	21.8274i		−	0.917472i
$567$		0			0
$568$			8.87630i			0.372441i
$569$	13.8231	−	23.9422i	0.579493	−	1.00371i	−0.416044	−	0.909344i	$-0.636584\pi$
$569$	13.8231	−	23.9422i	0.579493	−	1.00371i	0.995537	−	0.0943670i	$-0.0300827\pi$
$570$		0			0
$571$	−0.0760954	+	0.0439337i	−0.00318449	+	0.00183857i	−0.501591	−	0.865105i	$-0.667252\pi$
$571$	−0.0760954	+	0.0439337i	−0.00318449	+	0.00183857i	0.498407	+	0.866943i	$0.333919\pi$
$572$	4.57560	+	4.02774i	0.191315	+	0.168408i
$573$		0			0
$574$	2.43788	+	1.40751i	0.101755	+	0.0587483i
$575$		−	5.19755i		−	0.216753i
$576$		0			0
$577$	−34.7807			−1.44794			−0.723970	−	0.689831i	$-0.757685\pi$
$577$	−34.7807			−1.44794			−0.723970	+	0.689831i	$0.757685\pi$
$578$	−12.6363	+	21.8867i	−0.525599	+	0.910365i
$579$		0			0
$580$	−0.0918253	+	0.0530153i	−0.00381284	+	0.00220134i
$581$	−8.08485	+	4.66779i	−0.335416	+	0.193652i
$582$		0			0
$583$	7.24495	−	36.0729i	0.300055	−	1.49399i
$584$			14.6450i			0.606014i
$585$		0			0
$586$	11.7538			0.485544
$587$	−6.79402	−	3.92253i	−0.280419	−	0.161900i	0.353194	−	0.935550i	$-0.385096\pi$
$587$	−6.79402	−	3.92253i	−0.280419	−	0.161900i	−0.633613	+	0.773650i	$0.718429\pi$
$588$		0			0
$589$	10.5620	−	6.09796i	0.435199	−	0.251262i
$590$	−0.799257	−	1.38435i	−0.0329049	−	0.0569930i
$591$		0			0
$592$	2.07976	−	3.60224i	0.0854775	−	0.148051i
$593$	−33.3620			−1.37001			−0.685006	−	0.728538i	$-0.740200\pi$
$593$	−33.3620			−1.37001			−0.685006	+	0.728538i	$0.740200\pi$
$594$		0			0
$595$	−5.25670			−0.215504
$596$	10.3389	−	17.9074i	0.423496	−	0.733517i
$597$		0			0
$598$	−4.77642	−	8.27301i	−0.195322	−	0.338308i
$599$	4.28378	−	2.47324i	0.175031	−	0.101054i	−0.409925	−	0.912119i	$-0.634445\pi$
$599$	4.28378	−	2.47324i	0.175031	−	0.101054i	0.584956	+	0.811065i	$0.301112\pi$
$600$		0			0
$601$	21.5660	+	12.4512i	0.879697	+	0.507893i	0.870559	−	0.492065i	$-0.163758\pi$
$601$	21.5660	+	12.4512i	0.879697	+	0.507893i	0.00913864	+	0.999958i	$0.497091\pi$
$602$	1.02422			0.0417441
$603$		0			0
$604$		−	20.3009i		−	0.826031i
$605$	−10.9111	+	1.39531i	−0.443601	+	0.0567275i
$606$		0			0
$607$	11.0145	−	6.35925i	0.447066	−	0.258114i	−0.259524	−	0.965737i	$-0.583566\pi$
$607$	11.0145	−	6.35925i	0.447066	−	0.258114i	0.706590	+	0.707623i	$0.250232\pi$
$608$	1.61995	−	0.935276i	0.0656975	−	0.0379304i
$609$		0			0
$610$	6.21219	−	10.7598i	0.251524	−	0.435653i
$611$	−8.60910			−0.348287
$612$		0			0
$613$		−	0.697036i		−	0.0281530i	−0.999901	−	0.0140765i	$-0.995519\pi$
$613$		−	0.697036i		−	0.0281530i	0.999901	−	0.0140765i	$-0.00448084\pi$
$614$	3.86467	+	2.23127i	0.155965	+	0.0900466i
$615$		0			0
$616$	2.01279	+	1.77178i	0.0810975	+	0.0713872i
$617$	21.7066	−	12.5323i	0.873876	−	0.504532i	0.00524151	−	0.999986i	$-0.498332\pi$
$617$	21.7066	−	12.5323i	0.873876	−	0.504532i	0.868634	+	0.495454i	$0.164998\pi$
$618$		0			0
$619$	−7.63117	+	13.2176i	−0.306723	+	0.531259i	−0.977643	−	0.210270i	$-0.932566\pi$
$619$	−7.63117	+	13.2176i	−0.306723	+	0.531259i	0.670921	+	0.741529i	$0.265899\pi$
$620$		−	6.51996i		−	0.261848i
$621$		0			0
$622$		−	8.59321i		−	0.344556i
$623$	−2.91383	+	5.04691i	−0.116740	+	0.202200i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.02823	−	1.78094i	−0.0410963	−	0.0711808i
$627$		0			0
$628$	1.07419	−	1.86056i	0.0428650	−	0.0742444i
$629$	−27.0441			−1.07832
$630$		0			0
$631$	−16.4855			−0.656278			−0.328139	−	0.944629i	$-0.606421\pi$
$631$	−16.4855			−0.656278			−0.328139	+	0.944629i	$0.606421\pi$
$632$	10.8062	+	6.23895i	0.429847	+	0.248172i
$633$		0			0
$634$	3.40370	−	1.96513i	0.135178	−	0.0780452i
$635$	10.6787	+	18.4960i	0.423770	+	0.733991i
$636$		0			0
$637$	10.1015	+	5.83211i	0.400237	+	0.231077i
$638$	−0.112421	−	0.333210i	−0.00445078	−	0.0131919i
$639$		0			0
$640$		−	1.00000i		−	0.0395285i
$641$	5.30661	+	3.06377i	0.209599	+	0.121012i	0.601125	−	0.799155i	$-0.294719\pi$
$641$	5.30661	+	3.06377i	0.209599	+	0.121012i	−0.391526	+	0.920167i	$0.628053\pi$
$642$		0			0
$643$	−7.76854	−	13.4555i	−0.306361	−	0.530634i	0.671202	−	0.741274i	$-0.265778\pi$
$643$	−7.76854	−	13.4555i	−0.306361	−	0.530634i	−0.977564	+	0.210641i	$0.932445\pi$
$644$	−2.10113	−	3.63926i	−0.0827960	−	0.143407i
$645$		0			0
$646$	−10.5325	−	6.08091i	−0.414394	−	0.239250i
$647$		−	39.4895i		−	1.55249i	−0.630430	−	0.776246i	$-0.717121\pi$
$647$		−	39.4895i		−	1.55249i	0.630430	−	0.776246i	$-0.282879\pi$
$648$		0			0
$649$	5.02347	−	1.69485i	0.197188	−	0.0665287i
$650$	−1.59171	−	0.918976i	−0.0624321	−	0.0360452i
$651$		0			0
$652$	5.91940	+	10.2527i	0.231822	+	0.401527i
$653$	18.3721	−	10.6071i	0.718954	−	0.415088i	−0.0954134	−	0.995438i	$-0.530417\pi$
$653$	18.3721	−	10.6071i	0.718954	−	0.415088i	0.814368	+	0.580349i	$0.197084\pi$
$654$		0			0
$655$	−5.33742	−	3.08156i	−0.208550	−	0.120406i
$656$	3.48175			0.135939
$657$		0			0
$658$	−3.78710			−0.147637
$659$	21.5484	−	37.3230i	0.839407	−	1.45390i	−0.0509836	−	0.998699i	$-0.516236\pi$
$659$	21.5484	−	37.3230i	0.839407	−	1.45390i	0.890391	−	0.455197i	$-0.150431\pi$
$660$		0			0
$661$	4.38090	+	7.58794i	0.170397	+	0.295137i	0.938559	−	0.345119i	$-0.112162\pi$
$661$	4.38090	+	7.58794i	0.170397	+	0.295137i	−0.768162	+	0.640256i	$0.778828\pi$
$662$	−7.61257	−	13.1854i	−0.295871	−	0.512463i
$663$		0			0
$664$	−5.77334	+	9.99972i	−0.224049	+	0.388064i
$665$		−	1.51235i		−	0.0586466i
$666$		0			0
$667$			0.551099i			0.0213387i
$668$	11.4316	−	19.8001i	0.442302	−	0.766090i
$669$		0			0
$670$	−0.383842	+	0.221611i	−0.0148291	+	0.00856158i
$671$	30.9306	+	27.2271i	1.19406	+	1.05109i
$672$		0			0
$673$	−34.2563	−	19.7779i	−1.32049	−	0.762382i	−0.336679	−	0.941619i	$-0.609304\pi$
$673$	−34.2563	−	19.7779i	−1.32049	−	0.762382i	−0.983806	+	0.179237i	$0.942637\pi$
$674$		−	6.66725i		−	0.256813i
$675$		0			0
$676$	9.62193			0.370074
$677$	−17.5285	+	30.3603i	−0.673676	+	1.16684i	0.303178	+	0.952934i	$0.401952\pi$
$677$	−17.5285	+	30.3603i	−0.673676	+	1.16684i	−0.976854	+	0.213907i	$0.931381\pi$
$678$		0			0
$679$	7.89042	−	4.55553i	0.302806	−	0.174825i
$680$	−5.63067	+	3.25087i	−0.215926	+	0.124665i
$681$		0			0
$682$	21.2009	+	4.25802i	0.811824	+	0.163048i
$683$		−	46.3667i		−	1.77417i	−0.461602	−	0.887087i	$-0.652725\pi$
$683$		−	46.3667i		−	1.77417i	0.461602	−	0.887087i	$-0.347275\pi$
$684$		0			0
$685$	−10.1004			−0.385918
$686$	9.34493	+	5.39530i	0.356791	+	0.205993i
$687$		0			0
$688$	1.09708	−	0.633401i	0.0418259	−	0.0241482i
$689$	10.1947	+	17.6578i	0.388389	+	0.672709i
$690$		0			0
$691$	6.18944	−	10.7204i	0.235457	−	0.407824i	−0.723948	−	0.689854i	$-0.757675\pi$
$691$	6.18944	−	10.7204i	0.235457	−	0.407824i	0.959405	+	0.282030i	$0.0910079\pi$
$692$	−5.06533			−0.192555
$693$		0			0
$694$	−7.48804			−0.284242
$695$	6.19303	−	10.7266i	0.234915	−	0.406885i
$696$		0			0
$697$	−11.3187	−	19.6046i	−0.428726	−	0.742575i
$698$	−13.6389	+	7.87442i	−0.516240	+	0.298051i
$699$		0			0
$700$	−0.700188	−	0.404254i	−0.0264646	−	0.0152793i
$701$	41.3363			1.56125			0.780626	−	0.624999i	$-0.214900\pi$
$701$	41.3363			1.56125			0.780626	+	0.624999i	$0.214900\pi$
$702$		0			0
$703$		−	7.78059i		−	0.293450i
$704$	3.25169	+	0.653075i	0.122553	+	0.0246137i
$705$		0			0
$706$	14.8221	−	8.55757i	0.557839	−	0.322068i
$707$	8.00443	−	4.62136i	0.301037	−	0.173804i
$708$		0			0
$709$	5.28407	−	9.15227i	0.198447	−	0.343721i	−0.749578	−	0.661916i	$-0.769743\pi$
$709$	5.28407	−	9.15227i	0.198447	−	0.343721i	0.948025	+	0.318195i	$0.103077\pi$
$710$	8.87630			0.333121
$711$		0			0
$712$			7.20794i			0.270129i
$713$	−29.3477	−	16.9439i	−1.09908	−	0.634554i
$714$		0			0
$715$	4.02774	−	4.57560i	0.150629	−	0.171118i
$716$	−0.591638	+	0.341582i	−0.0221105	+	0.0127655i
$717$		0			0
$718$	−5.40697	+	9.36515i	−0.201786	+	0.349504i
$719$		−	31.7377i		−	1.18362i	−0.806079	−	0.591809i	$-0.798414\pi$
$719$		−	31.7377i		−	1.18362i	0.806079	−	0.591809i	$-0.201586\pi$
$720$		0			0
$721$		−	10.5257i		−	0.391996i
$722$	−7.75052	+	13.4243i	−0.288444	+	0.499600i
$723$		0			0
$724$	4.87307	+	8.44041i	0.181106	+	0.313685i
$725$	0.0530153	+	0.0918253i	0.00196894	+	0.00341030i
$726$		0			0
$727$	−11.1834	+	19.3702i	−0.414770	+	0.718402i	−0.995404	−	0.0957623i	$-0.969471\pi$
$727$	−11.1834	+	19.3702i	−0.414770	+	0.718402i	0.580635	+	0.814164i	$0.302804\pi$
$728$	−1.48600			−0.0550747
$729$		0			0
$730$	14.6450			0.542035
$731$	−7.13294	−	4.11821i	−0.263821	−	0.152317i
$732$		0			0
$733$	−7.78084	+	4.49227i	−0.287392	+	0.165926i	−0.636765	−	0.771058i	$-0.719728\pi$
$733$	−7.78084	+	4.49227i	−0.287392	+	0.165926i	0.349373	+	0.936984i	$0.386395\pi$
$734$	−0.210501	−	0.364599i	−0.00776974	−	0.0134576i
$735$		0			0
$736$	−4.50121	−	2.59877i	−0.165917	−	0.0957921i
$737$	−0.469933	−	1.39286i	−0.0173102	−	0.0513068i
$738$		0			0
$739$		−	34.8736i		−	1.28285i	−0.767187	−	0.641423i	$-0.778344\pi$
$739$		−	34.8736i		−	1.28285i	0.767187	−	0.641423i	$-0.221656\pi$
$740$	−3.60224	−	2.07976i	−0.132421	−	0.0764534i
$741$		0			0
$742$	4.48462	+	7.76760i	0.164636	+	0.285157i
$743$	−17.2037	−	29.7977i	−0.631142	−	1.09317i	−0.987319	−	0.158752i	$-0.949253\pi$
$743$	−17.2037	−	29.7977i	−0.631142	−	1.09317i	0.356176	−	0.934419i	$-0.384080\pi$
$744$		0			0
$745$	−17.9074	−	10.3389i	−0.656077	−	0.378786i
$746$		−	31.1764i		−	1.14145i
$747$		0			0
$748$	−6.89357	−	20.4322i	−0.252054	−	0.747077i
$749$	13.6638	+	7.88880i	0.499264	+	0.288250i
$750$		0			0
$751$	−10.4865	−	18.1631i	−0.382657	−	0.662782i	0.608784	−	0.793336i	$-0.291658\pi$
$751$	−10.4865	−	18.1631i	−0.382657	−	0.662782i	−0.991441	+	0.130554i	$0.958324\pi$
$752$	−4.05652	+	2.34204i	−0.147926	+	0.0854052i
$753$		0			0
$754$	0.168770	+	0.0974397i	0.00614626	+	0.00354854i
$755$	−20.3009			−0.738824
$756$		0			0
$757$	10.1082			0.367387			0.183694	−	0.982984i	$-0.441195\pi$
$757$	10.1082			0.367387			0.183694	+	0.982984i	$0.441195\pi$
$758$	6.87043	−	11.8999i	0.249545	−	0.432225i
$759$		0			0
$760$	−0.935276	−	1.61995i	−0.0339260	−	0.0587616i
$761$	4.66276	+	8.07613i	0.169025	+	0.292759i	0.938077	−	0.346426i	$-0.112605\pi$
$761$	4.66276	+	8.07613i	0.169025	+	0.292759i	−0.769052	+	0.639186i	$0.779272\pi$
$762$		0			0
$763$	1.26446	−	2.19010i	0.0457764	−	0.0792870i
$764$		−	5.87887i		−	0.212690i
$765$		0			0
$766$			9.24817i			0.334150i
$767$	−1.46900	+	2.54438i	−0.0530424	+	0.0918722i
$768$		0			0
$769$	2.46917	−	1.42557i	0.0890404	−	0.0514075i	−0.454819	−	0.890584i	$-0.650296\pi$
$769$	2.46917	−	1.42557i	0.0890404	−	0.0514075i	0.543859	+	0.839177i	$0.316963\pi$
$770$	1.77178	−	2.01279i	0.0638506	−	0.0725358i
$771$		0			0
$772$	1.52540	+	0.880691i	0.0549004	+	0.0316968i
$773$			39.7303i			1.42900i	0.699635	+	0.714500i	$0.253346\pi$
$773$			39.7303i			1.42900i	−0.699635	+	0.714500i	$0.746654\pi$
$774$		0			0
$775$	−6.51996			−0.234204
$776$	5.63450	−	9.75924i	0.202267	−	0.350336i
$777$		0			0
$778$	4.41058	−	2.54645i	0.158127	−	0.0912945i
$779$	5.64024	−	3.25639i	0.202083	−	0.116672i
$780$		0			0
$781$	−5.79689	+	28.8630i	−0.207429	+	1.03280i
$782$			33.7931i			1.20844i
$783$		0			0
$784$	6.34632			0.226654
$785$	−1.86056	−	1.07419i	−0.0664062	−	0.0383397i
$786$		0			0
$787$	−8.69628	+	5.02080i	−0.309989	+	0.178972i	−0.646921	−	0.762557i	$-0.723944\pi$
$787$	−8.69628	+	5.02080i	−0.309989	+	0.178972i	0.336933	+	0.941529i	$0.390611\pi$
$788$	1.13386	+	1.96390i	0.0403919	+	0.0699609i
$789$		0			0
$790$	6.23895	−	10.8062i	0.221972	−	0.384467i
$791$	0.653519			0.0232365
$792$		0			0
$793$	−22.8354			−0.810910
$794$	−9.04861	+	15.6726i	−0.321123	+	0.556201i
$795$		0			0
$796$	−11.5064	−	19.9297i	−0.407835	−	0.706390i
$797$	14.5687	−	8.41127i	0.516051	−	0.297942i	−0.219266	−	0.975665i	$-0.570366\pi$
$797$	14.5687	−	8.41127i	0.516051	−	0.297942i	0.735318	+	0.677723i	$0.237033\pi$
$798$		0			0
$799$	26.3744	+	15.2273i	0.933061	+	0.538703i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$			7.35100i			0.259573i
$803$	−9.56427	+	47.6210i	−0.337516	+	1.68051i
$804$		0			0
$805$	−3.63926	+	2.10113i	−0.128267	+	0.0740550i
$806$	−10.3779	+	5.99169i	−0.365546	+	0.211048i
$807$		0			0
$808$	5.71591	−	9.90025i	0.201085	−	0.348290i
$809$	−36.9210			−1.29807			−0.649037	−	0.760757i	$-0.724828\pi$
$809$	−36.9210			−1.29807			−0.649037	+	0.760757i	$0.724828\pi$
$810$		0			0
$811$		−	56.0473i		−	1.96809i	−0.177925	−	0.984044i	$-0.556938\pi$
$811$		−	56.0473i		−	1.96809i	0.177925	−	0.984044i	$-0.443062\pi$
$812$	0.0742414	+	0.0428633i	0.00260536	+	0.00150421i
$813$		0			0
$814$	9.11526	−	10.3551i	0.319490	−	0.362948i
$815$	10.2527	−	5.91940i	0.359137	−	0.207348i
$816$		0			0
$817$	1.18481	−	2.05215i	0.0414513	−	0.0717957i
$818$		−	8.44443i		−	0.295253i
$819$		0			0
$820$		−	3.48175i		−	0.121588i
$821$	−13.8065	+	23.9135i	−0.481850	+	0.834589i	−0.999783	−	0.0208325i	$-0.993368\pi$
$821$	−13.8065	+	23.9135i	−0.481850	+	0.834589i	0.517933	+	0.855421i	$0.326702\pi$
$822$		0			0
$823$	−24.0282	−	41.6180i	−0.837570	−	1.45071i	−0.891921	−	0.452191i	$-0.850642\pi$
$823$	−24.0282	−	41.6180i	−0.837570	−	1.45071i	0.0543515	−	0.998522i	$-0.482691\pi$
$824$	−6.50932	−	11.2745i	−0.226763	−	0.392765i
$825$		0			0
$826$	−0.646205	+	1.11926i	−0.0224844	+	0.0389440i
$827$	18.7015			0.650316			0.325158	−	0.945660i	$-0.394582\pi$
$827$	18.7015			0.650316			0.325158	+	0.945660i	$0.394582\pi$
$828$		0			0
$829$	23.4767			0.815378			0.407689	−	0.913121i	$-0.366335\pi$
$829$	23.4767			0.815378			0.407689	+	0.913121i	$0.366335\pi$
$830$	9.99972	+	5.77334i	0.347095	+	0.200396i
$831$		0			0
$832$	−1.59171	+	0.918976i	−0.0551827	+	0.0318598i
$833$	−20.6310	−	35.7340i	−0.714823	−	1.23811i
$834$		0			0
$835$	−19.8001	−	11.4316i	−0.685211	−	0.395607i
$836$	5.87837	−	1.98328i	0.203308	−	0.0685932i
$837$		0			0
$838$		−	29.9539i		−	1.03474i
$839$	2.82819	+	1.63286i	0.0976399	+	0.0563724i	0.548025	−	0.836462i	$-0.315380\pi$
$839$	2.82819	+	1.63286i	0.0976399	+	0.0563724i	−0.450385	+	0.892834i	$0.648713\pi$
$840$		0			0
$841$	14.4944	+	25.1050i	0.499806	+	0.865690i
$842$	4.82963	+	8.36516i	0.166440	+	0.288283i
$843$		0			0
$844$	6.07694	+	3.50852i	0.209177	+	0.120768i
$845$		−	9.62193i		−	0.331004i
$846$		0			0
$847$	5.38785	+	7.07579i	0.185129	+	0.243127i
$848$	9.60733	+	5.54680i	0.329917	+	0.190478i
$849$		0			0
$850$	3.25087	+	5.63067i	0.111504	+	0.193130i
$851$	−18.7228	+	10.8096i	−0.641811	+	0.370550i
$852$		0			0
$853$	31.3363	+	18.0920i	1.07293	+	0.619459i	0.928982	−	0.370125i	$-0.120685\pi$
$853$	31.3363	+	18.0920i	1.07293	+	0.619459i	0.143953	+	0.989585i	$0.454019\pi$
$854$	−10.0452			−0.343740
$855$		0			0
$856$	19.5145			0.666991
$857$	22.9067	−	39.6755i	0.782477	−	1.35529i	−0.148017	−	0.988985i	$-0.547289\pi$
$857$	22.9067	−	39.6755i	0.782477	−	1.35529i	0.930495	−	0.366306i	$-0.119378\pi$
$858$		0			0
$859$	25.7231	+	44.5537i	0.877661	+	1.52015i	0.853900	+	0.520437i	$0.174231\pi$
$859$	25.7231	+	44.5537i	0.877661	+	1.52015i	0.0237611	+	0.999718i	$0.492436\pi$
$860$	−0.633401	−	1.09708i	−0.0215988	−	0.0374102i
$861$		0			0
$862$	−3.71613	+	6.43652i	−0.126572	+	0.219229i
$863$			40.1888i			1.36804i	0.729462	+	0.684021i	$0.239771\pi$
$863$			40.1888i			1.36804i	−0.729462	+	0.684021i	$0.760229\pi$
$864$		0			0
$865$			5.06533i			0.172226i
$866$	−19.3030	+	33.4338i	−0.655943	+	1.13613i
$867$		0			0
$868$	−4.56519	+	2.63572i	−0.154953	+	0.0894620i
$869$	31.0639	+	27.3444i	1.05377	+	0.927595i
$870$		0			0
$871$	0.705483	+	0.407311i	0.0239044	+	0.0138012i
$872$		−	3.12788i		−	0.105923i
$873$		0			0
$874$	−9.72228			−0.328861
$875$	−0.404254	+	0.700188i	−0.0136663	+	0.0236707i
$876$		0			0
$877$	−7.65282	+	4.41836i	−0.258417	+	0.149197i	−0.623612	−	0.781734i	$-0.714336\pi$
$877$	−7.65282	+	4.41836i	−0.258417	+	0.149197i	0.365195	+	0.930931i	$0.381002\pi$
$878$	30.8607	−	17.8174i	1.04150	−	0.601310i
$879$		0			0
$880$	0.653075	−	3.25169i	0.0220152	−	0.109614i
$881$			28.9530i			0.975451i	0.872997	+	0.487725i	$0.162173\pi$
$881$			28.9530i			0.975451i	−0.872997	+	0.487725i	$0.837827\pi$
$882$		0			0
$883$	22.1157			0.744253			0.372127	−	0.928182i	$-0.378629\pi$
$883$	22.1157			0.744253			0.372127	+	0.928182i	$0.378629\pi$
$884$	10.3489	+	5.97494i	0.348071	+	0.200959i
$885$		0			0
$886$	19.2694	−	11.1252i	0.647368	−	0.373758i
$887$	17.5830	+	30.4547i	0.590380	+	1.02257i	0.994181	+	0.107721i	$0.0343553\pi$
$887$	17.5830	+	30.4547i	0.590380	+	1.02257i	−0.403802	+	0.914847i	$0.632311\pi$
$888$		0			0
$889$	8.63378	−	14.9541i	0.289568	−	0.501546i
$890$	7.20794			0.241611
$891$		0			0
$892$	−17.3266			−0.580136
$893$	−4.38090	+	7.58794i	−0.146601	+	0.253921i
$894$		0			0
$895$	0.341582	+	0.591638i	0.0114178	+	0.0197763i
$896$	−0.700188	+	0.404254i	−0.0233916	+	0.0135052i
$897$		0			0
$898$	−21.5944	−	12.4675i	−0.720615	−	0.416047i
$899$	0.691316			0.0230567
$900$		0			0
$901$		−	72.1276i		−	2.40292i
$902$	11.3216	+	2.27384i	0.376967	+	0.0757107i
$903$		0			0
$904$	0.700012	−	0.404152i	0.0232820	−	0.0134419i
$905$	8.44041	−	4.87307i	0.280569	−	0.161986i
$906$		0			0
$907$	23.6311	−	40.9302i	0.784657	−	1.35907i	−0.144547	−	0.989498i	$-0.546173\pi$
$907$	23.6311	−	40.9302i	0.784657	−	1.35907i	0.929204	−	0.369567i	$-0.120494\pi$
$908$	7.87967			0.261496
$909$		0			0
$910$			1.48600i			0.0492603i
$911$	−30.5270	−	17.6248i	−1.01141	−	0.583935i	−0.0998029	−	0.995007i	$-0.531821\pi$
$911$	−30.5270	−	17.6248i	−1.01141	−	0.583935i	−0.911603	+	0.411072i	$0.865155\pi$
$912$		0			0
$913$	−25.3037	+	28.7456i	−0.837430	+	0.951340i
$914$	−3.35432	+	1.93662i	−0.110951	+	0.0640577i
$915$		0			0
$916$	3.92425	−	6.79701i	0.129661	−	0.224579i
$917$			4.98292i			0.164551i
$918$		0			0
$919$			11.7900i			0.388916i	0.980911	+	0.194458i	$0.0622948\pi$
$919$			11.7900i			0.388916i	−0.980911	+	0.194458i	$0.937705\pi$
$920$	−2.59877	+	4.50121i	−0.0856790	+	0.148400i
$921$		0			0
$922$	4.36386	+	7.55843i	0.143716	+	0.248924i
$923$	−8.15710	−	14.1285i	−0.268494	−	0.465046i
$924$		0			0
$925$	−2.07976	+	3.60224i	−0.0683820	+	0.118441i
$926$	30.4202			0.999670
$927$		0			0
$928$	0.106031			0.00348063
$929$	−10.4435	−	6.02956i	−0.342640	−	0.197823i	0.318799	−	0.947822i	$-0.396721\pi$
$929$	−10.4435	−	6.02956i	−0.342640	−	0.197823i	−0.661439	+	0.749999i	$0.730054\pi$
$930$		0			0
$931$	10.2807	−	5.93556i	0.336936	−	0.194530i
$932$	−3.19402	−	5.53221i	−0.104624	−	0.181214i
$933$		0			0
$934$	−12.4070	−	7.16319i	−0.405970	−	0.234387i
$935$	−20.4322	+	6.89357i	−0.668206	+	0.225444i
$936$		0			0
$937$		−	53.5358i		−	1.74894i	−0.485080	−	0.874470i	$-0.661209\pi$
$937$		−	53.5358i		−	1.74894i	0.485080	−	0.874470i	$-0.338791\pi$
$938$	0.310339	+	0.179174i	0.0101329	+	0.00585024i
$939$		0			0
$940$	2.34204	+	4.05652i	0.0763888	+	0.132309i
$941$	−4.14260	−	7.17519i	−0.135045	−	0.233904i	0.790570	−	0.612372i	$-0.209784\pi$
$941$	−4.14260	−	7.17519i	−0.135045	−	0.233904i	−0.925615	+	0.378468i	$0.876451\pi$
$942$		0			0
$943$	−15.6721	−	9.04827i	−0.510353	−	0.294652i
$944$			1.59851i			0.0520272i
$945$		0			0
$946$	3.98103	−	1.34315i	0.129435	−	0.0436695i
$947$	−44.3316	−	25.5949i	−1.44058	−	0.831722i	−0.442696	−	0.896672i	$-0.645978\pi$
$947$	−44.3316	−	25.5949i	−1.44058	−	0.831722i	−0.997889	+	0.0649501i	$0.979311\pi$
$948$		0			0
$949$	−13.4584	−	23.3106i	−0.436878	−	0.756695i
$950$	−1.61995	+	0.935276i	−0.0525580	+	0.0303444i
$951$		0			0
$952$	4.55243	+	2.62835i	0.147545	+	0.0851853i
$953$	17.2842			0.559891			0.279945	−	0.960016i	$-0.409684\pi$
$953$	17.2842			0.559891			0.279945	+	0.960016i	$0.409684\pi$
$954$		0			0
$955$	−5.87887			−0.190236
$956$	−7.14471	+	12.3750i	−0.231076	+	0.400236i
$957$		0			0
$958$	−4.21713	−	7.30428i	−0.136249	−	0.235991i
$959$	4.08314	+	7.07220i	0.131851	+	0.228373i
$960$		0			0
$961$	−5.75493	+	9.96783i	−0.185643	+	0.321543i
$962$			7.64499i			0.246484i
$963$		0			0
$964$			6.44039i			0.207431i
$965$	0.880691	−	1.52540i	0.0283505	−	0.0491044i
$966$		0			0
$967$	−11.2321	+	6.48486i	−0.361200	+	0.208539i	−0.669607	−	0.742715i	$-0.733538\pi$
$967$	−11.2321	+	6.48486i	−0.361200	+	0.208539i	0.308407	+	0.951255i	$0.400204\pi$
$968$	10.1470	+	4.24720i	0.326136	+	0.136510i
$969$		0			0
$970$	−9.75924	−	5.63450i	−0.313350	−	0.180913i
$971$			0.242751i			0.00779026i	0.999992	+	0.00389513i	$0.00123986\pi$
$971$			0.242751i			0.00779026i	−0.999992	+	0.00389513i	$0.998760\pi$
$972$		0			0
$973$	−10.0142			−0.321041
$974$	−4.02490	+	6.97134i	−0.128966	+	0.223376i
$975$		0			0
$976$	−10.7598	+	6.21219i	−0.344414	+	0.198847i
$977$	−25.4078	+	14.6692i	−0.812866	+	0.469309i	−0.847950	−	0.530076i	$-0.822163\pi$
$977$	−25.4078	+	14.6692i	−0.812866	+	0.469309i	0.0350839	+	0.999384i	$0.488830\pi$
$978$		0			0
$979$	−4.70732	+	23.4380i	−0.150447	+	0.749081i
$980$		−	6.34632i		−	0.202726i
$981$		0			0
$982$	−0.741818			−0.0236724
$983$	−46.8439	−	27.0453i	−1.49409	−	0.862612i	−0.494112	−	0.869398i	$-0.664507\pi$
$983$	−46.8439	−	27.0453i	−1.49409	−	0.862612i	−0.999977	+	0.00678602i	$0.997840\pi$
$984$		0			0
$985$	1.96390	−	1.13386i	0.0625749	−	0.0361276i
$986$	−0.344692	−	0.597023i	−0.0109772	−	0.0190131i
$987$		0			0
$988$	−1.71899	+	2.97738i	−0.0546884	+	0.0947232i
$989$	−6.58427			−0.209368
$990$		0			0
$991$	−26.7484			−0.849690			−0.424845	−	0.905266i	$-0.639671\pi$
$991$	−26.7484			−0.849690			−0.424845	+	0.905266i	$0.639671\pi$
$992$	−3.25998	+	5.64645i	−0.103504	+	0.179275i
$993$		0			0
$994$	−3.58827	−	6.21507i	−0.113813	−	0.197130i
$995$	−19.9297	+	11.5064i	−0.631815	+	0.364778i
$996$		0			0
$997$	19.4039	+	11.2028i	0.614526	+	0.354797i	0.774735	−	0.632286i	$-0.217883\pi$
$997$	19.4039	+	11.2028i	0.614526	+	0.354797i	−0.160209	+	0.987083i	$0.551217\pi$
$998$	−5.61657			−0.177789
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.a.791.5		48
3.2	odd	2		990.2.t.b.461.6	yes	48
9.4	even	3		990.2.t.a.131.6	✓	48
9.5	odd	6		2970.2.t.b.2771.5		48
11.10	odd	2		2970.2.t.b.791.5		48
33.32	even	2		990.2.t.a.461.6	yes	48
99.32	even	6	inner	2970.2.t.a.2771.5		48
99.76	odd	6		990.2.t.b.131.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.6	✓	48	9.4	even	3
990.2.t.a.461.6	yes	48	33.32	even	2
990.2.t.b.131.6	yes	48	99.76	odd	6
990.2.t.b.461.6	yes	48	3.2	odd	2
2970.2.t.a.791.5		48	1.1	even	1	trivial
2970.2.t.a.2771.5		48	99.32	even	6	inner
2970.2.t.b.791.5		48	11.10	odd	2
2970.2.t.b.2771.5		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2970.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.700188 + 0.404254i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(3.25169 + 0.653075i) q^{11} +(-1.59171 + 0.918976i) q^{13} +(-0.700188 + 0.404254i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.50173 q^{17} +1.87055i q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.19142 + 2.48951i) q^{22} +(4.50121 - 2.59877i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.83795i q^{26} -0.808507i q^{28} +(-0.0530153 + 0.0918253i) q^{29} +(-3.25998 - 5.64645i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.25087 + 5.63067i) q^{34} -0.808507 q^{35} -4.15951 q^{37} +(-1.61995 - 0.935276i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-1.74087 - 3.01528i) q^{41} +(-1.09708 - 0.633401i) q^{43} +(-1.06027 - 3.14258i) q^{44} +5.19755i q^{46} +(4.05652 + 2.34204i) q^{47} +(-3.17316 - 5.49607i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.59171 + 0.918976i) q^{52} -11.0936i q^{53} +(-3.14258 + 1.06027i) q^{55} +(0.700188 + 0.404254i) q^{56} +(-0.0530153 - 0.0918253i) q^{58} +(1.38435 - 0.799257i) q^{59} +(10.7598 + 6.21219i) q^{61} +6.51996 q^{62} +1.00000 q^{64} +(0.918976 - 1.59171i) q^{65} +(-0.221611 - 0.383842i) q^{67} +(-3.25087 - 5.63067i) q^{68} +(0.404254 - 0.700188i) q^{70} +8.87630i q^{71} +14.6450i q^{73} +(2.07976 - 3.60224i) q^{74} +(1.61995 - 0.935276i) q^{76} +(2.01279 + 1.77178i) q^{77} +(10.8062 + 6.23895i) q^{79} -1.00000i q^{80} +3.48175 q^{82} +(-5.77334 + 9.99972i) q^{83} +(-5.63067 + 3.25087i) q^{85} +(1.09708 - 0.633401i) q^{86} +(3.25169 + 0.653075i) q^{88} +7.20794i q^{89} -1.48600 q^{91} +(-4.50121 - 2.59877i) q^{92} +(-4.05652 + 2.34204i) q^{94} +(-0.935276 - 1.61995i) q^{95} +(5.63450 - 9.75924i) q^{97} +6.34632 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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