LMFDB - Embedded newform 2970.2.t.a.791.11

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			791.11
Character	$\chi$	$=$	2970.791
Dual form			2970.2.t.a.2771.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.83014 + 1.63398i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(0.898862 + 3.19250i) q^{11} +(2.49573 - 1.44091i) q^{13} +(-2.83014 + 1.63398i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.88020 q^{17} +4.33972i q^{19} +(0.866025 + 0.500000i) q^{20} +(-3.21422 - 0.817812i) q^{22} +(-6.17351 + 3.56428i) q^{23} +(0.500000 - 0.866025i) q^{25} +2.88183i q^{26} -3.26796i q^{28} +(0.688200 - 1.19200i) q^{29} +(1.78294 + 3.08815i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.940102 - 1.62830i) q^{34} -3.26796 q^{35} -7.24005 q^{37} +(-3.75831 - 2.16986i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-3.83291 - 6.63880i) q^{41} +(6.89392 + 3.98021i) q^{43} +(2.31535 - 2.37469i) q^{44} -7.12855i q^{46} +(8.91993 + 5.14992i) q^{47} +(1.83978 + 3.18659i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.49573 - 1.44091i) q^{52} -3.25710i q^{53} +(-2.37469 - 2.31535i) q^{55} +(2.83014 + 1.63398i) q^{56} +(0.688200 + 1.19200i) q^{58} +(1.31366 - 0.758441i) q^{59} +(6.49131 + 3.74776i) q^{61} -3.56588 q^{62} +1.00000 q^{64} +(-1.44091 + 2.49573i) q^{65} +(1.84864 + 3.20194i) q^{67} +(0.940102 + 1.62830i) q^{68} +(1.63398 - 2.83014i) q^{70} +15.6364i q^{71} -11.3309i q^{73} +(3.62003 - 6.27007i) q^{74} +(3.75831 - 2.16986i) q^{76} +(-2.67258 + 10.5039i) q^{77} +(-11.3436 - 6.54921i) q^{79} -1.00000i q^{80} +7.66582 q^{82} +(-0.462740 + 0.801490i) q^{83} +(1.62830 - 0.940102i) q^{85} +(-6.89392 + 3.98021i) q^{86} +(0.898862 + 3.19250i) q^{88} -2.39265i q^{89} +9.41769 q^{91} +(6.17351 + 3.56428i) q^{92} +(-8.91993 + 5.14992i) q^{94} +(-2.16986 - 3.75831i) q^{95} +(-8.05367 + 13.9494i) q^{97} -3.67955 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	2.83014	+	1.63398i	1.06969	+	0.617586i	0.928097	−	0.372339i	$-0.121444\pi$
$7$	2.83014	+	1.63398i	1.06969	+	0.617586i	0.141594	+	0.989925i	$0.454777\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	0.898862	+	3.19250i	0.271017	+	0.962575i
$11$	0.898862	+	3.19250i	0.271017	+	0.962575i
$12$		0			0
$13$	2.49573	−	1.44091i	0.692192	−	0.399637i	−0.112240	−	0.993681i	$-0.535803\pi$
$13$	2.49573	−	1.44091i	0.692192	−	0.399637i	0.804433	+	0.594044i	$0.202469\pi$
$14$	−2.83014	+	1.63398i	−0.756385	+	0.436699i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.88020			−0.456016			−0.228008	−	0.973659i	$-0.573221\pi$
$17$	−1.88020			−0.456016			−0.228008	+	0.973659i	$0.573221\pi$
$18$		0			0
$19$			4.33972i			0.995600i	0.867292	+	0.497800i	$0.165859\pi$
$19$			4.33972i			0.995600i	−0.867292	+	0.497800i	$0.834141\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	−3.21422	−	0.817812i	−0.685273	−	0.174358i
$23$	−6.17351	+	3.56428i	−1.28727	+	0.743203i	−0.978166	−	0.207827i	$-0.933361\pi$
$23$	−6.17351	+	3.56428i	−1.28727	+	0.743203i	−0.309099	+	0.951030i	$0.600028\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			2.88183i			0.565173i
$27$		0			0
$28$		−	3.26796i		−	0.617586i
$29$	0.688200	−	1.19200i	0.127796	−	0.221348i	−0.795027	−	0.606574i	$-0.792543\pi$
$29$	0.688200	−	1.19200i	0.127796	−	0.221348i	0.922822	+	0.385226i	$0.125877\pi$
$30$		0			0
$31$	1.78294	+	3.08815i	0.320226	+	0.554647i	0.980534	−	0.196347i	$-0.0629079\pi$
$31$	1.78294	+	3.08815i	0.320226	+	0.554647i	−0.660309	+	0.750994i	$0.729575\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	0.940102	−	1.62830i	0.161226	−	0.279252i
$35$	−3.26796			−0.552386
$36$		0			0
$37$	−7.24005			−1.19026			−0.595129	−	0.803630i	$-0.702899\pi$
$37$	−7.24005			−1.19026			−0.595129	+	0.803630i	$0.702899\pi$
$38$	−3.75831	−	2.16986i	−0.609678	−	0.351998i
$39$		0			0
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	−3.83291	−	6.63880i	−0.598600	−	1.03681i	−0.993028	−	0.117879i	$-0.962391\pi$
$41$	−3.83291	−	6.63880i	−0.598600	−	1.03681i	0.394428	−	0.918927i	$-0.370943\pi$
$42$		0			0
$43$	6.89392	+	3.98021i	1.05131	+	0.606976i	0.923017	−	0.384760i	$-0.125716\pi$
$43$	6.89392	+	3.98021i	1.05131	+	0.606976i	0.128296	+	0.991736i	$0.459049\pi$
$44$	2.31535	−	2.37469i	0.349053	−	0.357997i
$45$		0			0
$46$		−	7.12855i		−	1.05105i
$47$	8.91993	+	5.14992i	1.30111	+	0.751194i	0.980594	−	0.196051i	$-0.0628118\pi$
$47$	8.91993	+	5.14992i	1.30111	+	0.751194i	0.320512	+	0.947245i	$0.396145\pi$
$48$		0			0
$49$	1.83978	+	3.18659i	0.262825	+	0.455227i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−2.49573	−	1.44091i	−0.346096	−	0.199819i
$53$		−	3.25710i		−	0.447398i	−0.974658	−	0.223699i	$-0.928187\pi$
$53$		−	3.25710i		−	0.447398i	0.974658	−	0.223699i	$-0.0718132\pi$
$54$		0			0
$55$	−2.37469	−	2.31535i	−0.320203	−	0.312202i
$56$	2.83014	+	1.63398i	0.378193	+	0.218350i
$57$		0			0
$58$	0.688200	+	1.19200i	0.0903651	+	0.156517i
$59$	1.31366	−	0.758441i	0.171024	−	0.0987406i	−0.412045	−	0.911164i	$-0.635185\pi$
$59$	1.31366	−	0.758441i	0.171024	−	0.0987406i	0.583068	+	0.812423i	$0.301852\pi$
$60$		0			0
$61$	6.49131	+	3.74776i	0.831128	+	0.479852i	0.854239	−	0.519881i	$-0.174024\pi$
$61$	6.49131	+	3.74776i	0.831128	+	0.479852i	−0.0231111	+	0.999733i	$0.507357\pi$
$62$	−3.56588			−0.452868
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.44091	+	2.49573i	−0.178723	+	0.309558i
$66$		0			0
$67$	1.84864	+	3.20194i	0.225847	+	0.391179i	0.956573	−	0.291492i	$-0.0941516\pi$
$67$	1.84864	+	3.20194i	0.225847	+	0.391179i	−0.730726	+	0.682671i	$0.760818\pi$
$68$	0.940102	+	1.62830i	0.114004	+	0.197461i
$69$		0			0
$70$	1.63398	−	2.83014i	0.195298	−	0.338266i
$71$			15.6364i			1.85570i	0.372959	+	0.927848i	$0.378343\pi$
$71$			15.6364i			1.85570i	−0.372959	+	0.927848i	$0.621657\pi$
$72$		0			0
$73$		−	11.3309i		−	1.32618i	−0.748540	−	0.663090i	$-0.769245\pi$
$73$		−	11.3309i		−	1.32618i	0.748540	−	0.663090i	$-0.230755\pi$
$74$	3.62003	−	6.27007i	0.420819	−	0.728881i
$75$		0			0
$76$	3.75831	−	2.16986i	0.431107	−	0.248900i
$77$	−2.67258	+	10.5039i	−0.304568	+	1.19703i
$78$		0			0
$79$	−11.3436	−	6.54921i	−1.27625	−	0.736843i	−0.300093	−	0.953910i	$-0.597018\pi$
$79$	−11.3436	−	6.54921i	−1.27625	−	0.736843i	−0.976157	+	0.217067i	$0.930351\pi$
$80$		−	1.00000i		−	0.111803i
$81$		0			0
$82$	7.66582			0.846548
$83$	−0.462740	+	0.801490i	−0.0507924	+	0.0879749i	−0.890304	−	0.455367i	$-0.849508\pi$
$83$	−0.462740	+	0.801490i	−0.0507924	+	0.0879749i	0.839511	+	0.543342i	$0.182841\pi$
$84$		0			0
$85$	1.62830	−	0.940102i	0.176614	−	0.101968i
$86$	−6.89392	+	3.98021i	−0.743390	+	0.429197i
$87$		0			0
$88$	0.898862	+	3.19250i	0.0958190	+	0.340321i
$89$		−	2.39265i		−	0.253620i	−0.991927	−	0.126810i	$-0.959526\pi$
$89$		−	2.39265i		−	0.253620i	0.991927	−	0.126810i	$-0.0404739\pi$
$90$		0			0
$91$	9.41769			0.987242
$92$	6.17351	+	3.56428i	0.643633	+	0.371601i
$93$		0			0
$94$	−8.91993	+	5.14992i	−0.920021	+	0.531174i
$95$	−2.16986	−	3.75831i	−0.222623	−	0.385594i
$96$		0			0
$97$	−8.05367	+	13.9494i	−0.817726	+	1.41634i	0.0896275	+	0.995975i	$0.471432\pi$
$97$	−8.05367	+	13.9494i	−0.817726	+	1.41634i	−0.907354	+	0.420368i	$0.861901\pi$
$98$	−3.67955			−0.371691
$99$		0			0
$100$	−1.00000			−0.100000
$101$	1.81753	−	3.14805i	0.180851	−	0.313243i	−0.761320	−	0.648377i	$-0.775448\pi$
$101$	1.81753	−	3.14805i	0.180851	−	0.313243i	0.942171	+	0.335134i	$0.108782\pi$
$102$		0			0
$103$	1.93445	+	3.35057i	0.190607	+	0.330141i	0.945452	−	0.325763i	$-0.105621\pi$
$103$	1.93445	+	3.35057i	0.190607	+	0.330141i	−0.754845	+	0.655904i	$0.772288\pi$
$104$	2.49573	−	1.44091i	0.244727	−	0.141293i
$105$		0			0
$106$	2.82074	+	1.62855i	0.273974	+	0.158179i
$107$	−7.19194			−0.695271			−0.347635	−	0.937630i	$-0.613015\pi$
$107$	−7.19194			−0.695271			−0.347635	+	0.937630i	$0.613015\pi$
$108$		0			0
$109$		−	12.6752i		−	1.21406i	−0.794678	−	0.607031i	$-0.792360\pi$
$109$		−	12.6752i		−	1.21406i	0.794678	−	0.607031i	$-0.207640\pi$
$110$	3.19250	−	0.898862i	0.304393	−	0.0857031i
$111$		0			0
$112$	−2.83014	+	1.63398i	−0.267423	+	0.154397i
$113$	2.95268	−	1.70473i	0.277765	−	0.160368i	−0.354646	−	0.935001i	$-0.615399\pi$
$113$	2.95268	−	1.70473i	0.277765	−	0.160368i	0.632411	+	0.774633i	$0.282065\pi$
$114$		0			0
$115$	3.56428	−	6.17351i	0.332370	−	0.575682i
$116$	−1.37640			−0.127796
$117$		0			0
$118$			1.51688i			0.139640i
$119$	−5.32123	−	3.07221i	−0.487796	−	0.281629i
$120$		0			0
$121$	−9.38409	+	5.73923i	−0.853100	+	0.521748i
$122$	−6.49131	+	3.74776i	−0.587696	+	0.339306i
$123$		0			0
$124$	1.78294	−	3.08815i	0.160113	−	0.277324i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	6.58147i		−	0.584011i	−0.956417	−	0.292006i	$-0.905677\pi$
$127$		−	6.58147i		−	0.584011i	0.956417	−	0.292006i	$-0.0943226\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.44091	−	2.49573i	−0.126376	−	0.218890i
$131$	2.79118	+	4.83446i	0.243866	+	0.422389i	0.961812	−	0.273710i	$-0.0882508\pi$
$131$	2.79118	+	4.83446i	0.243866	+	0.422389i	−0.717946	+	0.696099i	$0.754917\pi$
$132$		0			0
$133$	−7.09101	+	12.2820i	−0.614868	+	1.06498i
$134$	−3.69728			−0.319397
$135$		0			0
$136$	−1.88020			−0.161226
$137$	4.52136	+	2.61041i	0.386286	+	0.223022i	0.680549	−	0.732702i	$-0.261741\pi$
$137$	4.52136	+	2.61041i	0.386286	+	0.223022i	−0.294264	+	0.955724i	$0.595074\pi$
$138$		0			0
$139$	−10.2061	+	5.89247i	−0.865666	+	0.499793i	−0.865906	−	0.500207i	$-0.833257\pi$
$139$	−10.2061	+	5.89247i	−0.865666	+	0.499793i	0.000239343		1.00000i	$0.499924\pi$
$140$	1.63398	+	2.83014i	0.138096	+	0.239190i
$141$		0			0
$142$	−13.5415	−	7.81819i	−1.13638	−	0.656088i
$143$	6.84343	+	6.67245i	0.572277	+	0.557978i
$144$		0			0
$145$			1.37640i			0.114304i
$146$	9.81284	+	5.66544i	0.812116	+	0.468875i
$147$		0			0
$148$	3.62003	+	6.27007i	0.297564	+	0.515397i
$149$	−1.35163	−	2.34110i	−0.110730	−	0.191790i	0.805335	−	0.592820i	$-0.201986\pi$
$149$	−1.35163	−	2.34110i	−0.110730	−	0.191790i	−0.916065	+	0.401030i	$0.868652\pi$
$150$		0			0
$151$	−9.07019	−	5.23668i	−0.738122	−	0.426155i	0.0832643	−	0.996527i	$-0.473465\pi$
$151$	−9.07019	−	5.23668i	−0.738122	−	0.426155i	−0.821386	+	0.570373i	$0.806799\pi$
$152$			4.33972i			0.351998i
$153$		0			0
$154$	−7.76038	−	7.56648i	−0.625349	−	0.609724i
$155$	−3.08815	−	1.78294i	−0.248046	−	0.143209i
$156$		0			0
$157$	4.83418	+	8.37305i	0.385810	+	0.668242i	0.991881	−	0.127168i	$-0.0405888\pi$
$157$	4.83418	+	8.37305i	0.385810	+	0.668242i	−0.606072	+	0.795410i	$0.707255\pi$
$158$	11.3436	−	6.54921i	0.902445	−	0.521027i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−23.2958			−1.83597
$162$		0			0
$163$	−20.0875			−1.57337			−0.786687	−	0.617352i	$-0.788206\pi$
$163$	−20.0875			−1.57337			−0.786687	+	0.617352i	$0.788206\pi$
$164$	−3.83291	+	6.63880i	−0.299300	+	0.518403i
$165$		0			0
$166$	−0.462740	−	0.801490i	−0.0359156	−	0.0622077i
$167$	10.1839	+	17.6390i	0.788052	+	1.36495i	0.927159	+	0.374668i	$0.122243\pi$
$167$	10.1839	+	17.6390i	0.788052	+	1.36495i	−0.139107	+	0.990277i	$0.544423\pi$
$168$		0			0
$169$	−2.34754	+	4.06606i	−0.180580	+	0.312773i
$170$			1.88020i			0.144205i
$171$		0			0
$172$		−	7.96041i		−	0.606976i
$173$	−6.26488	+	10.8511i	−0.476310	+	0.824994i	−0.999632	−	0.0271419i	$-0.991359\pi$
$173$	−6.26488	+	10.8511i	−0.476310	+	0.824994i	0.523321	+	0.852135i	$0.324693\pi$
$174$		0			0
$175$	2.83014	−	1.63398i	0.213938	−	0.123517i
$176$	−3.21422	−	0.817812i	−0.242281	−	0.0616449i
$177$		0			0
$178$	2.07209	+	1.19632i	0.155310	+	0.0896683i
$179$			22.5880i			1.68831i	0.536103	+	0.844153i	$0.319896\pi$
$179$			22.5880i			1.68831i	−0.536103	+	0.844153i	$0.680104\pi$
$180$		0			0
$181$	−16.0655			−1.19414			−0.597069	−	0.802190i	$-0.703668\pi$
$181$	−16.0655			−1.19414			−0.597069	+	0.802190i	$0.703668\pi$
$182$	−4.70884	+	8.15596i	−0.349043	+	0.604560i
$183$		0			0
$184$	−6.17351	+	3.56428i	−0.455117	+	0.262762i
$185$	6.27007	−	3.62003i	0.460985	−	0.266150i
$186$		0			0
$187$	−1.69004	−	6.00255i	−0.123588	−	0.438950i
$188$		−	10.2998i		−	0.751194i
$189$		0			0
$190$	4.33972			0.314836
$191$	−1.49071	−	0.860659i	−0.107864	−	0.0622751i	0.445098	−	0.895482i	$-0.353169\pi$
$191$	−1.49071	−	0.860659i	−0.107864	−	0.0622751i	−0.552961	+	0.833207i	$0.686502\pi$
$192$		0			0
$193$	10.9926	−	6.34656i	0.791262	−	0.456836i	−0.0491444	−	0.998792i	$-0.515649\pi$
$193$	10.9926	−	6.34656i	0.791262	−	0.456836i	0.840407	+	0.541956i	$0.182316\pi$
$194$	−8.05367	−	13.9494i	−0.578220	−	1.00151i
$195$		0			0
$196$	1.83978	−	3.18659i	0.131413	−	0.227613i
$197$	0.626855			0.0446615			0.0223308	−	0.999751i	$-0.492891\pi$
$197$	0.626855			0.0446615			0.0223308	+	0.999751i	$0.492891\pi$
$198$		0			0
$199$	−16.8127			−1.19182			−0.595909	−	0.803052i	$-0.703208\pi$
$199$	−16.8127			−1.19182			−0.595909	+	0.803052i	$0.703208\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	1.81753	+	3.14805i	0.127881	+	0.221496i
$203$	3.89540	−	2.24901i	0.273403	−	0.157850i
$204$		0			0
$205$	6.63880	+	3.83291i	0.463674	+	0.267702i
$206$	−3.86890			−0.269559
$207$		0			0
$208$			2.88183i			0.199819i
$209$	−13.8545	+	3.90081i	−0.958339	+	0.269824i
$210$		0			0
$211$	−10.0105	+	5.77955i	−0.689150	+	0.397881i	−0.803293	−	0.595584i	$-0.796921\pi$
$211$	−10.0105	+	5.77955i	−0.689150	+	0.397881i	0.114144	+	0.993464i	$0.463588\pi$
$212$	−2.82074	+	1.62855i	−0.193729	+	0.111849i
$213$		0			0
$214$	3.59597	−	6.22840i	0.245815	−	0.425765i
$215$	−7.96041			−0.542896
$216$		0			0
$217$			11.6532i			0.791068i
$218$	10.9770	+	6.33759i	0.743459	+	0.429236i
$219$		0			0
$220$	−0.817812	+	3.21422i	−0.0551369	+	0.216702i
$221$	−4.69249	+	2.70921i	−0.315651	+	0.182241i
$222$		0			0
$223$	−6.53996	+	11.3275i	−0.437948	+	0.758549i	−0.997531	−	0.0702259i	$-0.977628\pi$
$223$	−6.53996	+	11.3275i	−0.437948	+	0.758549i	0.559583	+	0.828774i	$0.310961\pi$
$224$		−	3.26796i		−	0.218350i
$225$		0			0
$226$			3.40946i			0.226794i
$227$	10.9195	−	18.9130i	0.724749	−	1.25530i	−0.234328	−	0.972158i	$-0.575289\pi$
$227$	10.9195	−	18.9130i	0.724749	−	1.25530i	0.959077	−	0.283145i	$-0.0913778\pi$
$228$		0			0
$229$	0.226279	+	0.391926i	0.0149529	+	0.0258992i	0.873405	−	0.486994i	$-0.161907\pi$
$229$	0.226279	+	0.391926i	0.0149529	+	0.0258992i	−0.858452	+	0.512894i	$0.828573\pi$
$230$	3.56428	+	6.17351i	0.235021	+	0.407069i
$231$		0			0
$232$	0.688200	−	1.19200i	0.0451826	−	0.0782585i
$233$	28.9074			1.89379			0.946893	−	0.321549i	$-0.104204\pi$
$233$	28.9074			1.89379			0.946893	+	0.321549i	$0.104204\pi$
$234$		0			0
$235$	−10.2998			−0.671888
$236$	−1.31366	−	0.758441i	−0.0855118	−	0.0493703i
$237$		0			0
$238$	5.32123	−	3.07221i	0.344924	−	0.199142i
$239$	6.53619	+	11.3210i	0.422791	+	0.732296i	0.996211	−	0.0869659i	$-0.0277171\pi$
$239$	6.53619	+	11.3210i	0.422791	+	0.732296i	−0.573420	+	0.819261i	$0.694384\pi$
$240$		0			0
$241$	20.5969	+	11.8916i	1.32676	+	0.766006i	0.984797	−	0.173707i	$-0.0555747\pi$
$241$	20.5969	+	11.8916i	1.32676	+	0.766006i	0.341964	+	0.939713i	$0.388908\pi$
$242$	−0.278271	−	10.9965i	−0.0178880	−	0.706880i
$243$		0			0
$244$		−	7.49552i		−	0.479852i
$245$	−3.18659	−	1.83978i	−0.203584	−	0.117539i
$246$		0			0
$247$	6.25316	+	10.8308i	0.397879	+	0.689146i
$248$	1.78294	+	3.08815i	0.113217	+	0.196097i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$			5.83695i			0.368425i	0.982886	+	0.184212i	$0.0589734\pi$
$251$			5.83695i			0.368425i	−0.982886	+	0.184212i	$0.941027\pi$
$252$		0			0
$253$	−16.9281	−	16.5051i	−1.06426	−	1.03767i
$254$	5.69972	+	3.29074i	0.357633	+	0.206479i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.461731	+	0.266581i	−0.0288020	+	0.0166289i	−0.514332	−	0.857591i	$-0.671960\pi$
$257$	−0.461731	+	0.266581i	−0.0288020	+	0.0166289i	0.485530	+	0.874220i	$0.338627\pi$
$258$		0			0
$259$	−20.4903	−	11.8301i	−1.27321	−	0.735086i
$260$	2.88183			0.178723
$261$		0			0
$262$	−5.58236			−0.344879
$263$	1.99471	−	3.45494i	0.122999	−	0.213041i	−0.797950	−	0.602724i	$-0.794082\pi$
$263$	1.99471	−	3.45494i	0.122999	−	0.213041i	0.920949	+	0.389683i	$0.127415\pi$
$264$		0			0
$265$	1.62855	+	2.82074i	0.100041	+	0.173276i
$266$	−7.09101	−	12.2820i	−0.434778	−	0.753057i
$267$		0			0
$268$	1.84864	−	3.20194i	0.112924	−	0.195590i
$269$		−	18.0847i		−	1.10265i	−0.834292	−	0.551323i	$-0.814123\pi$
$269$		−	18.0847i		−	1.10265i	0.834292	−	0.551323i	$-0.185877\pi$
$270$		0			0
$271$		−	0.0590289i		−	0.00358575i	−0.999998	−	0.00179288i	$-0.999429\pi$
$271$		−	0.0590289i		−	0.00358575i	0.999998	−	0.00179288i	$-0.000570691\pi$
$272$	0.940102	−	1.62830i	0.0570020	−	0.0987304i
$273$		0			0
$274$	−4.52136	+	2.61041i	−0.273145	+	0.157700i
$275$	3.21422	+	0.817812i	0.193825	+	0.0493159i
$276$		0			0
$277$	6.37510	+	3.68067i	0.383043	+	0.221150i	0.679141	−	0.734008i	$-0.262352\pi$
$277$	6.37510	+	3.68067i	0.383043	+	0.221150i	−0.296099	+	0.955157i	$0.595686\pi$
$278$		−	11.7849i		−	0.706814i
$279$		0			0
$280$	−3.26796			−0.195298
$281$	−11.7245	+	20.3075i	−0.699428	+	1.21144i	0.269237	+	0.963074i	$0.413228\pi$
$281$	−11.7245	+	20.3075i	−0.699428	+	1.21144i	−0.968665	+	0.248371i	$0.920105\pi$
$282$		0			0
$283$	−8.86343	+	5.11730i	−0.526876	+	0.304192i	−0.739743	−	0.672889i	$-0.765053\pi$
$283$	−8.86343	+	5.11730i	−0.526876	+	0.304192i	0.212867	+	0.977081i	$0.431720\pi$
$284$	13.5415	−	7.81819i	0.803540	−	0.463924i
$285$		0			0
$286$	−9.20023	+	2.59036i	−0.544021	+	0.153171i
$287$		−	25.0516i		−	1.47875i
$288$		0			0
$289$	−13.4648			−0.792049
$290$	−1.19200	−	0.688200i	−0.0699965	−	0.0404125i
$291$		0			0
$292$	−9.81284	+	5.66544i	−0.574253	+	0.331545i
$293$	−11.5431	−	19.9933i	−0.674357	−	1.16802i	−0.976656	−	0.214808i	$-0.931087\pi$
$293$	−11.5431	−	19.9933i	−0.674357	−	1.16802i	0.302299	−	0.953213i	$-0.402246\pi$
$294$		0			0
$295$	−0.758441	+	1.31366i	−0.0441581	+	0.0764841i
$296$	−7.24005			−0.420819
$297$		0			0
$298$	2.70327			0.156596
$299$	−10.2716	+	17.7910i	−0.594023	+	1.02888i
$300$		0			0
$301$	13.0071	+	22.5290i	0.749719	+	1.29855i
$302$	9.07019	−	5.23668i	0.521931	−	0.301337i
$303$		0			0
$304$	−3.75831	−	2.16986i	−0.215554	−	0.124450i
$305$	−7.49552			−0.429192
$306$		0			0
$307$			26.5900i			1.51757i	0.651339	+	0.758787i	$0.274207\pi$
$307$			26.5900i			1.51757i	−0.651339	+	0.758787i	$0.725793\pi$
$308$	10.4330	−	2.93744i	0.594473	−	0.167376i
$309$		0			0
$310$	3.08815	−	1.78294i	0.175395	−	0.101264i
$311$	−17.4411	+	10.0696i	−0.988992	+	0.570995i	−0.904973	−	0.425470i	$-0.860109\pi$
$311$	−17.4411	+	10.0696i	−0.988992	+	0.570995i	−0.0840190	+	0.996464i	$0.526776\pi$
$312$		0			0
$313$	14.9929	−	25.9684i	0.847446	−	1.46782i	−0.0360335	−	0.999351i	$-0.511472\pi$
$313$	14.9929	−	25.9684i	0.847446	−	1.46782i	0.883480	−	0.468469i	$-0.155194\pi$
$314$	−9.66836			−0.545617
$315$		0			0
$316$			13.0984i			0.736843i
$317$	12.7330	+	7.35141i	0.715157	+	0.412896i	0.812968	−	0.582309i	$-0.197851\pi$
$317$	12.7330	+	7.35141i	0.715157	+	0.412896i	−0.0978106	+	0.995205i	$0.531184\pi$
$318$		0			0
$319$	4.42405	+	1.12564i	0.247699	+	0.0630236i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	11.6479	−	20.1748i	0.649112	−	1.12430i
$323$		−	8.15955i		−	0.454010i
$324$		0			0
$325$		−	2.88183i		−	0.159855i
$326$	10.0438	−	17.3963i	0.556272	−	0.963491i
$327$		0			0
$328$	−3.83291	−	6.63880i	−0.211637	−	0.366566i
$329$	16.8297	+	29.1500i	0.927854	+	1.60709i
$330$		0			0
$331$	6.84351	−	11.8533i	0.376153	−	0.651517i	−0.614346	−	0.789037i	$-0.710580\pi$
$331$	6.84351	−	11.8533i	0.376153	−	0.651517i	0.990499	+	0.137520i	$0.0439133\pi$
$332$	0.925481			0.0507924
$333$		0			0
$334$	−20.3677			−1.11447
$335$	−3.20194	−	1.84864i	−0.174941	−	0.101002i
$336$		0			0
$337$	−15.5359	+	8.96965i	−0.846294	+	0.488608i	−0.859399	−	0.511306i	$-0.829162\pi$
$337$	−15.5359	+	8.96965i	−0.846294	+	0.488608i	0.0131049	+	0.999914i	$0.495828\pi$
$338$	−2.34754	−	4.06606i	−0.127689	−	0.221164i
$339$		0			0
$340$	−1.62830	−	0.940102i	−0.0883072	−	0.0509842i
$341$	−8.25628	+	8.46786i	−0.447103	+	0.458560i
$342$		0			0
$343$		−	10.8511i		−	0.585903i
$344$	6.89392	+	3.98021i	0.371695	+	0.214598i
$345$		0			0
$346$	−6.26488	−	10.8511i	−0.336802	−	0.583359i
$347$	−9.69853	−	16.7983i	−0.520644	−	0.901782i	−0.999712	−	0.0240042i	$-0.992358\pi$
$347$	−9.69853	−	16.7983i	−0.520644	−	0.901782i	0.479068	−	0.877778i	$-0.340975\pi$
$348$		0			0
$349$	20.3082	+	11.7250i	1.08707	+	0.627623i	0.932796	−	0.360404i	$-0.117361\pi$
$349$	20.3082	+	11.7250i	1.08707	+	0.627623i	0.154279	+	0.988027i	$0.450695\pi$
$350$			3.26796i			0.174680i
$351$		0			0
$352$	2.31535	−	2.37469i	0.123409	−	0.126571i
$353$	−9.72262	−	5.61336i	−0.517483	−	0.298769i	0.218421	−	0.975855i	$-0.429909\pi$
$353$	−9.72262	−	5.61336i	−0.517483	−	0.298769i	−0.735904	+	0.677086i	$0.763243\pi$
$354$		0			0
$355$	−7.81819	−	13.5415i	−0.414946	−	0.718708i
$356$	−2.07209	+	1.19632i	−0.109821	+	0.0634050i
$357$		0			0
$358$	−19.5618	−	11.2940i	−1.03387	−	0.596906i
$359$	5.59649			0.295372			0.147686	−	0.989034i	$-0.452818\pi$
$359$	5.59649			0.295372			0.147686	+	0.989034i	$0.452818\pi$
$360$		0			0
$361$	0.166851			0.00878161
$362$	8.03274	−	13.9131i	0.422191	−	0.731257i
$363$		0			0
$364$	−4.70884	−	8.15596i	−0.246811	−	0.427488i
$365$	5.66544	+	9.81284i	0.296543	+	0.513627i
$366$		0			0
$367$	−2.50320	+	4.33566i	−0.130666	+	0.226320i	−0.923933	−	0.382553i	$-0.875045\pi$
$367$	−2.50320	+	4.33566i	−0.130666	+	0.226320i	0.793268	+	0.608873i	$0.208378\pi$
$368$		−	7.12855i		−	0.371601i
$369$		0			0
$370$			7.24005i			0.376392i
$371$	5.32204	−	9.21805i	0.276307	−	0.478577i
$372$		0			0
$373$	23.8159	−	13.7501i	1.23314	−	0.711953i	0.265456	−	0.964123i	$-0.414478\pi$
$373$	23.8159	−	13.7501i	1.23314	−	0.711953i	0.967683	+	0.252170i	$0.0811442\pi$
$374$	6.04338	+	1.53765i	0.312496	+	0.0795102i
$375$		0			0
$376$	8.91993	+	5.14992i	0.460010	+	0.265587i
$377$		−	3.96655i		−	0.204288i
$378$		0			0
$379$	33.0775			1.69908			0.849538	−	0.527527i	$-0.176881\pi$
$379$	33.0775			1.69908			0.849538	+	0.527527i	$0.176881\pi$
$380$	−2.16986	+	3.75831i	−0.111311	+	0.192797i
$381$		0			0
$382$	1.49071	−	0.860659i	0.0762711	−	0.0440352i
$383$	27.2719	−	15.7454i	1.39353	−	0.804555i	0.399826	−	0.916591i	$-0.369071\pi$
$383$	27.2719	−	15.7454i	1.39353	−	0.804555i	0.993704	+	0.112036i	$0.0357373\pi$
$384$		0			0
$385$	−2.93744	−	10.4330i	−0.149706	−	0.531713i
$386$			12.6931i			0.646063i
$387$		0			0
$388$	16.1073			0.817726
$389$	−33.1700	−	19.1507i	−1.68179	−	0.970980i	−0.960474	−	0.278371i	$-0.910206\pi$
$389$	−33.1700	−	19.1507i	−1.68179	−	0.970980i	−0.721313	−	0.692609i	$-0.756461\pi$
$390$		0			0
$391$	11.6074	−	6.70156i	0.587014	−	0.338913i
$392$	1.83978	+	3.18659i	0.0929228	+	0.160947i
$393$		0			0
$394$	−0.313427	+	0.542872i	−0.0157902	+	0.0273495i
$395$	13.0984			0.659053
$396$		0			0
$397$	4.36717			0.219182			0.109591	−	0.993977i	$-0.465046\pi$
$397$	4.36717			0.219182			0.109591	+	0.993977i	$0.465046\pi$
$398$	8.40633	−	14.5602i	0.421371	−	0.729836i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	9.63542	−	5.56301i	0.481170	−	0.277804i	−0.239734	−	0.970839i	$-0.577060\pi$
$401$	9.63542	−	5.56301i	0.481170	−	0.277804i	0.720904	+	0.693035i	$0.243727\pi$
$402$		0			0
$403$	8.89950	+	5.13813i	0.443316	+	0.255948i
$404$	−3.63506			−0.180851
$405$		0			0
$406$			4.49802i			0.223233i
$407$	−6.50781	−	23.1139i	−0.322580	−	1.14571i
$408$		0			0
$409$	4.54551	−	2.62435i	0.224761	−	0.129766i	−0.383392	−	0.923586i	$-0.625244\pi$
$409$	4.54551	−	2.62435i	0.224761	−	0.129766i	0.608153	+	0.793820i	$0.291911\pi$
$410$	−6.63880	+	3.83291i	−0.327867	+	0.189294i
$411$		0			0
$412$	1.93445	−	3.35057i	0.0953035	−	0.165071i
$413$	4.95710			0.243923
$414$		0			0
$415$		−	0.925481i		−	0.0454301i
$416$	−2.49573	−	1.44091i	−0.122363	−	0.0706466i
$417$		0			0
$418$	3.54907	−	13.9488i	0.173591	−	0.682258i
$419$	−15.2701	+	8.81620i	−0.745994	+	0.430700i	−0.824245	−	0.566234i	$-0.808400\pi$
$419$	−15.2701	+	8.81620i	−0.745994	+	0.430700i	0.0782508	+	0.996934i	$0.475067\pi$
$420$		0			0
$421$	8.85232	−	15.3327i	0.431435	−	0.747268i	−0.565562	−	0.824706i	$-0.691341\pi$
$421$	8.85232	−	15.3327i	0.431435	−	0.747268i	0.996997	+	0.0774378i	$0.0246739\pi$
$422$		−	11.5591i		−	0.562688i
$423$		0			0
$424$		−	3.25710i		−	0.158179i
$425$	−0.940102	+	1.62830i	−0.0456016	+	0.0789843i
$426$		0			0
$427$	12.2475	+	21.2133i	0.592699	+	1.02659i
$428$	3.59597	+	6.22840i	0.173818	+	0.301061i
$429$		0			0
$430$	3.98021	−	6.89392i	0.191943	−	0.332454i
$431$	−34.6411			−1.66860			−0.834301	−	0.551310i	$-0.814128\pi$
$431$	−34.6411			−1.66860			−0.834301	+	0.551310i	$0.814128\pi$
$432$		0			0
$433$	23.6691			1.13747			0.568733	−	0.822522i	$-0.307434\pi$
$433$	23.6691			1.13747			0.568733	+	0.822522i	$0.307434\pi$
$434$	−10.0919	−	5.82658i	−0.484428	−	0.279685i
$435$		0			0
$436$	−10.9770	+	6.33759i	−0.525705	+	0.303516i
$437$	−15.4679	−	26.7913i	−0.739932	−	1.28160i
$438$		0			0
$439$	30.7259	+	17.7396i	1.46647	+	0.846665i	0.999297	−	0.0375029i	$-0.0119403\pi$
$439$	30.7259	+	17.7396i	1.46647	+	0.846665i	0.467170	+	0.884168i	$0.345274\pi$
$440$	−2.37469	−	2.31535i	−0.113209	−	0.110380i
$441$		0			0
$442$		−	5.41842i		−	0.257728i
$443$	34.1454	+	19.7138i	1.62230	+	0.936633i	0.986304	+	0.164937i	$0.0527420\pi$
$443$	34.1454	+	19.7138i	1.62230	+	0.936633i	0.635991	+	0.771696i	$0.280591\pi$
$444$		0			0
$445$	1.19632	+	2.07209i	0.0567112	+	0.0982267i
$446$	−6.53996	−	11.3275i	−0.309676	−	0.536375i
$447$		0			0
$448$	2.83014	+	1.63398i	0.133711	+	0.0771983i
$449$			25.8480i			1.21984i	0.792462	+	0.609921i	$0.208799\pi$
$449$			25.8480i			1.21984i	−0.792462	+	0.609921i	$0.791201\pi$
$450$		0			0
$451$	17.7491	−	18.2039i	0.835772	−	0.857189i
$452$	−2.95268	−	1.70473i	−0.138883	−	0.0801839i
$453$		0			0
$454$	10.9195	+	18.9130i	0.512475	+	0.887633i
$455$	−8.15596	+	4.70884i	−0.382357	+	0.220754i
$456$		0			0
$457$	−11.7176	−	6.76513i	−0.548124	−	0.316460i	0.200241	−	0.979747i	$-0.435828\pi$
$457$	−11.7176	−	6.76513i	−0.548124	−	0.316460i	−0.748365	+	0.663287i	$0.769161\pi$
$458$	−0.452557			−0.0211466
$459$		0			0
$460$	−7.12855			−0.332370
$461$	−5.94147	+	10.2909i	−0.276722	+	0.479296i	−0.970568	−	0.240827i	$-0.922581\pi$
$461$	−5.94147	+	10.2909i	−0.276722	+	0.479296i	0.693846	+	0.720123i	$0.255915\pi$
$462$		0			0
$463$	−2.56020	−	4.43439i	−0.118982	−	0.206083i	0.800382	−	0.599490i	$-0.204630\pi$
$463$	−2.56020	−	4.43439i	−0.118982	−	0.206083i	−0.919365	+	0.393406i	$0.871297\pi$
$464$	0.688200	+	1.19200i	0.0319489	+	0.0553371i
$465$		0			0
$466$	−14.4537	+	25.0345i	−0.669554	+	1.15970i
$467$			3.00206i			0.138919i	0.997585	+	0.0694595i	$0.0221274\pi$
$467$			3.00206i			0.138919i	−0.997585	+	0.0694595i	$0.977873\pi$
$468$		0			0
$469$			12.0826i			0.557921i
$470$	5.14992	−	8.91993i	0.237548	−	0.411446i
$471$		0			0
$472$	1.31366	−	0.758441i	0.0604660	−	0.0349101i
$473$	−6.51012	+	25.5865i	−0.299336	+	1.17647i
$474$		0			0
$475$	3.75831	+	2.16986i	0.172443	+	0.0995600i
$476$			6.14443i			0.281629i
$477$		0			0
$478$	−13.0724			−0.597917
$479$	15.8657	−	27.4801i	0.724921	−	1.25560i	−0.234086	−	0.972216i	$-0.575210\pi$
$479$	15.8657	−	27.4801i	0.724921	−	1.25560i	0.959007	−	0.283384i	$-0.0914571\pi$
$480$		0			0
$481$	−18.0693	+	10.4323i	−0.823887	+	0.475671i
$482$	−20.5969	+	11.8916i	−0.938162	+	0.541648i
$483$		0			0
$484$	9.66237	+	5.25725i	0.439198	+	0.238966i
$485$		−	16.1073i		−	0.731397i
$486$		0			0
$487$	−21.3724			−0.968476			−0.484238	−	0.874936i	$-0.660903\pi$
$487$	−21.3724			−0.968476			−0.484238	+	0.874936i	$0.660903\pi$
$488$	6.49131	+	3.74776i	0.293848	+	0.169653i
$489$		0			0
$490$	3.18659	−	1.83978i	0.143955	−	0.0831126i
$491$	−14.5893	−	25.2694i	−0.658406	−	1.14039i	−0.981028	−	0.193865i	$-0.937898\pi$
$491$	−14.5893	−	25.2694i	−0.658406	−	1.14039i	0.322622	−	0.946528i	$-0.395436\pi$
$492$		0			0
$493$	−1.29396	+	2.24120i	−0.0582769	+	0.100938i
$494$	−12.5063			−0.562686
$495$		0			0
$496$	−3.56588			−0.160113
$497$	−25.5495	+	44.2530i	−1.14605	+	1.98502i
$498$		0			0
$499$	−19.2299	−	33.3072i	−0.860850	−	1.49104i	−0.871109	−	0.491089i	$-0.836599\pi$
$499$	−19.2299	−	33.3072i	−0.860850	−	1.49104i	0.0102592	−	0.999947i	$-0.496734\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$		0			0
$502$	−5.05494	−	2.91847i	−0.225613	−	0.130258i
$503$	37.0022			1.64984			0.824922	−	0.565246i	$-0.191219\pi$
$503$	37.0022			1.64984			0.824922	+	0.565246i	$0.191219\pi$
$504$		0			0
$505$			3.63506i			0.161758i
$506$	22.7579	−	6.40758i	1.01171	−	0.284852i
$507$		0			0
$508$	−5.69972	+	3.29074i	−0.252884	+	0.146003i
$509$	−27.4788	+	15.8649i	−1.21798	+	0.703199i	−0.964485	−	0.264139i	$-0.914912\pi$
$509$	−27.4788	+	15.8649i	−1.21798	+	0.703199i	−0.253491	+	0.967338i	$0.581579\pi$
$510$		0			0
$511$	18.5144	−	32.0679i	0.819030	−	1.41860i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	0.533162i		−	0.0235167i
$515$	−3.35057	−	1.93445i	−0.147644	−	0.0852420i
$516$		0			0
$517$	−8.42334	+	33.1059i	−0.370458	+	1.45600i
$518$	20.4903	−	11.8301i	0.900293	−	0.519785i
$519$		0			0
$520$	−1.44091	+	2.49573i	−0.0631882	+	0.109445i
$521$		−	15.5516i		−	0.681329i	−0.940185	−	0.340664i	$-0.889348\pi$
$521$		−	15.5516i		−	0.681329i	0.940185	−	0.340664i	$-0.110652\pi$
$522$		0			0
$523$		−	27.1075i		−	1.18533i	−0.805450	−	0.592664i	$-0.798076\pi$
$523$		−	27.1075i		−	1.18533i	0.805450	−	0.592664i	$-0.201924\pi$
$524$	2.79118	−	4.83446i	0.121933	−	0.211195i
$525$		0			0
$526$	1.99471	+	3.45494i	0.0869736	+	0.150643i
$527$	−3.35229	−	5.80634i	−0.146028	−	0.252928i
$528$		0			0
$529$	13.9081	−	24.0896i	0.604701	−	1.04737i
$530$	−3.25710			−0.141480
$531$		0			0
$532$	14.1820			0.614868
$533$	−19.1319	−	11.0458i	−0.828693	−	0.478446i
$534$		0			0
$535$	6.22840	−	3.59597i	0.269277	−	0.155467i
$536$	1.84864	+	3.20194i	0.0798491	+	0.138303i
$537$		0			0
$538$	15.6618	+	9.04237i	0.675230	+	0.389844i
$539$	−8.51947	+	8.73779i	−0.366959	+	0.376363i
$540$		0			0
$541$			7.54485i			0.324379i	0.986760	+	0.162189i	$0.0518555\pi$
$541$			7.54485i			0.324379i	−0.986760	+	0.162189i	$0.948144\pi$
$542$	0.0511206	+	0.0295145i	0.00219582	+	0.00126776i
$543$		0			0
$544$	0.940102	+	1.62830i	0.0403065	+	0.0698130i
$545$	6.33759	+	10.9770i	0.271473	+	0.470205i
$546$		0			0
$547$	32.5884	+	18.8149i	1.39338	+	0.804469i	0.993688	−	0.112180i	$-0.0357833\pi$
$547$	32.5884	+	18.8149i	1.39338	+	0.804469i	0.399693	+	0.916649i	$0.369117\pi$
$548$		−	5.22081i		−	0.223022i
$549$		0			0
$550$	−2.31535	+	2.37469i	−0.0987270	+	0.101257i
$551$	5.17293	+	2.98659i	0.220374	+	0.127233i
$552$		0			0
$553$	−21.4025	−	37.0703i	−0.910128	−	1.57639i
$554$	−6.37510	+	3.68067i	−0.270852	+	0.156377i
$555$		0			0
$556$	10.2061	+	5.89247i	0.432833	+	0.249896i
$557$	16.4844			0.698468			0.349234	−	0.937036i	$-0.386442\pi$
$557$	16.4844			0.698468			0.349234	+	0.937036i	$0.386442\pi$
$558$		0			0
$559$	22.9405			0.970281
$560$	1.63398	−	2.83014i	0.0690482	−	0.119595i
$561$		0			0
$562$	−11.7245	−	20.3075i	−0.494570	−	0.856621i
$563$	−3.03905	−	5.26379i	−0.128081	−	0.221842i	0.794852	−	0.606803i	$-0.207548\pi$
$563$	−3.03905	−	5.26379i	−0.128081	−	0.221842i	−0.922933	+	0.384961i	$0.874215\pi$
$564$		0			0
$565$	−1.70473	+	2.95268i	−0.0717186	+	0.124220i
$566$		−	10.2346i		−	0.430192i
$567$		0			0
$568$			15.6364i			0.656088i
$569$	−8.67474	+	15.0251i	−0.363664	+	0.629885i	−0.988561	−	0.150823i	$-0.951808\pi$
$569$	−8.67474	+	15.0251i	−0.363664	+	0.629885i	0.624897	+	0.780707i	$0.285141\pi$
$570$		0			0
$571$	−3.31059	+	1.91137i	−0.138544	+	0.0799883i	−0.567670	−	0.823256i	$-0.692155\pi$
$571$	−3.31059	+	1.91137i	−0.138544	+	0.0799883i	0.429126	+	0.903245i	$0.358822\pi$
$572$	2.35679	−	9.26281i	0.0985425	−	0.387298i
$573$		0			0
$574$	21.6953	+	12.5258i	0.905545	+	0.522817i
$575$			7.12855i			0.297281i
$576$		0			0
$577$	−23.5042			−0.978494			−0.489247	−	0.872145i	$-0.662728\pi$
$577$	−23.5042			−0.978494			−0.489247	+	0.872145i	$0.662728\pi$
$578$	6.73242	−	11.6609i	0.280032	−	0.485029i
$579$		0			0
$580$	1.19200	−	0.688200i	0.0494950	−	0.0285760i
$581$	−2.61924	+	1.51222i	−0.108664	+	0.0627373i
$582$		0			0
$583$	10.3983	−	2.92769i	0.430654	−	0.121252i
$584$		−	11.3309i		−	0.468875i
$585$		0			0
$586$	23.0863			0.953685
$587$	8.03882	+	4.64121i	0.331797	+	0.191563i	0.656639	−	0.754205i	$-0.271978\pi$
$587$	8.03882	+	4.64121i	0.331797	+	0.191563i	−0.324841	+	0.945769i	$0.605311\pi$
$588$		0			0
$589$	−13.4017	+	7.73746i	−0.552207	+	0.318817i
$590$	−0.758441	−	1.31366i	−0.0312245	−	0.0540824i
$591$		0			0
$592$	3.62003	−	6.27007i	0.148782	−	0.257698i
$593$	24.8486			1.02041			0.510205	−	0.860053i	$-0.329570\pi$
$593$	24.8486			1.02041			0.510205	+	0.860053i	$0.329570\pi$
$594$		0			0
$595$	6.14443			0.251897
$596$	−1.35163	+	2.34110i	−0.0553651	+	0.0958951i
$597$		0			0
$598$	−10.2716	−	17.7910i	−0.420038	−	0.727527i
$599$	25.6362	−	14.8011i	1.04747	−	0.604755i	0.125527	−	0.992090i	$-0.459938\pi$
$599$	25.6362	−	14.8011i	1.04747	−	0.604755i	0.921939	+	0.387336i	$0.126604\pi$
$600$		0			0
$601$	2.39420	+	1.38229i	0.0976617	+	0.0563850i	0.548035	−	0.836455i	$-0.315376\pi$
$601$	2.39420	+	1.38229i	0.0976617	+	0.0563850i	−0.450374	+	0.892840i	$0.648709\pi$
$602$	−26.0143			−1.06026
$603$		0			0
$604$			10.4734i			0.426155i
$605$	5.25725	−	9.66237i	0.213738	−	0.392831i
$606$		0			0
$607$	33.7561	−	19.4891i	1.37012	−	0.791039i	0.379176	−	0.925324i	$-0.376207\pi$
$607$	33.7561	−	19.4891i	1.37012	−	0.791039i	0.990943	+	0.134286i	$0.0428741\pi$
$608$	3.75831	−	2.16986i	0.152419	−	0.0879994i
$609$		0			0
$610$	3.74776	−	6.49131i	0.151742	−	0.262826i
$611$	29.6824			1.20082
$612$		0			0
$613$			23.9844i			0.968722i	0.874868	+	0.484361i	$0.160948\pi$
$613$			23.9844i			0.968722i	−0.874868	+	0.484361i	$0.839052\pi$
$614$	−23.0276	−	13.2950i	−0.929320	−	0.536543i
$615$		0			0
$616$	−2.67258	+	10.5039i	−0.107681	+	0.423215i
$617$	−11.5361	+	6.66039i	−0.464427	+	0.268137i	−0.713904	−	0.700244i	$-0.753075\pi$
$617$	−11.5361	+	6.66039i	−0.464427	+	0.268137i	0.249477	+	0.968381i	$0.419741\pi$
$618$		0			0
$619$	−13.4689	+	23.3289i	−0.541362	+	0.937666i	0.457465	+	0.889228i	$0.348758\pi$
$619$	−13.4689	+	23.3289i	−0.541362	+	0.937666i	−0.998826	+	0.0484380i	$0.984576\pi$
$620$			3.56588i			0.143209i
$621$		0			0
$622$		−	20.1392i		−	0.807508i
$623$	3.90954	−	6.77152i	0.156632	−	0.271295i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	14.9929	+	25.9684i	0.599235	+	1.03791i
$627$		0			0
$628$	4.83418	−	8.37305i	0.192905	−	0.334121i
$629$	13.6128			0.542777
$630$		0			0
$631$	34.3706			1.36827			0.684136	−	0.729354i	$-0.260179\pi$
$631$	34.3706			1.36827			0.684136	+	0.729354i	$0.260179\pi$
$632$	−11.3436	−	6.54921i	−0.451223	−	0.260513i
$633$		0			0
$634$	−12.7330	+	7.35141i	−0.505692	+	0.291962i
$635$	3.29074	+	5.69972i	0.130589	+	0.226187i
$636$		0			0
$637$	9.18319	+	5.30192i	0.363851	+	0.210070i
$638$	−3.18685	+	3.26852i	−0.126169	+	0.129402i
$639$		0			0
$640$		−	1.00000i		−	0.0395285i
$641$	−17.6637	−	10.1981i	−0.697673	−	0.402802i	0.108807	−	0.994063i	$-0.465297\pi$
$641$	−17.6637	−	10.1981i	−0.697673	−	0.402802i	−0.806480	+	0.591261i	$0.798630\pi$
$642$		0			0
$643$	−13.7828	−	23.8725i	−0.543539	−	0.941438i	−0.998697	−	0.0510272i	$-0.983750\pi$
$643$	−13.7828	−	23.8725i	−0.543539	−	0.941438i	0.455158	−	0.890411i	$-0.349583\pi$
$644$	11.6479	+	20.1748i	0.458992	+	0.794997i
$645$		0			0
$646$	7.06638	+	4.07978i	0.278023	+	0.160517i
$647$			41.7451i			1.64117i	0.571525	+	0.820585i	$0.306352\pi$
$647$			41.7451i			1.64117i	−0.571525	+	0.820585i	$0.693648\pi$
$648$		0			0
$649$	3.60212	+	3.51212i	0.141395	+	0.137863i
$650$	2.49573	+	1.44091i	0.0978908	+	0.0565173i
$651$		0			0
$652$	10.0438	+	17.3963i	0.393344	+	0.681291i
$653$	10.9169	−	6.30286i	0.427210	−	0.246650i	−0.270947	−	0.962594i	$-0.587337\pi$
$653$	10.9169	−	6.30286i	0.427210	−	0.246650i	0.698157	+	0.715944i	$0.254004\pi$
$654$		0			0
$655$	−4.83446	−	2.79118i	−0.188898	−	0.109060i
$656$	7.66582			0.299300
$657$		0			0
$658$	−33.6595			−1.31218
$659$	2.55561	−	4.42644i	0.0995523	−	0.172430i	−0.811947	−	0.583731i	$-0.801592\pi$
$659$	2.55561	−	4.42644i	0.0995523	−	0.172430i	0.911499	+	0.411301i	$0.134926\pi$
$660$		0			0
$661$	16.2241	+	28.1010i	0.631045	+	1.09300i	0.987338	+	0.158628i	$0.0507070\pi$
$661$	16.2241	+	28.1010i	0.631045	+	1.09300i	−0.356293	+	0.934374i	$0.615960\pi$
$662$	6.84351	+	11.8533i	0.265981	+	0.460692i
$663$		0			0
$664$	−0.462740	+	0.801490i	−0.0179578	+	0.0311038i
$665$		−	14.1820i		−	0.549955i
$666$		0			0
$667$			9.81174i			0.379912i
$668$	10.1839	−	17.6390i	0.394026	−	0.682473i
$669$		0			0
$670$	3.20194	−	1.84864i	0.123702	−	0.0714192i
$671$	−6.12993	+	24.0922i	−0.236643	+	0.930070i
$672$		0			0
$673$	38.8482	+	22.4290i	1.49749	+	0.864574i	0.999996	−	0.00289542i	$-0.000921643\pi$
$673$	38.8482	+	22.4290i	1.49749	+	0.864574i	0.497490	+	0.867469i	$0.334255\pi$
$674$		−	17.9393i		−	0.690996i
$675$		0			0
$676$	4.69508			0.180580
$677$	−9.57175	+	16.5788i	−0.367872	+	0.637174i	−0.989233	−	0.146351i	$-0.953247\pi$
$677$	−9.57175	+	16.5788i	−0.367872	+	0.637174i	0.621360	+	0.783525i	$0.286580\pi$
$678$		0			0
$679$	−45.5859	+	26.3191i	−1.74943	+	1.01003i
$680$	1.62830	−	0.940102i	0.0624426	−	0.0360513i
$681$		0			0
$682$	−3.20524	−	11.3841i	−0.122735	−	0.435919i
$683$		−	41.9745i		−	1.60611i	−0.595906	−	0.803054i	$-0.703207\pi$
$683$		−	41.9745i		−	1.60611i	0.595906	−	0.803054i	$-0.296793\pi$
$684$		0			0
$685$	−5.22081			−0.199477
$686$	9.39731	+	5.42554i	0.358791	+	0.207148i
$687$		0			0
$688$	−6.89392	+	3.98021i	−0.262828	+	0.151744i
$689$	−4.69321	−	8.12887i	−0.178797	−	0.309685i
$690$		0			0
$691$	−11.6175	+	20.1221i	−0.441950	+	0.765480i	−0.997834	−	0.0657796i	$-0.979047\pi$
$691$	−11.6175	+	20.1221i	−0.441950	+	0.765480i	0.555884	+	0.831260i	$0.312380\pi$
$692$	12.5298			0.476310
$693$		0			0
$694$	19.3971			0.736302
$695$	5.89247	−	10.2061i	0.223514	−	0.387138i
$696$		0			0
$697$	7.20665	+	12.4823i	0.272971	+	0.472800i
$698$	−20.3082	+	11.7250i	−0.768678	+	0.443796i
$699$		0			0
$700$	−2.83014	−	1.63398i	−0.106969	−	0.0617586i
$701$	−2.01452			−0.0760872			−0.0380436	−	0.999276i	$-0.512113\pi$
$701$	−2.01452			−0.0760872			−0.0380436	+	0.999276i	$0.512113\pi$
$702$		0			0
$703$		−	31.4198i		−	1.18502i
$704$	0.898862	+	3.19250i	0.0338771	+	0.120322i
$705$		0			0
$706$	9.72262	−	5.61336i	0.365916	−	0.211262i
$707$	10.2877	−	5.93961i	0.386909	−	0.223382i
$708$		0			0
$709$	−10.3159	+	17.8676i	−0.387420	+	0.671032i	−0.992102	−	0.125436i	$-0.959967\pi$
$709$	−10.3159	+	17.8676i	−0.387420	+	0.671032i	0.604681	+	0.796468i	$0.293300\pi$
$710$	15.6364			0.586823
$711$		0			0
$712$		−	2.39265i		−	0.0896683i
$713$	−22.0140	−	12.7098i	−0.824431	−	0.475985i
$714$		0			0
$715$	−9.26281	−	2.35679i	−0.346410	−	0.0881391i
$716$	19.5618	−	11.2940i	0.731058	−	0.422076i
$717$		0			0
$718$	−2.79825	+	4.84670i	−0.104430	+	0.180877i
$719$			38.6759i			1.44237i	0.692743	+	0.721185i	$0.256402\pi$
$719$			38.6759i			1.44237i	−0.692743	+	0.721185i	$0.743598\pi$
$720$		0			0
$721$			12.6434i			0.470865i
$722$	−0.0834253	+	0.144497i	−0.00310477	+	0.00537762i
$723$		0			0
$724$	8.03274	+	13.9131i	0.298534	+	0.517077i
$725$	−0.688200	−	1.19200i	−0.0255591	−	0.0442697i
$726$		0			0
$727$	8.24260	−	14.2766i	0.305701	−	0.529490i	−0.671716	−	0.740809i	$-0.734443\pi$
$727$	8.24260	−	14.2766i	0.305701	−	0.529490i	0.977417	+	0.211319i	$0.0677759\pi$
$728$	9.41769			0.349043
$729$		0			0
$730$	−11.3309			−0.419375
$731$	−12.9620	−	7.48360i	−0.479416	−	0.276791i
$732$		0			0
$733$	−19.7637	+	11.4106i	−0.729989	+	0.421459i	−0.818418	−	0.574623i	$-0.805149\pi$
$733$	−19.7637	+	11.4106i	−0.729989	+	0.421459i	0.0884293	+	0.996082i	$0.471815\pi$
$734$	−2.50320	−	4.33566i	−0.0923946	−	0.160032i
$735$		0			0
$736$	6.17351	+	3.56428i	0.227558	+	0.131381i
$737$	−8.56052	+	8.77989i	−0.315331	+	0.323411i
$738$		0			0
$739$		−	13.0567i		−	0.480299i	−0.970736	−	0.240149i	$-0.922804\pi$
$739$		−	13.0567i		−	0.480299i	0.970736	−	0.240149i	$-0.0771964\pi$
$740$	−6.27007	−	3.62003i	−0.230492	−	0.133075i
$741$		0			0
$742$	5.32204	+	9.21805i	0.195378	+	0.338405i
$743$	5.08792	+	8.81253i	0.186658	+	0.323300i	0.944134	−	0.329562i	$-0.106901\pi$
$743$	5.08792	+	8.81253i	0.186658	+	0.323300i	−0.757476	+	0.652863i	$0.773568\pi$
$744$		0			0
$745$	2.34110	+	1.35163i	0.0857712	+	0.0495200i
$746$			27.5002i			1.00685i
$747$		0			0
$748$	−4.35334	+	4.46489i	−0.159174	+	0.163253i
$749$	−20.3542	−	11.7515i	−0.743725	−	0.429390i
$750$		0			0
$751$	13.0380	+	22.5825i	0.475764	+	0.824047i	0.999615	−	0.0277630i	$-0.00883837\pi$
$751$	13.0380	+	22.5825i	0.475764	+	0.824047i	−0.523851	+	0.851810i	$0.675505\pi$
$752$	−8.91993	+	5.14992i	−0.325276	+	0.187798i
$753$		0			0
$754$	3.43513	+	1.98327i	0.125100	+	0.0722266i
$755$	10.4734			0.381164
$756$		0			0
$757$	15.5500			0.565176			0.282588	−	0.959241i	$-0.408807\pi$
$757$	15.5500			0.565176			0.282588	+	0.959241i	$0.408807\pi$
$758$	−16.5387	+	28.6459i	−0.600714	+	1.04047i
$759$		0			0
$760$	−2.16986	−	3.75831i	−0.0787091	−	0.136328i
$761$	−14.8760	−	25.7659i	−0.539253	−	0.934014i	−0.998944	−	0.0459348i	$-0.985373\pi$
$761$	−14.8760	−	25.7659i	−0.539253	−	0.934014i	0.459691	−	0.888079i	$-0.347960\pi$
$762$		0			0
$763$	20.7110	−	35.8725i	0.749788	−	1.29867i
$764$			1.72132i			0.0622751i
$765$		0			0
$766$			31.4909i			1.13781i
$767$	2.18569	−	3.78573i	0.0789208	−	0.136695i
$768$		0			0
$769$	23.5942	−	13.6221i	0.850830	−	0.491227i	−0.0101010	−	0.999949i	$-0.503215\pi$
$769$	23.5942	−	13.6221i	0.850830	−	0.491227i	0.860931	+	0.508722i	$0.169882\pi$
$770$	10.5039	+	2.67258i	0.378535	+	0.0963130i
$771$		0			0
$772$	−10.9926	−	6.34656i	−0.395631	−	0.228418i
$773$		−	50.9522i		−	1.83262i	−0.400466	−	0.916312i	$-0.631152\pi$
$773$		−	50.9522i		−	1.83262i	0.400466	−	0.916312i	$-0.368848\pi$
$774$		0			0
$775$	3.56588			0.128090
$776$	−8.05367	+	13.9494i	−0.289110	+	0.500753i
$777$		0			0
$778$	33.1700	−	19.1507i	1.18920	−	0.686587i
$779$	28.8105	−	16.6338i	1.03224	−	0.595966i
$780$		0			0
$781$	−49.9191	+	14.0549i	−1.78625	+	0.502925i
$782$			13.4031i			0.479295i
$783$		0			0
$784$	−3.67955			−0.131413
$785$	−8.37305	−	4.83418i	−0.298847	−	0.172539i
$786$		0			0
$787$	−3.16619	+	1.82800i	−0.112863	+	0.0651612i	−0.555369	−	0.831604i	$-0.687423\pi$
$787$	−3.16619	+	1.82800i	−0.112863	+	0.0651612i	0.442506	+	0.896765i	$0.354090\pi$
$788$	−0.313427	−	0.542872i	−0.0111654	−	0.0193390i
$789$		0			0
$790$	−6.54921	+	11.3436i	−0.233010	+	0.403586i
$791$	11.1420			0.396164
$792$		0			0
$793$	21.6008			0.767067
$794$	−2.18358	+	3.78208i	−0.0774925	+	0.134221i
$795$		0			0
$796$	8.40633	+	14.5602i	0.297954	+	0.516072i
$797$	−1.24075	+	0.716346i	−0.0439495	+	0.0253743i	−0.521814	−	0.853059i	$-0.674744\pi$
$797$	−1.24075	+	0.716346i	−0.0439495	+	0.0253743i	0.477864	+	0.878434i	$0.341411\pi$
$798$		0			0
$799$	−16.7713	−	9.68290i	−0.593325	−	0.342557i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$			11.1260i			0.392874i
$803$	36.1738	−	10.1849i	1.27655	−	0.359417i
$804$		0			0
$805$	20.1748	−	11.6479i	0.711067	−	0.410535i
$806$	−8.89950	+	5.13813i	−0.313472	+	0.180983i
$807$		0			0
$808$	1.81753	−	3.14805i	0.0639405	−	0.110748i
$809$	47.3250			1.66386			0.831929	−	0.554882i	$-0.187237\pi$
$809$	47.3250			1.66386			0.831929	+	0.554882i	$0.187237\pi$
$810$		0			0
$811$		−	19.8112i		−	0.695664i	−0.937557	−	0.347832i	$-0.886918\pi$
$811$		−	19.8112i		−	0.695664i	0.937557	−	0.347832i	$-0.113082\pi$
$812$	−3.89540	−	2.24901i	−0.136702	−	0.0789248i
$813$		0			0
$814$	23.2711	+	5.92100i	0.815651	+	0.207531i
$815$	17.3963	−	10.0438i	0.609365	−	0.351817i
$816$		0			0
$817$	−17.2730	+	29.9177i	−0.604305	+	1.04669i
$818$			5.24870i			0.183517i
$819$		0			0
$820$		−	7.66582i		−	0.267702i
$821$	10.8369	−	18.7700i	0.378210	−	0.655079i	−0.612592	−	0.790399i	$-0.709873\pi$
$821$	10.8369	−	18.7700i	0.378210	−	0.655079i	0.990802	+	0.135321i	$0.0432064\pi$
$822$		0			0
$823$	20.1692	+	34.9340i	0.703053	+	1.21772i	0.967390	+	0.253293i	$0.0815136\pi$
$823$	20.1692	+	34.9340i	0.703053	+	1.21772i	−0.264337	+	0.964430i	$0.585153\pi$
$824$	1.93445	+	3.35057i	0.0673898	+	0.116722i
$825$		0			0
$826$	−2.47855	+	4.29298i	−0.0862399	+	0.149372i
$827$	38.9841			1.35561			0.677805	−	0.735242i	$-0.262931\pi$
$827$	38.9841			1.35561			0.677805	+	0.735242i	$0.262931\pi$
$828$		0			0
$829$	28.1575			0.977952			0.488976	−	0.872297i	$-0.337371\pi$
$829$	28.1575			0.977952			0.488976	+	0.872297i	$0.337371\pi$
$830$	0.801490	+	0.462740i	0.0278201	+	0.0160620i
$831$		0			0
$832$	2.49573	−	1.44091i	0.0865240	−	0.0499547i
$833$	−3.45915	−	5.99143i	−0.119853	−	0.207591i
$834$		0			0
$835$	−17.6390	−	10.1839i	−0.610422	−	0.352427i
$836$	10.3055	+	10.0480i	0.356422	+	0.347517i
$837$		0			0
$838$		−	17.6324i		−	0.609101i
$839$	2.08528	+	1.20394i	0.0719918	+	0.0415645i	0.535564	−	0.844495i	$-0.320099\pi$
$839$	2.08528	+	1.20394i	0.0719918	+	0.0415645i	−0.463572	+	0.886059i	$0.653432\pi$
$840$		0			0
$841$	13.5528	+	23.4741i	0.467337	+	0.809451i
$842$	8.85232	+	15.3327i	0.305071	+	0.528398i
$843$		0			0
$844$	10.0105	+	5.77955i	0.344575	+	0.198940i
$845$		−	4.69508i		−	0.161516i
$846$		0			0
$847$	−35.9360	+	0.909380i	−1.23478	+	0.0312467i
$848$	2.82074	+	1.62855i	0.0968645	+	0.0559247i
$849$		0			0
$850$	−0.940102	−	1.62830i	−0.0322452	−	0.0558504i
$851$	44.6965	−	25.8055i	1.53218	−	0.884603i
$852$		0			0
$853$	0.00677959	+	0.00391420i	0.000232129	+	0.000134020i	0.500116	−	0.865958i	$-0.333291\pi$
$853$	0.00677959	+	0.00391420i	0.000232129	+	0.000134020i	−0.499884	+	0.866092i	$0.666624\pi$
$854$	−24.4951			−0.838204
$855$		0			0
$856$	−7.19194			−0.245815
$857$	6.78272	−	11.7480i	0.231693	−	0.401304i	−0.726613	−	0.687047i	$-0.758907\pi$
$857$	6.78272	−	11.7480i	0.231693	−	0.401304i	0.958307	+	0.285742i	$0.0922401\pi$
$858$		0			0
$859$	−4.78235	−	8.28327i	−0.163172	−	0.282622i	0.772833	−	0.634610i	$-0.218839\pi$
$859$	−4.78235	−	8.28327i	−0.163172	−	0.282622i	−0.936004	+	0.351988i	$0.885506\pi$
$860$	3.98021	+	6.89392i	0.135724	+	0.235081i
$861$		0			0
$862$	17.3205	−	30.0000i	0.589940	−	1.02181i
$863$			4.90873i			0.167095i	0.996504	+	0.0835476i	$0.0266251\pi$
$863$			4.90873i			0.167095i	−0.996504	+	0.0835476i	$0.973375\pi$
$864$		0			0
$865$		−	12.5298i		−	0.426025i
$866$	−11.8346	+	20.4981i	−0.402155	+	0.696553i
$867$		0			0
$868$	10.0919	−	5.82658i	0.342543	−	0.197767i
$869$	10.7120	−	42.1011i	0.363381	−	1.42818i
$870$		0			0
$871$	9.22744	+	5.32746i	0.312660	+	0.180514i
$872$		−	12.6752i		−	0.429236i
$873$		0			0
$874$	30.9359			1.04642
$875$	−1.63398	+	2.83014i	−0.0552386	+	0.0956760i
$876$		0			0
$877$	33.7633	−	19.4933i	1.14011	−	0.658241i	0.193650	−	0.981071i	$-0.437968\pi$
$877$	33.7633	−	19.4933i	1.14011	−	0.658241i	0.946457	+	0.322830i	$0.104634\pi$
$878$	−30.7259	+	17.7396i	−1.03695	+	0.598682i
$879$		0			0
$880$	3.19250	−	0.898862i	0.107619	−	0.0303006i
$881$			31.1989i			1.05112i	0.850758	+	0.525558i	$0.176143\pi$
$881$			31.1989i			1.05112i	−0.850758	+	0.525558i	$0.823857\pi$
$882$		0			0
$883$	−15.2943			−0.514693			−0.257347	−	0.966319i	$-0.582848\pi$
$883$	−15.2943			−0.514693			−0.257347	+	0.966319i	$0.582848\pi$
$884$	4.69249	+	2.70921i	0.157825	+	0.0911206i
$885$		0			0
$886$	−34.1454	+	19.7138i	−1.14714	+	0.662299i
$887$	−12.7148	−	22.0226i	−0.426921	−	0.739448i	0.569677	−	0.821869i	$-0.307068\pi$
$887$	−12.7148	−	22.0226i	−0.426921	−	0.739448i	−0.996598	+	0.0824205i	$0.973735\pi$
$888$		0			0
$889$	10.7540	−	18.6265i	0.360677	−	0.624712i
$890$	−2.39265			−0.0802017
$891$		0			0
$892$	13.0799			0.437948
$893$	−22.3492	+	38.7100i	−0.747888	+	1.29538i
$894$		0			0
$895$	−11.2940	−	19.5618i	−0.377517	−	0.653878i
$896$	−2.83014	+	1.63398i	−0.0945482	+	0.0545874i
$897$		0			0
$898$	−22.3850	−	12.9240i	−0.746998	−	0.431280i
$899$	4.90808			0.163694
$900$		0			0
$901$			6.12402i			0.204021i
$902$	6.89051	+	24.4731i	0.229429	+	0.814866i
$903$		0			0
$904$	2.95268	−	1.70473i	0.0982048	−	0.0566986i
$905$	13.9131	−	8.03274i	0.462487	−	0.267017i
$906$		0			0
$907$	10.7067	−	18.5446i	0.355511	−	0.615763i	−0.631694	−	0.775218i	$-0.717640\pi$
$907$	10.7067	−	18.5446i	0.355511	−	0.615763i	0.987205	+	0.159454i	$0.0509735\pi$
$908$	−21.8389			−0.724749
$909$		0			0
$910$		−	9.41769i		−	0.312193i
$911$	−16.9252	−	9.77174i	−0.560755	−	0.323752i	0.192693	−	0.981259i	$-0.438278\pi$
$911$	−16.9252	−	9.77174i	−0.560755	−	0.323752i	−0.753449	+	0.657507i	$0.771611\pi$
$912$		0			0
$913$	−2.97469	−	0.756869i	−0.0984480	−	0.0250487i
$914$	11.7176	−	6.76513i	0.387582	−	0.223771i
$915$		0			0
$916$	0.226279	−	0.391926i	0.00747646	−	0.0129496i
$917$			18.2429i			0.602434i
$918$		0			0
$919$			4.69659i			0.154926i	0.996995	+	0.0774632i	$0.0246820\pi$
$919$			4.69659i			0.154926i	−0.996995	+	0.0774632i	$0.975318\pi$
$920$	3.56428	−	6.17351i	0.117511	−	0.203534i
$921$		0			0
$922$	−5.94147	−	10.2909i	−0.195672	−	0.338914i
$923$	22.5307	+	39.0242i	0.741606	+	1.28450i
$924$		0			0
$925$	−3.62003	+	6.27007i	−0.119026	+	0.206159i
$926$	5.12039			0.168266
$927$		0			0
$928$	−1.37640			−0.0451826
$929$	12.9688	+	7.48755i	0.425493	+	0.245659i	0.697425	−	0.716658i	$-0.254329\pi$
$929$	12.9688	+	7.48755i	0.425493	+	0.245659i	−0.271932	+	0.962317i	$0.587662\pi$
$930$		0			0
$931$	−13.8289	+	7.98411i	−0.453223	+	0.261669i
$932$	−14.4537	−	25.0345i	−0.473446	−	0.820033i
$933$		0			0
$934$	−2.59986	−	1.50103i	−0.0850701	−	0.0491153i
$935$	4.46489	+	4.35334i	0.146018	+	0.142369i
$936$		0			0
$937$			10.3961i			0.339626i	0.985476	+	0.169813i	$0.0543164\pi$
$937$			10.3961i			0.339626i	−0.985476	+	0.169813i	$0.945684\pi$
$938$	−10.4638	−	6.04128i	−0.341655	−	0.197255i
$939$		0			0
$940$	5.14992	+	8.91993i	0.167972	+	0.290936i
$941$	−25.8519	−	44.7768i	−0.842748	−	1.45968i	−0.887562	−	0.460687i	$-0.847603\pi$
$941$	−25.8519	−	44.7768i	−0.842748	−	1.45968i	0.0448143	−	0.998995i	$-0.485730\pi$
$942$		0			0
$943$	47.3250	+	27.3231i	1.54111	+	0.889763i
$944$			1.51688i			0.0493703i
$945$		0			0
$946$	−18.9035	−	18.4312i	−0.614605	−	0.599249i
$947$	9.41189	+	5.43396i	0.305845	+	0.176580i	0.645066	−	0.764127i	$-0.276830\pi$
$947$	9.41189	+	5.43396i	0.305845	+	0.176580i	−0.339220	+	0.940707i	$0.610163\pi$
$948$		0			0
$949$	−16.3268	−	28.2789i	−0.529991	−	0.917972i
$950$	−3.75831	+	2.16986i	−0.121936	+	0.0703995i
$951$		0			0
$952$	−5.32123	−	3.07221i	−0.172462	−	0.0995710i
$953$	49.8541			1.61493			0.807467	−	0.589913i	$-0.200838\pi$
$953$	49.8541			1.61493			0.807467	+	0.589913i	$0.200838\pi$
$954$		0			0
$955$	1.72132			0.0557006
$956$	6.53619	−	11.3210i	0.211396	−	0.366148i
$957$		0			0
$958$	15.8657	+	27.4801i	0.512597	+	0.887843i
$959$	8.53070	+	14.7756i	0.275471	+	0.477129i
$960$		0			0
$961$	9.14224	−	15.8348i	0.294911	−	0.510801i
$962$		−	20.8646i		−	0.672701i
$963$		0			0
$964$		−	23.7832i		−	0.766006i
$965$	−6.34656	+	10.9926i	−0.204303	+	0.353863i
$966$		0			0
$967$	33.1745	−	19.1533i	1.06682	−	0.615928i	0.139509	−	0.990221i	$-0.455448\pi$
$967$	33.1745	−	19.1533i	1.06682	−	0.615928i	0.927311	+	0.374292i	$0.122114\pi$
$968$	−9.38409	+	5.73923i	−0.301616	+	0.184466i
$969$		0			0
$970$	13.9494	+	8.05367i	0.447887	+	0.258588i
$971$		−	26.2790i		−	0.843333i	−0.906751	−	0.421667i	$-0.861445\pi$
$971$		−	26.2790i		−	0.843333i	0.906751	−	0.421667i	$-0.138555\pi$
$972$		0			0
$973$	−38.5127			−1.23466
$974$	10.6862	−	18.5090i	0.342408	−	0.593068i
$975$		0			0
$976$	−6.49131	+	3.74776i	−0.207782	+	0.119963i
$977$	29.5918	−	17.0848i	0.946725	−	0.546592i	0.0546627	−	0.998505i	$-0.482592\pi$
$977$	29.5918	−	17.0848i	0.946725	−	0.546592i	0.892062	+	0.451913i	$0.149258\pi$
$978$		0			0
$979$	7.63853	−	2.15066i	0.244128	−	0.0687354i
$980$			3.67955i			0.117539i
$981$		0			0
$982$	29.1786			0.931127
$983$	4.41072	+	2.54653i	0.140680	+	0.0812217i	0.568688	−	0.822553i	$-0.307451\pi$
$983$	4.41072	+	2.54653i	0.140680	+	0.0812217i	−0.428008	+	0.903775i	$0.640784\pi$
$984$		0			0
$985$	−0.542872	+	0.313427i	−0.0172973	+	0.00998663i
$986$	−1.29396	−	2.24120i	−0.0412080	−	0.0713743i
$987$		0			0
$988$	6.25316	−	10.8308i	0.198939	−	0.344573i
$989$	−56.7462			−1.80442
$990$		0			0
$991$	51.0722			1.62236			0.811181	−	0.584795i	$-0.198825\pi$
$991$	51.0722			1.62236			0.811181	+	0.584795i	$0.198825\pi$
$992$	1.78294	−	3.08815i	0.0566085	−	0.0980487i
$993$		0			0
$994$	−25.5495	−	44.2530i	−0.810381	−	1.40362i
$995$	14.5602	−	8.40633i	0.461589	−	0.266499i
$996$		0			0
$997$	2.51845	+	1.45403i	0.0797600	+	0.0460495i	0.539350	−	0.842082i	$-0.318670\pi$
$997$	2.51845	+	1.45403i	0.0797600	+	0.0460495i	−0.459590	+	0.888131i	$0.652003\pi$
$998$	38.4599			1.21743
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.a.791.11		48
3.2	odd	2		990.2.t.b.461.16	yes	48
9.4	even	3		990.2.t.a.131.16	✓	48
9.5	odd	6		2970.2.t.b.2771.11		48
11.10	odd	2		2970.2.t.b.791.11		48
33.32	even	2		990.2.t.a.461.16	yes	48
99.32	even	6	inner	2970.2.t.a.2771.11		48
99.76	odd	6		990.2.t.b.131.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.16	✓	48	9.4	even	3
990.2.t.a.461.16	yes	48	33.32	even	2
990.2.t.b.131.16	yes	48	99.76	odd	6
990.2.t.b.461.16	yes	48	3.2	odd	2
2970.2.t.a.791.11		48	1.1	even	1	trivial
2970.2.t.a.2771.11		48	99.32	even	6	inner
2970.2.t.b.791.11		48	11.10	odd	2
2970.2.t.b.2771.11		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.83014 + 1.63398i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(0.898862 + 3.19250i) q^{11} +(2.49573 - 1.44091i) q^{13} +(-2.83014 + 1.63398i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.88020 q^{17} +4.33972i q^{19} +(0.866025 + 0.500000i) q^{20} +(-3.21422 - 0.817812i) q^{22} +(-6.17351 + 3.56428i) q^{23} +(0.500000 - 0.866025i) q^{25} +2.88183i q^{26} -3.26796i q^{28} +(0.688200 - 1.19200i) q^{29} +(1.78294 + 3.08815i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.940102 - 1.62830i) q^{34} -3.26796 q^{35} -7.24005 q^{37} +(-3.75831 - 2.16986i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-3.83291 - 6.63880i) q^{41} +(6.89392 + 3.98021i) q^{43} +(2.31535 - 2.37469i) q^{44} -7.12855i q^{46} +(8.91993 + 5.14992i) q^{47} +(1.83978 + 3.18659i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.49573 - 1.44091i) q^{52} -3.25710i q^{53} +(-2.37469 - 2.31535i) q^{55} +(2.83014 + 1.63398i) q^{56} +(0.688200 + 1.19200i) q^{58} +(1.31366 - 0.758441i) q^{59} +(6.49131 + 3.74776i) q^{61} -3.56588 q^{62} +1.00000 q^{64} +(-1.44091 + 2.49573i) q^{65} +(1.84864 + 3.20194i) q^{67} +(0.940102 + 1.62830i) q^{68} +(1.63398 - 2.83014i) q^{70} +15.6364i q^{71} -11.3309i q^{73} +(3.62003 - 6.27007i) q^{74} +(3.75831 - 2.16986i) q^{76} +(-2.67258 + 10.5039i) q^{77} +(-11.3436 - 6.54921i) q^{79} -1.00000i q^{80} +7.66582 q^{82} +(-0.462740 + 0.801490i) q^{83} +(1.62830 - 0.940102i) q^{85} +(-6.89392 + 3.98021i) q^{86} +(0.898862 + 3.19250i) q^{88} -2.39265i q^{89} +9.41769 q^{91} +(6.17351 + 3.56428i) q^{92} +(-8.91993 + 5.14992i) q^{94} +(-2.16986 - 3.75831i) q^{95} +(-8.05367 + 13.9494i) q^{97} -3.67955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 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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