LMFDB - Embedded newform 1456.2.cc.g.673.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(225,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.225"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,2,0,0,0,0,0,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.12
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.g.225.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.56651 + 2.71328i) q^{3} +2.28231i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-3.40791 + 5.90267i) q^{9} +(-4.77925 + 2.75930i) q^{11} +(-2.83231 - 2.23115i) q^{13} +(-6.19254 + 3.57527i) q^{15} +(2.80387 - 4.85644i) q^{17} +(4.25993 + 2.45947i) q^{19} -3.13302i q^{21} +(0.971308 + 1.68235i) q^{23} -0.208948 q^{25} -11.9550 q^{27} +(-1.89756 - 3.28666i) q^{29} +0.689198i q^{31} +(-14.9735 - 8.64496i) q^{33} +(1.14116 - 1.97654i) q^{35} +(-5.40812 + 3.12238i) q^{37} +(1.61688 - 11.1800i) q^{39} +(-3.61843 + 2.08910i) q^{41} +(-4.11581 + 7.12880i) q^{43} +(-13.4717 - 7.77791i) q^{45} -5.55704i q^{47} +(0.500000 + 0.866025i) q^{49} +17.5692 q^{51} +6.06641 q^{53} +(-6.29759 - 10.9077i) q^{55} +15.4112i q^{57} +(12.9109 + 7.45409i) q^{59} +(3.70884 - 6.42391i) q^{61} +(5.90267 - 3.40791i) q^{63} +(5.09218 - 6.46421i) q^{65} +(-7.90904 + 4.56629i) q^{67} +(-3.04313 + 5.27085i) q^{69} +(10.7813 + 6.22456i) q^{71} -5.00071i q^{73} +(-0.327319 - 0.566933i) q^{75} +5.51861 q^{77} -6.90219 q^{79} +(-8.50397 - 14.7293i) q^{81} +15.8599i q^{83} +(11.0839 + 6.39930i) q^{85} +(5.94508 - 10.2972i) q^{87} +(-7.21272 + 4.16427i) q^{89} +(1.33728 + 3.34839i) q^{91} +(-1.86999 + 1.07964i) q^{93} +(-5.61329 + 9.72250i) q^{95} +(3.58245 + 2.06833i) q^{97} -37.6138i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) $ 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	1.56651	+	2.71328i	0.904425	+	1.56651i	0.821687	+	0.569939i	$0.193033\pi$
$3$	1.56651	+	2.71328i	0.904425	+	1.56651i	0.0827383	+	0.996571i	$0.473633\pi$
$4$		0			0
$5$			2.28231i			1.02068i	0.859972	+	0.510340i	$0.170481\pi$
$5$			2.28231i			1.02068i	−0.859972	+	0.510340i	$0.829519\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	−3.40791	+	5.90267i	−1.13597	+	1.96756i
$10$		0			0
$11$	−4.77925	+	2.75930i	−1.44100	+	0.831961i	−0.997916	−	0.0645194i	$-0.979449\pi$
$11$	−4.77925	+	2.75930i	−1.44100	+	0.831961i	−0.443083	+	0.896481i	$0.646115\pi$
$12$		0			0
$13$	−2.83231	−	2.23115i	−0.785541	−	0.618809i
$13$	−2.83231	−	2.23115i	−0.785541	−	0.618809i
$14$		0			0
$15$	−6.19254	+	3.57527i	−1.59891	+	0.923130i
$16$		0			0
$17$	2.80387	−	4.85644i	0.680038	−	1.17786i	−0.294931	−	0.955519i	$-0.595297\pi$
$17$	2.80387	−	4.85644i	0.680038	−	1.17786i	0.974969	−	0.222342i	$-0.0713701\pi$
$18$		0			0
$19$	4.25993	+	2.45947i	0.977296	+	0.564242i	0.901453	−	0.432878i	$-0.142502\pi$
$19$	4.25993	+	2.45947i	0.977296	+	0.564242i	0.0758432	+	0.997120i	$0.475835\pi$
$20$		0			0
$21$		−	3.13302i		−	0.683681i
$22$		0			0
$23$	0.971308	+	1.68235i	0.202532	+	0.350795i	0.949343	−	0.314240i	$-0.101750\pi$
$23$	0.971308	+	1.68235i	0.202532	+	0.350795i	−0.746812	+	0.665035i	$0.768416\pi$
$24$		0			0
$25$	−0.208948			−0.0417896
$26$		0			0
$27$	−11.9550			−2.30075
$28$		0			0
$29$	−1.89756	−	3.28666i	−0.352367	−	0.610318i	0.634297	−	0.773090i	$-0.281290\pi$
$29$	−1.89756	−	3.28666i	−0.352367	−	0.610318i	−0.986664	+	0.162772i	$0.947957\pi$
$30$		0			0
$31$			0.689198i			0.123784i	0.998083	+	0.0618918i	$0.0197134\pi$
$31$			0.689198i			0.123784i	−0.998083	+	0.0618918i	$0.980287\pi$
$32$		0			0
$33$	−14.9735	−	8.64496i	−2.60655	−	1.50489i
$34$		0			0
$35$	1.14116	−	1.97654i	0.192891	−	0.334096i
$36$		0			0
$37$	−5.40812	+	3.12238i	−0.889090	+	0.513316i	−0.873645	−	0.486564i	$-0.838250\pi$
$37$	−5.40812	+	3.12238i	−0.889090	+	0.513316i	−0.0154451	+	0.999881i	$0.504917\pi$
$38$		0			0
$39$	1.61688	−	11.1800i	0.258908	−	1.79023i
$40$		0			0
$41$	−3.61843	+	2.08910i	−0.565103	+	0.326263i	−0.755191	−	0.655504i	$-0.772456\pi$
$41$	−3.61843	+	2.08910i	−0.565103	+	0.326263i	0.190088	+	0.981767i	$0.439123\pi$
$42$		0			0
$43$	−4.11581	+	7.12880i	−0.627656	+	1.08713i	0.360365	+	0.932811i	$0.382652\pi$
$43$	−4.11581	+	7.12880i	−0.627656	+	1.08713i	−0.988021	+	0.154320i	$0.950681\pi$
$44$		0			0
$45$	−13.4717	−	7.77791i	−2.00825	−	1.15946i
$46$		0			0
$47$		−	5.55704i		−	0.810578i	−0.914189	−	0.405289i	$-0.867171\pi$
$47$		−	5.55704i		−	0.810578i	0.914189	−	0.405289i	$-0.132829\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	17.5692			2.46017
$52$		0			0
$53$	6.06641			0.833286			0.416643	−	0.909070i	$-0.363207\pi$
$53$	6.06641			0.833286			0.416643	+	0.909070i	$0.363207\pi$
$54$		0			0
$55$	−6.29759	−	10.9077i	−0.849167	−	1.47080i
$56$		0			0
$57$			15.4112i			2.04126i
$58$		0			0
$59$	12.9109	+	7.45409i	1.68085	+	0.970440i	0.961097	+	0.276212i	$0.0890793\pi$
$59$	12.9109	+	7.45409i	1.68085	+	0.970440i	0.719755	+	0.694228i	$0.244254\pi$
$60$		0			0
$61$	3.70884	−	6.42391i	0.474869	−	0.822497i	−0.524717	−	0.851277i	$-0.675829\pi$
$61$	3.70884	−	6.42391i	0.474869	−	0.822497i	0.999586	+	0.0287799i	$0.00916220\pi$
$62$		0			0
$63$	5.90267	−	3.40791i	0.743667	−	0.429356i
$64$		0			0
$65$	5.09218	−	6.46421i	0.631607	−	0.801787i
$66$		0			0
$67$	−7.90904	+	4.56629i	−0.966243	+	0.557861i	−0.898089	−	0.439814i	$-0.855044\pi$
$67$	−7.90904	+	4.56629i	−0.966243	+	0.557861i	−0.0681541	+	0.997675i	$0.521711\pi$
$68$		0			0
$69$	−3.04313	+	5.27085i	−0.366349	+	0.634536i
$70$		0			0
$71$	10.7813	+	6.22456i	1.27950	+	0.738719i	0.976756	−	0.214353i	$-0.0687643\pi$
$71$	10.7813	+	6.22456i	1.27950	+	0.738719i	0.302743	+	0.953072i	$0.402098\pi$
$72$		0			0
$73$		−	5.00071i		−	0.585289i	−0.956221	−	0.292645i	$-0.905465\pi$
$73$		−	5.00071i		−	0.585289i	0.956221	−	0.292645i	$-0.0945353\pi$
$74$		0			0
$75$	−0.327319	−	0.566933i	−0.0377956	−	0.0654638i
$76$		0			0
$77$	5.51861			0.628904
$78$		0			0
$79$	−6.90219			−0.776557			−0.388279	−	0.921542i	$-0.626930\pi$
$79$	−6.90219			−0.776557			−0.388279	+	0.921542i	$0.626930\pi$
$80$		0			0
$81$	−8.50397	−	14.7293i	−0.944885	−	1.63659i
$82$		0			0
$83$			15.8599i			1.74085i	0.492299	+	0.870426i	$0.336157\pi$
$83$			15.8599i			1.74085i	−0.492299	+	0.870426i	$0.663843\pi$
$84$		0			0
$85$	11.0839	+	6.39930i	1.20222	+	0.694102i
$86$		0			0
$87$	5.94508	−	10.2972i	0.637380	−	1.10397i
$88$		0			0
$89$	−7.21272	+	4.16427i	−0.764547	+	0.441411i	−0.830926	−	0.556383i	$-0.812189\pi$
$89$	−7.21272	+	4.16427i	−0.764547	+	0.441411i	0.0663791	+	0.997794i	$0.478855\pi$
$90$		0			0
$91$	1.33728	+	3.34839i	0.140185	+	0.351006i
$92$		0			0
$93$	−1.86999	+	1.07964i	−0.193908	+	0.111953i
$94$		0			0
$95$	−5.61329	+	9.72250i	−0.575911	+	0.997507i
$96$		0			0
$97$	3.58245	+	2.06833i	0.363743	+	0.210007i	0.670721	−	0.741709i	$-0.265985\pi$
$97$	3.58245	+	2.06833i	0.363743	+	0.210007i	−0.306979	+	0.951716i	$0.599318\pi$
$98$		0			0
$99$		−	37.6138i		−	3.78033i
$100$		0			0
$101$	1.78834	+	3.09750i	0.177947	+	0.308213i	0.941177	−	0.337914i	$-0.109721\pi$
$101$	1.78834	+	3.09750i	0.177947	+	0.308213i	−0.763230	+	0.646127i	$0.776388\pi$
$102$		0			0
$103$	−14.3212			−1.41111			−0.705553	−	0.708658i	$-0.749301\pi$
$103$	−14.3212			−1.41111			−0.705553	+	0.708658i	$0.749301\pi$
$104$		0			0
$105$	7.15053			0.697820
$106$		0			0
$107$	−1.68911	−	2.92562i	−0.163292	−	0.282830i	0.772755	−	0.634704i	$-0.218878\pi$
$107$	−1.68911	−	2.92562i	−0.163292	−	0.282830i	−0.936047	+	0.351874i	$0.885545\pi$
$108$		0			0
$109$			4.47958i			0.429066i	0.976717	+	0.214533i	$0.0688229\pi$
$109$			4.47958i			0.429066i	−0.976717	+	0.214533i	$0.931177\pi$
$110$		0			0
$111$	−16.9438	−	9.78248i	−1.60823	−	0.928512i
$112$		0			0
$113$	−1.24684	+	2.15960i	−0.117293	+	0.203158i	−0.918694	−	0.394970i	$-0.870755\pi$
$113$	−1.24684	+	2.15960i	−0.117293	+	0.203158i	0.801401	+	0.598128i	$0.204088\pi$
$114$		0			0
$115$	−3.83966	+	2.21683i	−0.358050	+	0.206720i
$116$		0			0
$117$	22.8220	−	9.11464i	2.10989	−	0.842649i
$118$		0			0
$119$	−4.85644	+	2.80387i	−0.445189	+	0.257030i
$120$		0			0
$121$	9.72751	−	16.8485i	0.884319	−	1.53169i
$122$		0			0
$123$	−11.3366	−	6.54519i	−1.02219	−	0.590160i
$124$		0			0
$125$			10.9347i			0.978027i
$126$		0			0
$127$	1.59450	+	2.76176i	0.141489	+	0.245066i	0.928058	−	0.372437i	$-0.121478\pi$
$127$	1.59450	+	2.76176i	0.141489	+	0.245066i	−0.786568	+	0.617503i	$0.788144\pi$
$128$		0			0
$129$	−25.7899			−2.27067
$130$		0			0
$131$	6.25472			0.546477			0.273239	−	0.961946i	$-0.411905\pi$
$131$	6.25472			0.546477			0.273239	+	0.961946i	$0.411905\pi$
$132$		0			0
$133$	−2.45947	−	4.25993i	−0.213263	−	0.369383i
$134$		0			0
$135$		−	27.2851i		−	2.34833i
$136$		0			0
$137$	−10.6367	−	6.14108i	−0.908751	−	0.524668i	−0.0287222	−	0.999587i	$-0.509144\pi$
$137$	−10.6367	−	6.14108i	−0.908751	−	0.524668i	−0.880029	+	0.474920i	$0.842477\pi$
$138$		0			0
$139$	−7.98744	+	13.8347i	−0.677486	+	1.17344i	0.298250	+	0.954488i	$0.403597\pi$
$139$	−7.98744	+	13.8347i	−0.677486	+	1.17344i	−0.975736	+	0.218952i	$0.929736\pi$
$140$		0			0
$141$	15.0778	−	8.70517i	1.26978	−	0.733107i
$142$		0			0
$143$	19.6927	+	2.84803i	1.64679	+	0.238164i
$144$		0			0
$145$	7.50119	−	4.33081i	0.622940	−	0.359654i
$146$		0			0
$147$	−1.56651	+	2.71328i	−0.129204	+	0.223787i
$148$		0			0
$149$	11.1484	+	6.43654i	0.913313	+	0.527302i	0.881496	−	0.472192i	$-0.156537\pi$
$149$	11.1484	+	6.43654i	0.913313	+	0.527302i	0.0318176	+	0.999494i	$0.489870\pi$
$150$		0			0
$151$		−	20.8187i		−	1.69421i	−0.531429	−	0.847103i	$-0.678345\pi$
$151$		−	20.8187i		−	1.69421i	0.531429	−	0.847103i	$-0.321655\pi$
$152$		0			0
$153$	19.1107	+	33.1006i	1.54501	+	2.67603i
$154$		0			0
$155$	−1.57297			−0.126344
$156$		0			0
$157$	8.72747			0.696528			0.348264	−	0.937397i	$-0.386771\pi$
$157$	8.72747			0.696528			0.348264	+	0.937397i	$0.386771\pi$
$158$		0			0
$159$	9.50309	+	16.4598i	0.753644	+	1.30535i
$160$		0			0
$161$		−	1.94262i		−	0.153100i
$162$		0			0
$163$	−8.58558	−	4.95689i	−0.672475	−	0.388253i	0.124539	−	0.992215i	$-0.460255\pi$
$163$	−8.58558	−	4.95689i	−0.672475	−	0.388253i	−0.797014	+	0.603961i	$0.793588\pi$
$164$		0			0
$165$	19.7305	−	34.1742i	1.53602	−	2.66046i
$166$		0			0
$167$	−8.32845	+	4.80843i	−0.644475	+	0.372088i	−0.786336	−	0.617799i	$-0.788025\pi$
$167$	−8.32845	+	4.80843i	−0.644475	+	0.372088i	0.141861	+	0.989887i	$0.454691\pi$
$168$		0			0
$169$	3.04395	+	12.6386i	0.234150	+	0.972201i
$170$		0			0
$171$	−29.0349	+	16.7633i	−2.22036	+	1.28192i
$172$		0			0
$173$	1.61275	−	2.79336i	0.122615	−	0.212375i	−0.798183	−	0.602415i	$-0.794205\pi$
$173$	1.61275	−	2.79336i	0.122615	−	0.212375i	0.920798	+	0.390040i	$0.127539\pi$
$174$		0			0
$175$	0.180954	+	0.104474i	0.0136789	+	0.00789749i
$176$		0			0
$177$			46.7077i			3.51076i
$178$		0			0
$179$	−7.90651	−	13.6945i	−0.590961	−	1.02357i	−0.994103	−	0.108437i	$-0.965416\pi$
$179$	−7.90651	−	13.6945i	−0.590961	−	1.02357i	0.403143	−	0.915137i	$-0.367918\pi$
$180$		0			0
$181$	−23.4244			−1.74112			−0.870561	−	0.492061i	$-0.836244\pi$
$181$	−23.4244			−1.74112			−0.870561	+	0.492061i	$0.836244\pi$
$182$		0			0
$183$	23.2398			1.71793
$184$		0			0
$185$	−7.12625	−	12.3430i	−0.523932	−	0.907477i
$186$		0			0
$187$			30.9469i			2.26306i
$188$		0			0
$189$	10.3534	+	5.97752i	0.753097	+	0.434801i
$190$		0			0
$191$	11.8735	−	20.5655i	0.859136	−	1.48807i	−0.0136190	−	0.999907i	$-0.504335\pi$
$191$	11.8735	−	20.5655i	0.859136	−	1.48807i	0.872755	−	0.488159i	$-0.162331\pi$
$192$		0			0
$193$	−13.4735	+	7.77890i	−0.969840	+	0.559938i	−0.899188	−	0.437563i	$-0.855842\pi$
$193$	−13.4735	+	7.77890i	−0.969840	+	0.559938i	−0.0706528	+	0.997501i	$0.522508\pi$
$194$		0			0
$195$	25.5161	+	3.69023i	1.82725	+	0.264263i
$196$		0			0
$197$	13.8500	−	7.99633i	0.986775	−	0.569715i	0.0824661	−	0.996594i	$-0.473720\pi$
$197$	13.8500	−	7.99633i	0.986775	−	0.569715i	0.904309	+	0.426879i	$0.140387\pi$
$198$		0			0
$199$	−4.93072	+	8.54025i	−0.349529	+	0.605402i	−0.986166	−	0.165762i	$-0.946992\pi$
$199$	−4.93072	+	8.54025i	−0.349529	+	0.605402i	0.636637	+	0.771164i	$0.280325\pi$
$200$		0			0
$201$	−24.7792	−	14.3063i	−1.74779	−	1.00909i
$202$		0			0
$203$			3.79511i			0.266365i
$204$		0			0
$205$	−4.76798	−	8.25838i	−0.333010	−	0.576790i
$206$		0			0
$207$	−13.2405			−0.920279
$208$		0			0
$209$	−27.1457			−1.87771
$210$		0			0
$211$	−1.00748	−	1.74501i	−0.0693580	−	0.120132i	0.829261	−	0.558862i	$-0.188762\pi$
$211$	−1.00748	−	1.74501i	−0.0693580	−	0.120132i	−0.898619	+	0.438730i	$0.855428\pi$
$212$		0			0
$213$			39.0033i			2.67246i
$214$		0			0
$215$	−16.2701	−	9.39357i	−1.10961	−	0.640636i
$216$		0			0
$217$	0.344599	−	0.596863i	0.0233929	−	0.0405177i
$218$		0			0
$219$	13.5683	−	7.83367i	0.916862	−	0.529350i
$220$		0			0
$221$	−18.7769	+	7.49910i	−1.26307	+	0.504444i
$222$		0			0
$223$	−0.0881439	+	0.0508899i	−0.00590255	+	0.00340784i	−0.502948	−	0.864316i	$-0.667751\pi$
$223$	−0.0881439	+	0.0508899i	−0.00590255	+	0.00340784i	0.497046	+	0.867724i	$0.334418\pi$
$224$		0			0
$225$	0.712076	−	1.23335i	0.0474717	−	0.0822234i
$226$		0			0
$227$	4.54259	+	2.62266i	0.301502	+	0.174072i	0.643117	−	0.765768i	$-0.277641\pi$
$227$	4.54259	+	2.62266i	0.301502	+	0.174072i	−0.341615	+	0.939840i	$0.610974\pi$
$228$		0			0
$229$			21.4484i			1.41735i	0.705535	+	0.708675i	$0.250707\pi$
$229$			21.4484i			1.41735i	−0.705535	+	0.708675i	$0.749293\pi$
$230$		0			0
$231$	8.64496	+	14.9735i	0.568796	+	0.985184i
$232$		0			0
$233$	24.3319			1.59403			0.797017	−	0.603957i	$-0.206410\pi$
$233$	24.3319			1.59403			0.797017	+	0.603957i	$0.206410\pi$
$234$		0			0
$235$	12.6829			0.827342
$236$		0			0
$237$	−10.8124	−	18.7275i	−0.702338	−	1.21648i
$238$		0			0
$239$			10.7950i			0.698273i	0.937072	+	0.349137i	$0.113525\pi$
$239$			10.7950i			0.698273i	−0.937072	+	0.349137i	$0.886475\pi$
$240$		0			0
$241$	12.3164	+	7.11090i	0.793372	+	0.458053i	0.841148	−	0.540805i	$-0.181880\pi$
$241$	12.3164	+	7.11090i	0.793372	+	0.458053i	−0.0477765	+	0.998858i	$0.515214\pi$
$242$		0			0
$243$	8.71055	−	15.0871i	0.558782	−	0.967839i
$244$		0			0
$245$	−1.97654	+	1.14116i	−0.126277	+	0.0729058i
$246$		0			0
$247$	−6.57800	−	16.4705i	−0.418548	−	1.04800i
$248$		0			0
$249$	−43.0323	+	24.8447i	−2.72706	+	1.57447i
$250$		0			0
$251$	13.7068	−	23.7408i	0.865163	−	1.49851i	−0.00172317	−	0.999999i	$-0.500549\pi$
$251$	13.7068	−	23.7408i	0.865163	−	1.49851i	0.866886	−	0.498507i	$-0.166118\pi$
$252$		0			0
$253$	−9.28425	−	5.36027i	−0.583696	−	0.336997i
$254$		0			0
$255$			40.0983i			2.51105i
$256$		0			0
$257$	11.3311	+	19.6261i	0.706816	+	1.22424i	0.966032	+	0.258422i	$0.0832025\pi$
$257$	11.3311	+	19.6261i	0.706816	+	1.22424i	−0.259216	+	0.965819i	$0.583464\pi$
$258$		0			0
$259$	6.24476			0.388031
$260$		0			0
$261$	25.8668			1.60111
$262$		0			0
$263$	11.4268	+	19.7918i	0.704606	+	1.22041i	0.966834	+	0.255407i	$0.0822095\pi$
$263$	11.4268	+	19.7918i	0.704606	+	1.22041i	−0.262228	+	0.965006i	$0.584457\pi$
$264$		0			0
$265$			13.8454i			0.850519i
$266$		0			0
$267$	−22.5976	−	13.0467i	−1.38295	−	0.798447i
$268$		0			0
$269$	4.81428	−	8.33858i	0.293532	−	0.508412i	−0.681110	−	0.732181i	$-0.738503\pi$
$269$	4.81428	−	8.33858i	0.293532	−	0.508412i	0.974642	+	0.223769i	$0.0718360\pi$
$270$		0			0
$271$	13.5355	−	7.81473i	0.822223	−	0.474711i	−0.0289592	−	0.999581i	$-0.509219\pi$
$271$	13.5355	−	7.81473i	0.822223	−	0.474711i	0.851183	+	0.524870i	$0.175886\pi$
$272$		0			0
$273$	−6.99024	+	8.87368i	−0.423068	+	0.537060i
$274$		0			0
$275$	0.998615	−	0.576551i	0.0602188	−	0.0347673i
$276$		0			0
$277$	2.09131	−	3.62225i	0.125655	−	0.217640i	−0.796334	−	0.604857i	$-0.793230\pi$
$277$	2.09131	−	3.62225i	0.125655	−	0.217640i	0.921989	+	0.387217i	$0.126564\pi$
$278$		0			0
$279$	−4.06811	−	2.34873i	−0.243552	−	0.140615i
$280$		0			0
$281$			5.13123i			0.306103i	0.988218	+	0.153052i	$0.0489101\pi$
$281$			5.13123i			0.306103i	−0.988218	+	0.153052i	$0.951090\pi$
$282$		0			0
$283$	−3.11540	−	5.39603i	−0.185191	−	0.320761i	0.758450	−	0.651732i	$-0.225957\pi$
$283$	−3.11540	−	5.39603i	−0.185191	−	0.320761i	−0.943641	+	0.330971i	$0.892624\pi$
$284$		0			0
$285$	−35.1731			−2.08347
$286$		0			0
$287$	4.17820			0.246631
$288$		0			0
$289$	−7.22336	−	12.5112i	−0.424903	−	0.735954i
$290$		0			0
$291$			12.9602i			0.759742i
$292$		0			0
$293$	6.08862	+	3.51526i	0.355701	+	0.205364i	0.667193	−	0.744885i	$-0.267496\pi$
$293$	6.08862	+	3.51526i	0.355701	+	0.205364i	−0.311492	+	0.950249i	$0.600829\pi$
$294$		0			0
$295$	−17.0126	+	29.4666i	−0.990510	+	1.71561i
$296$		0			0
$297$	57.1362	−	32.9876i	3.31538	−	1.91413i
$298$		0			0
$299$	1.00254	−	6.93208i	0.0579784	−	0.400892i
$300$		0			0
$301$	7.12880	−	4.11581i	0.410897	−	0.237232i
$302$		0			0
$303$	−5.60292	+	9.70454i	−0.321879	+	0.557511i
$304$		0			0
$305$	14.6614	+	8.46474i	0.839507	+	0.484689i
$306$		0			0
$307$			6.83879i			0.390311i	0.980772	+	0.195155i	$0.0625211\pi$
$307$			6.83879i			0.390311i	−0.980772	+	0.195155i	$0.937479\pi$
$308$		0			0
$309$	−22.4342	−	38.8572i	−1.27624	−	2.21051i
$310$		0			0
$311$	−14.5179			−0.823237			−0.411619	−	0.911356i	$-0.635036\pi$
$311$	−14.5179			−0.823237			−0.411619	+	0.911356i	$0.635036\pi$
$312$		0			0
$313$	30.8100			1.74148			0.870742	−	0.491741i	$-0.163639\pi$
$313$	30.8100			1.74148			0.870742	+	0.491741i	$0.163639\pi$
$314$		0			0
$315$	7.77791	+	13.4717i	0.438236	+	0.759047i
$316$		0			0
$317$		−	6.78232i		−	0.380933i	−0.981694	−	0.190467i	$-0.939000\pi$
$317$		−	6.78232i		−	0.380933i	0.981694	−	0.190467i	$-0.0610001\pi$
$318$		0			0
$319$	18.1378	+	10.4719i	1.01552	+	0.586312i
$320$		0			0
$321$	5.29201	−	9.16602i	0.295371	−	0.511598i
$322$		0			0
$323$	23.8886	−	13.7921i	1.32920	−	0.767412i
$324$		0			0
$325$	0.591805	+	0.466194i	0.0328274	+	0.0258598i
$326$		0			0
$327$	−12.1543	+	7.01731i	−0.672136	+	0.388058i
$328$		0			0
$329$	−2.77852	+	4.81254i	−0.153185	+	0.265324i
$330$		0			0
$331$	3.53558	+	2.04127i	0.194333	+	0.112198i	0.594010	−	0.804458i	$-0.297544\pi$
$331$	3.53558	+	2.04127i	0.194333	+	0.112198i	−0.399676	+	0.916656i	$0.630877\pi$
$332$		0			0
$333$		−	42.5632i		−	2.33245i
$334$		0			0
$335$	−10.4217	−	18.0509i	−0.569398	−	0.986226i
$336$		0			0
$337$	24.1656			1.31638			0.658192	−	0.752850i	$-0.271321\pi$
$337$	24.1656			1.31638			0.658192	+	0.752850i	$0.271321\pi$
$338$		0			0
$339$	−7.81278			−0.424332
$340$		0			0
$341$	−1.90171	−	3.29385i	−0.102983	−	0.178372i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	−12.0297	−	6.94537i	−0.647659	−	0.373926i
$346$		0			0
$347$	4.56601	−	7.90855i	0.245116	−	0.424553i	−0.717048	−	0.697024i	$-0.754507\pi$
$347$	4.56601	−	7.90855i	0.245116	−	0.424553i	0.962164	+	0.272470i	$0.0878406\pi$
$348$		0			0
$349$	22.8546	−	13.1951i	1.22338	−	0.706317i	0.257741	−	0.966214i	$-0.417022\pi$
$349$	22.8546	−	13.1951i	1.22338	−	0.706317i	0.965636	+	0.259897i	$0.0836885\pi$
$350$		0			0
$351$	33.8604	+	26.6735i	1.80733	+	1.42373i
$352$		0			0
$353$	−10.2461	+	5.91561i	−0.545346	+	0.314856i	−0.747243	−	0.664551i	$-0.768623\pi$
$353$	−10.2461	+	5.91561i	−0.545346	+	0.314856i	0.201897	+	0.979407i	$0.435290\pi$
$354$		0			0
$355$	−14.2064	+	24.6062i	−0.753997	+	1.30596i
$356$		0			0
$357$	−15.2153	−	8.78458i	−0.805281	−	0.464929i
$358$		0			0
$359$			30.9827i			1.63520i	0.575784	+	0.817602i	$0.304697\pi$
$359$			30.9827i			1.63520i	−0.575784	+	0.817602i	$0.695303\pi$
$360$		0			0
$361$	2.59803	+	4.49991i	0.136738	+	0.236837i
$362$		0			0
$363$	60.9530			3.19920
$364$		0			0
$365$	11.4132			0.597393
$366$		0			0
$367$	−8.83531	−	15.3032i	−0.461200	−	0.798821i	0.537821	−	0.843059i	$-0.319247\pi$
$367$	−8.83531	−	15.3032i	−0.461200	−	0.798821i	−0.999021	+	0.0442377i	$0.985914\pi$
$368$		0			0
$369$		−	28.4779i		−	1.48250i
$370$		0			0
$371$	−5.25367	−	3.03321i	−0.272757	−	0.157476i
$372$		0			0
$373$	−8.85830	+	15.3430i	−0.458665	+	0.794432i	−0.998891	−	0.0470887i	$-0.985006\pi$
$373$	−8.85830	+	15.3430i	−0.458665	+	0.794432i	0.540225	+	0.841520i	$0.318339\pi$
$374$		0			0
$375$	−29.6688	+	17.1293i	−1.53209	+	0.884552i
$376$		0			0
$377$	−1.95857	+	13.5426i	−0.100872	+	0.697478i
$378$		0			0
$379$	−9.81629	+	5.66744i	−0.504229	+	0.291117i	−0.730458	−	0.682957i	$-0.760693\pi$
$379$	−9.81629	+	5.66744i	−0.504229	+	0.291117i	0.226229	+	0.974074i	$0.427360\pi$
$380$		0			0
$381$	−4.99560	+	8.65264i	−0.255933	+	0.443288i
$382$		0			0
$383$	−8.01229	−	4.62590i	−0.409409	−	0.236372i	0.281127	−	0.959671i	$-0.409292\pi$
$383$	−8.01229	−	4.62590i	−0.409409	−	0.236372i	−0.690536	+	0.723298i	$0.742625\pi$
$384$		0			0
$385$			12.5952i			0.641910i
$386$		0			0
$387$	−28.0526	−	48.5886i	−1.42600	−	2.46990i
$388$		0			0
$389$	20.3817			1.03339			0.516696	−	0.856169i	$-0.327162\pi$
$389$	20.3817			1.03339			0.516696	+	0.856169i	$0.327162\pi$
$390$		0			0
$391$	10.8937			0.550917
$392$		0			0
$393$	9.79808	+	16.9708i	0.494248	+	0.856063i
$394$		0			0
$395$		−	15.7530i		−	0.792617i
$396$		0			0
$397$	−19.9223	−	11.5022i	−0.999874	−	0.577277i	−0.0916629	−	0.995790i	$-0.529218\pi$
$397$	−19.9223	−	11.5022i	−0.999874	−	0.577277i	−0.908211	+	0.418513i	$0.862552\pi$
$398$		0			0
$399$	7.70558	−	13.3465i	0.385762	−	0.668159i
$400$		0			0
$401$	1.41918	−	0.819366i	0.0708706	−	0.0409172i	−0.464146	−	0.885759i	$-0.653639\pi$
$401$	1.41918	−	0.819366i	0.0708706	−	0.0409172i	0.535017	+	0.844842i	$0.320305\pi$
$402$		0			0
$403$	1.53770	−	1.95202i	0.0765985	−	0.0972372i
$404$		0			0
$405$	33.6169	−	19.4087i	1.67044	−	0.964427i
$406$		0			0
$407$	17.2312	−	29.8453i	0.854119	−	1.47938i
$408$		0			0
$409$	30.0529	+	17.3510i	1.48602	+	0.857953i	0.999873	−	0.0159247i	$-0.00506921\pi$
$409$	30.0529	+	17.3510i	1.48602	+	0.857953i	0.486145	+	0.873878i	$0.338403\pi$
$410$		0			0
$411$		−	38.4803i		−	1.89809i
$412$		0			0
$413$	−7.45409	−	12.9109i	−0.366792	−	0.635302i
$414$		0			0
$415$	−36.1973			−1.77686
$416$		0			0
$417$	−50.0496			−2.45094
$418$		0			0
$419$	4.70812	+	8.15471i	0.230007	+	0.398384i	0.957810	−	0.287403i	$-0.0927918\pi$
$419$	4.70812	+	8.15471i	0.230007	+	0.398384i	−0.727803	+	0.685786i	$0.759458\pi$
$420$		0			0
$421$			19.0258i			0.927260i	0.886029	+	0.463630i	$0.153453\pi$
$421$			19.0258i			0.927260i	−0.886029	+	0.463630i	$0.846547\pi$
$422$		0			0
$423$	32.8014	+	18.9379i	1.59486	+	0.920792i
$424$		0			0
$425$	−0.585863	+	1.01474i	−0.0284185	+	0.0492223i
$426$		0			0
$427$	−6.42391	+	3.70884i	−0.310875	+	0.179484i
$428$		0			0
$429$	23.1214	+	57.8933i	1.11631	+	2.79511i
$430$		0			0
$431$	28.8278	−	16.6438i	1.38859	−	0.801702i	0.395432	−	0.918495i	$-0.370595\pi$
$431$	28.8278	−	16.6438i	1.38859	−	0.801702i	0.993156	+	0.116793i	$0.0372614\pi$
$432$		0			0
$433$	−17.6832	+	30.6282i	−0.849799	+	1.47190i	0.0315876	+	0.999501i	$0.489944\pi$
$433$	−17.6832	+	30.6282i	−0.849799	+	1.47190i	−0.881387	+	0.472395i	$0.843390\pi$
$434$		0			0
$435$	23.5014	+	13.5685i	1.12680	+	0.650561i
$436$		0			0
$437$			9.55562i			0.457107i
$438$		0			0
$439$	9.96961	+	17.2679i	0.475823	+	0.824150i	0.999616	−	0.0276954i	$-0.00881684\pi$
$439$	9.96961	+	17.2679i	0.475823	+	0.824150i	−0.523793	+	0.851846i	$0.675484\pi$
$440$		0			0
$441$	−6.81582			−0.324563
$442$		0			0
$443$	22.0434			1.04731			0.523656	−	0.851930i	$-0.324568\pi$
$443$	22.0434			1.04731			0.523656	+	0.851930i	$0.324568\pi$
$444$		0			0
$445$	−9.50415	−	16.4617i	−0.450540	−	0.780358i
$446$		0			0
$447$			40.3316i			1.90762i
$448$		0			0
$449$	−10.8523	−	6.26556i	−0.512150	−	0.295690i	0.221567	−	0.975145i	$-0.428883\pi$
$449$	−10.8523	−	6.26556i	−0.512150	−	0.295690i	−0.733717	+	0.679455i	$0.762216\pi$
$450$		0			0
$451$	11.5289	−	19.9687i	0.542876	−	0.940288i
$452$		0			0
$453$	56.4870	−	32.6128i	2.65399	−	1.53228i
$454$		0			0
$455$	−7.64206	+	3.05208i	−0.358265	+	0.143084i
$456$		0			0
$457$	2.08491	−	1.20372i	0.0975280	−	0.0563078i	−0.450443	−	0.892805i	$-0.648734\pi$
$457$	2.08491	−	1.20372i	0.0975280	−	0.0563078i	0.547971	+	0.836497i	$0.315401\pi$
$458$		0			0
$459$	−33.5204	+	58.0590i	−1.56460	+	2.70996i
$460$		0			0
$461$	−8.92556	−	5.15317i	−0.415705	−	0.240007i	0.277533	−	0.960716i	$-0.410483\pi$
$461$	−8.92556	−	5.15317i	−0.415705	−	0.240007i	−0.693238	+	0.720709i	$0.743816\pi$
$462$		0			0
$463$		−	0.929297i		−	0.0431881i	−0.999767	−	0.0215941i	$-0.993126\pi$
$463$		−	0.929297i		−	0.0431881i	0.999767	−	0.0215941i	$-0.00687414\pi$
$464$		0			0
$465$	−2.46407	−	4.26789i	−0.114268	−	0.197919i
$466$		0			0
$467$	−4.95471			−0.229277			−0.114638	−	0.993407i	$-0.536571\pi$
$467$	−4.95471			−0.229277			−0.114638	+	0.993407i	$0.536571\pi$
$468$		0			0
$469$	9.13257			0.421703
$470$		0			0
$471$	13.6717	+	23.6800i	0.629957	+	1.09112i
$472$		0			0
$473$		−	45.4271i		−	2.08874i
$474$		0			0
$475$	−0.890105	−	0.513902i	−0.0408408	−	0.0235794i
$476$		0			0
$477$	−20.6738	+	35.8080i	−0.946587	+	1.63954i
$478$		0			0
$479$	−4.19244	+	2.42050i	−0.191557	+	0.110596i	−0.592711	−	0.805415i	$-0.701943\pi$
$479$	−4.19244	+	2.42050i	−0.191557	+	0.110596i	0.401154	+	0.916011i	$0.368609\pi$
$480$		0			0
$481$	22.2840	+	3.22278i	1.01606	+	0.146946i
$482$		0			0
$483$	5.27085	−	3.04313i	0.239832	−	0.138467i
$484$		0			0
$485$	−4.72057	+	8.17627i	−0.214350	+	0.371265i
$486$		0			0
$487$	4.19960	+	2.42464i	0.190302	+	0.109871i	0.592124	−	0.805847i	$-0.298290\pi$
$487$	4.19960	+	2.42464i	0.190302	+	0.109871i	−0.401822	+	0.915718i	$0.631623\pi$
$488$		0			0
$489$		−	31.0601i		−	1.40458i
$490$		0			0
$491$	21.3449	+	36.9704i	0.963280	+	1.66845i	0.714167	+	0.699975i	$0.246806\pi$
$491$	21.3449	+	36.9704i	0.963280	+	1.66845i	0.249113	+	0.968474i	$0.419861\pi$
$492$		0			0
$493$	−21.2820			−0.958492
$494$		0			0
$495$	85.8465			3.85851
$496$		0			0
$497$	−6.22456	−	10.7813i	−0.279210	−	0.483605i
$498$		0			0
$499$		−	4.34945i		−	0.194708i	−0.995250	−	0.0973542i	$-0.968962\pi$
$499$		−	4.34945i		−	0.194708i	0.995250	−	0.0973542i	$-0.0310380\pi$
$500$		0			0
$501$	−26.0932	−	15.0649i	−1.16576	−	0.673051i
$502$		0			0
$503$	21.7833	−	37.7298i	0.971271	−	1.68229i	0.279542	−	0.960133i	$-0.409817\pi$
$503$	21.7833	−	37.7298i	0.971271	−	1.68229i	0.691729	−	0.722157i	$-0.256849\pi$
$504$		0			0
$505$	−7.06947	+	4.08156i	−0.314587	+	0.181627i
$506$		0			0
$507$	−29.5236	+	28.0576i	−1.31119	+	1.24608i
$508$		0			0
$509$	−16.1044	+	9.29788i	−0.713815	+	0.412121i	−0.812472	−	0.583000i	$-0.801879\pi$
$509$	−16.1044	+	9.29788i	−0.713815	+	0.412121i	0.0986568	+	0.995122i	$0.468545\pi$
$510$		0			0
$511$	−2.50036	+	4.33074i	−0.110609	+	0.191581i
$512$		0			0
$513$	−50.9277	−	29.4031i	−2.24851	−	1.29818i
$514$		0			0
$515$		−	32.6853i		−	1.44029i
$516$		0			0
$517$	15.3336	+	26.5585i	0.674370	+	1.16804i
$518$		0			0
$519$	10.1055			0.443584
$520$		0			0
$521$	9.30988			0.407873			0.203937	−	0.978984i	$-0.434626\pi$
$521$	9.30988			0.407873			0.203937	+	0.978984i	$0.434626\pi$
$522$		0			0
$523$	−7.25998	−	12.5747i	−0.317457	−	0.549851i	0.662500	−	0.749062i	$-0.269496\pi$
$523$	−7.25998	−	12.5747i	−0.317457	−	0.549851i	−0.979957	+	0.199211i	$0.936162\pi$
$524$		0			0
$525$			0.654638i			0.0285708i
$526$		0			0
$527$	3.34705	+	1.93242i	0.145800	+	0.0841776i
$528$		0			0
$529$	9.61312	−	16.6504i	0.417962	−	0.723931i
$530$		0			0
$531$	−87.9981	+	50.8058i	−3.81879	+	2.20478i
$532$		0			0
$533$	14.9096	+	2.15627i	0.645806	+	0.0933986i
$534$		0			0
$535$	6.67717	−	3.85507i	0.288679	−	0.166669i
$536$		0			0
$537$	24.7713	−	42.9051i	1.06896	−	1.85149i
$538$		0			0
$539$	−4.77925	−	2.75930i	−0.205857	−	0.118852i
$540$		0			0
$541$		−	4.10390i		−	0.176440i	−0.996101	−	0.0882202i	$-0.971882\pi$
$541$		−	4.10390i		−	0.176440i	0.996101	−	0.0882202i	$-0.0281179\pi$
$542$		0			0
$543$	−36.6946	−	63.5568i	−1.57471	−	2.72748i
$544$		0			0
$545$	−10.2238			−0.437939
$546$		0			0
$547$	8.59559			0.367521			0.183761	−	0.982971i	$-0.441173\pi$
$547$	8.59559			0.367521			0.183761	+	0.982971i	$0.441173\pi$
$548$		0			0
$549$	25.2788	+	43.7842i	1.07887	+	1.86866i
$550$		0			0
$551$		−	18.6680i		−	0.795281i
$552$		0			0
$553$	5.97747	+	3.45110i	0.254188	+	0.146756i
$554$		0			0
$555$	22.3267	−	38.6709i	0.947715	−	1.64149i
$556$		0			0
$557$	−4.75687	+	2.74638i	−0.201555	+	0.116368i	−0.597381	−	0.801958i	$-0.703792\pi$
$557$	−4.75687	+	2.74638i	−0.201555	+	0.116368i	0.395826	+	0.918326i	$0.370458\pi$
$558$		0			0
$559$	27.5627	−	11.0080i	1.16578	−	0.465587i
$560$		0			0
$561$	−83.9675	+	48.4786i	−3.54511	+	2.04677i
$562$		0			0
$563$	4.87578	−	8.44509i	0.205489	−	0.355918i	−0.744799	−	0.667289i	$-0.767455\pi$
$563$	4.87578	−	8.44509i	0.205489	−	0.355918i	0.950289	+	0.311371i	$0.100788\pi$
$564$		0			0
$565$	−4.92888	−	2.84569i	−0.207359	−	0.119719i
$566$		0			0
$567$			17.0079i			0.714266i
$568$		0			0
$569$	−3.77537	−	6.53913i	−0.158272	−	0.274134i	0.775974	−	0.630765i	$-0.217259\pi$
$569$	−3.77537	−	6.53913i	−0.158272	−	0.274134i	−0.934245	+	0.356631i	$0.883925\pi$
$570$		0			0
$571$	18.0170			0.753989			0.376995	−	0.926215i	$-0.376958\pi$
$571$	18.0170			0.753989			0.376995	+	0.926215i	$0.376958\pi$
$572$		0			0
$573$	74.3998			3.10810
$574$		0			0
$575$	−0.202953	−	0.351524i	−0.00846372	−	0.0146596i
$576$		0			0
$577$		−	31.8628i		−	1.32646i	−0.748413	−	0.663232i	$-0.769184\pi$
$577$		−	31.8628i		−	1.32646i	0.748413	−	0.663232i	$-0.230816\pi$
$578$		0			0
$579$	−42.2126	−	24.3715i	−1.75430	−	1.01284i
$580$		0			0
$581$	7.92996	−	13.7351i	0.328990	−	0.569828i
$582$		0			0
$583$	−28.9929	+	16.7391i	−1.20076	+	0.693261i
$584$		0			0
$585$	20.8024	+	52.0869i	0.860075	+	2.15353i
$586$		0			0
$587$	18.9279	−	10.9280i	0.781239	−	0.451048i	−0.0556303	−	0.998451i	$-0.517717\pi$
$587$	18.9279	−	10.9280i	0.781239	−	0.451048i	0.836869	+	0.547403i	$0.184383\pi$
$588$		0			0
$589$	−1.69507	+	2.93594i	−0.0698440	+	0.120973i
$590$		0			0
$591$	43.3925	+	25.0527i	1.78493	+	1.03053i
$592$		0			0
$593$		−	21.1110i		−	0.866924i	−0.901172	−	0.433462i	$-0.857292\pi$
$593$		−	21.1110i		−	0.866924i	0.901172	−	0.433462i	$-0.142708\pi$
$594$		0			0
$595$	−6.39930	−	11.0839i	−0.262346	−	0.454396i
$596$		0			0
$597$	−30.8961			−1.26449
$598$		0			0
$599$	5.84631			0.238874			0.119437	−	0.992842i	$-0.461891\pi$
$599$	5.84631			0.238874			0.119437	+	0.992842i	$0.461891\pi$
$600$		0			0
$601$	6.63755	+	11.4966i	0.270751	+	0.468955i	0.969054	−	0.246847i	$-0.0793946\pi$
$601$	6.63755	+	11.4966i	0.270751	+	0.468955i	−0.698303	+	0.715802i	$0.746061\pi$
$602$		0			0
$603$		−	62.2460i		−	2.53485i
$604$		0			0
$605$	38.4536	+	22.2012i	1.56336	+	0.902608i
$606$		0			0
$607$	−8.45702	+	14.6480i	−0.343260	+	0.594544i	−0.985036	−	0.172348i	$-0.944865\pi$
$607$	−8.45702	+	14.6480i	−0.343260	+	0.594544i	0.641776	+	0.766892i	$0.278198\pi$
$608$		0			0
$609$	−10.2972	+	5.94508i	−0.417263	+	0.240907i
$610$		0			0
$611$	−12.3986	+	15.7393i	−0.501593	+	0.636743i
$612$		0			0
$613$	16.8024	−	9.70084i	0.678641	−	0.391813i	−0.120702	−	0.992689i	$-0.538515\pi$
$613$	16.8024	−	9.70084i	0.678641	−	0.391813i	0.799343	+	0.600875i	$0.205181\pi$
$614$		0			0
$615$	14.9382	−	25.8737i	0.602365	−	1.04333i
$616$		0			0
$617$	−13.4303	−	7.75400i	−0.540685	−	0.312164i	0.204672	−	0.978831i	$-0.434387\pi$
$617$	−13.4303	−	7.75400i	−0.540685	−	0.312164i	−0.745356	+	0.666666i	$0.767721\pi$
$618$		0			0
$619$		−	21.0676i		−	0.846779i	−0.905948	−	0.423389i	$-0.860840\pi$
$619$		−	21.0676i		−	0.846779i	0.905948	−	0.423389i	$-0.139160\pi$
$620$		0			0
$621$	−11.6120	−	20.1126i	−0.465974	−	0.807091i
$622$		0			0
$623$	8.32853			0.333676
$624$		0			0
$625$	−26.0011			−1.04004
$626$		0			0
$627$	−42.5241	−	73.6539i	−1.69825	−	2.94145i
$628$		0			0
$629$			35.0190i			1.39630i
$630$		0			0
$631$	−30.4409	−	17.5750i	−1.21183	−	0.699651i	−0.248674	−	0.968587i	$-0.579995\pi$
$631$	−30.4409	−	17.5750i	−1.21183	−	0.699651i	−0.963158	+	0.268936i	$0.913328\pi$
$632$		0			0
$633$	3.15647	−	5.46716i	0.125458	−	0.217300i
$634$		0			0
$635$	−6.30319	+	3.63915i	−0.250134	+	0.144415i
$636$		0			0
$637$	0.516077	−	3.56843i	0.0204477	−	0.141386i
$638$		0			0
$639$	−73.4831	+	42.4255i	−2.90695	+	1.67833i
$640$		0			0
$641$	8.16151	−	14.1362i	0.322360	−	0.558345i	−0.658614	−	0.752481i	$-0.728857\pi$
$641$	8.16151	−	14.1362i	0.322360	−	0.558345i	0.980975	+	0.194136i	$0.0621904\pi$
$642$		0			0
$643$	−20.3656	−	11.7581i	−0.803142	−	0.463694i	0.0414269	−	0.999142i	$-0.486810\pi$
$643$	−20.3656	−	11.7581i	−0.803142	−	0.463694i	−0.844569	+	0.535447i	$0.820143\pi$
$644$		0			0
$645$		−	58.8605i		−	2.31763i
$646$		0			0
$647$	−1.56502	−	2.71069i	−0.0615271	−	0.106568i	0.833621	−	0.552337i	$-0.186264\pi$
$647$	−1.56502	−	2.71069i	−0.0615271	−	0.106568i	−0.895148	+	0.445769i	$0.852930\pi$
$648$		0			0
$649$	−82.2724			−3.22948
$650$		0			0
$651$	2.15927			0.0846286
$652$		0			0
$653$	−9.95585	−	17.2440i	−0.389603	−	0.674811i	0.602794	−	0.797897i	$-0.294054\pi$
$653$	−9.95585	−	17.2440i	−0.389603	−	0.674811i	−0.992396	+	0.123086i	$0.960721\pi$
$654$		0			0
$655$			14.2752i			0.557779i
$656$		0			0
$657$	29.5176	+	17.0420i	1.15159	+	0.664871i
$658$		0			0
$659$	0.655393	−	1.13517i	0.0255305	−	0.0442201i	−0.852978	−	0.521947i	$-0.825206\pi$
$659$	0.655393	−	1.13517i	0.0255305	−	0.0442201i	0.878508	+	0.477727i	$0.158539\pi$
$660$		0			0
$661$	3.39402	−	1.95954i	0.132012	−	0.0762172i	−0.432540	−	0.901615i	$-0.642382\pi$
$661$	3.39402	−	1.95954i	0.132012	−	0.0762172i	0.564552	+	0.825398i	$0.309049\pi$
$662$		0			0
$663$	−49.7613	−	39.1994i	−1.93257	−	1.52238i
$664$		0			0
$665$	9.72250	−	5.61329i	0.377022	−	0.217674i
$666$		0			0
$667$	3.68622	−	6.38472i	0.142731	−	0.247217i
$668$		0			0
$669$	−0.276157	−	0.159439i	−0.0106768	−	0.00616428i
$670$		0			0
$671$			40.9353i			1.58029i
$672$		0			0
$673$	1.68733	+	2.92254i	0.0650418	+	0.112656i	0.896713	−	0.442613i	$-0.145949\pi$
$673$	1.68733	+	2.92254i	0.0650418	+	0.112656i	−0.831671	+	0.555269i	$0.812615\pi$
$674$		0			0
$675$	2.49798			0.0961474
$676$		0			0
$677$	−22.9100			−0.880504			−0.440252	−	0.897874i	$-0.645111\pi$
$677$	−22.9100			−0.880504			−0.440252	+	0.897874i	$0.645111\pi$
$678$		0			0
$679$	−2.06833	−	3.58245i	−0.0793752	−	0.137482i
$680$		0			0
$681$			16.4337i			0.629741i
$682$		0			0
$683$	28.3581	+	16.3725i	1.08509	+	0.626478i	0.932266	−	0.361775i	$-0.117829\pi$
$683$	28.3581	+	16.3725i	1.08509	+	0.626478i	0.152827	+	0.988253i	$0.451162\pi$
$684$		0			0
$685$	14.0159	−	24.2762i	0.535518	−	0.927545i
$686$		0			0
$687$	−58.1954	+	33.5991i	−2.22029	+	1.28189i
$688$		0			0
$689$	−17.1819	−	13.5351i	−0.654580	−	0.515645i
$690$		0			0
$691$	30.8378	−	17.8042i	1.17313	−	0.677305i	0.218712	−	0.975789i	$-0.429815\pi$
$691$	30.8378	−	17.8042i	1.17313	−	0.677305i	0.954414	+	0.298485i	$0.0964812\pi$
$692$		0			0
$693$	−18.8069	+	32.5745i	−0.714416	+	1.23740i
$694$		0			0
$695$	−31.5750	−	18.2298i	−1.19771	−	0.691497i
$696$		0			0
$697$			23.4302i			0.887484i
$698$		0			0
$699$	38.1161	+	66.0191i	1.44168	+	2.49707i
$700$		0			0
$701$	40.6474			1.53523			0.767616	−	0.640910i	$-0.221443\pi$
$701$	40.6474			1.53523			0.767616	+	0.640910i	$0.221443\pi$
$702$		0			0
$703$	−30.7177			−1.15854
$704$		0			0
$705$	19.8679	+	34.4122i	0.748269	+	1.29604i
$706$		0			0
$707$		−	3.57669i		−	0.134515i
$708$		0			0
$709$	31.4372	+	18.1503i	1.18065	+	0.681647i	0.956164	−	0.292831i	$-0.0945972\pi$
$709$	31.4372	+	18.1503i	1.18065	+	0.681647i	0.224484	+	0.974478i	$0.427931\pi$
$710$		0			0
$711$	23.5220	−	40.7414i	0.882146	−	1.52792i
$712$		0			0
$713$	−1.15948	+	0.669424i	−0.0434227	+	0.0250701i
$714$		0			0
$715$	−6.50009	+	44.9450i	−0.243090	+	1.68085i
$716$		0			0
$717$	−29.2899	+	16.9105i	−1.09385	+	0.631536i
$718$		0			0
$719$	−4.81863	+	8.34611i	−0.179705	+	0.311257i	−0.941779	−	0.336232i	$-0.890848\pi$
$719$	−4.81863	+	8.34611i	−0.179705	+	0.311257i	0.762075	+	0.647489i	$0.224181\pi$
$720$		0			0
$721$	12.4025	+	7.16058i	0.461893	+	0.266674i
$722$		0			0
$723$			44.5572i			1.65710i
$724$		0			0
$725$	0.396490	+	0.686741i	0.0147253	+	0.0255049i
$726$		0			0
$727$	−44.8859			−1.66473			−0.832363	−	0.554231i	$-0.813012\pi$
$727$	−44.8859			−1.66473			−0.832363	+	0.554231i	$0.813012\pi$
$728$		0			0
$729$	3.55684			0.131735
$730$		0			0
$731$	23.0804	+	39.9764i	0.853660	+	1.47858i
$732$		0			0
$733$			10.4486i			0.385928i	0.981206	+	0.192964i	$0.0618101\pi$
$733$			10.4486i			0.385928i	−0.981206	+	0.192964i	$0.938190\pi$
$734$		0			0
$735$	−6.19254	−	3.57527i	−0.228415	−	0.131876i
$736$		0			0
$737$	25.1995	−	43.6469i	0.928237	−	1.60775i
$738$		0			0
$739$	25.7001	−	14.8379i	0.945393	−	0.545823i	0.0537459	−	0.998555i	$-0.482884\pi$
$739$	25.7001	−	14.8379i	0.945393	−	0.545823i	0.891647	+	0.452732i	$0.149551\pi$
$740$		0			0
$741$	34.3846	−	43.6492i	1.26315	−	1.60349i
$742$		0			0
$743$	−25.0641	+	14.4708i	−0.919513	+	0.530881i	−0.883480	−	0.468469i	$-0.844806\pi$
$743$	−25.0641	+	14.4708i	−0.919513	+	0.530881i	−0.0360335	+	0.999351i	$0.511472\pi$
$744$		0			0
$745$	−14.6902	+	25.4441i	−0.538207	+	0.932201i
$746$		0			0
$747$	−93.6159	−	54.0492i	−3.42523	−	1.97756i
$748$		0			0
$749$			3.37821i			0.123437i
$750$		0			0
$751$	7.05213	+	12.2147i	0.257336	+	0.445719i	0.965527	−	0.260301i	$-0.0838219\pi$
$751$	7.05213	+	12.2147i	0.257336	+	0.445719i	−0.708191	+	0.706021i	$0.750489\pi$
$752$		0			0
$753$	85.8871			3.12990
$754$		0			0
$755$	47.5149			1.72924
$756$		0			0
$757$	1.00814	+	1.74616i	0.0366416	+	0.0634652i	0.883765	−	0.467932i	$-0.155001\pi$
$757$	1.00814	+	1.74616i	0.0366416	+	0.0634652i	−0.847123	+	0.531397i	$0.821667\pi$
$758$		0			0
$759$		−	33.5876i		−	1.21915i
$760$		0			0
$761$	0.0420235	+	0.0242623i	0.00152335	+	0.000879506i	0.500761	−	0.865585i	$-0.333053\pi$
$761$	0.0420235	+	0.0242623i	0.00152335	+	0.000879506i	−0.499238	+	0.866465i	$0.666387\pi$
$762$		0			0
$763$	2.23979	−	3.87943i	0.0810858	−	0.140445i
$764$		0			0
$765$	−75.5460	+	43.6165i	−2.73137	+	1.57696i
$766$		0			0
$767$	−19.9364	−	49.9184i	−0.719861	−	1.80245i
$768$		0			0
$769$	−19.3050	+	11.1458i	−0.696156	+	0.401926i	−0.805914	−	0.592032i	$-0.798326\pi$
$769$	−19.3050	+	11.1458i	−0.696156	+	0.401926i	0.109758	+	0.993958i	$0.464992\pi$
$770$		0			0
$771$	−35.5006	+	61.4889i	−1.27852	+	2.21447i
$772$		0			0
$773$	−15.9029	−	9.18155i	−0.571988	−	0.330237i	0.185955	−	0.982558i	$-0.440462\pi$
$773$	−15.9029	−	9.18155i	−0.571988	−	0.330237i	−0.757943	+	0.652321i	$0.773795\pi$
$774$		0			0
$775$		−	0.144007i		−	0.00517287i
$776$		0			0
$777$	9.78248	+	16.9438i	0.350945	+	0.607854i
$778$		0			0
$779$	−20.5523			−0.736364
$780$		0			0
$781$	−68.7018			−2.45834
$782$		0			0
$783$	22.6854	+	39.2922i	0.810708	+	1.40419i
$784$		0			0
$785$			19.9188i			0.710932i
$786$		0			0
$787$	−28.7354	−	16.5904i	−1.02430	−	0.591383i	−0.108957	−	0.994046i	$-0.534751\pi$
$787$	−28.7354	−	16.5904i	−1.02430	−	0.591383i	−0.915348	+	0.402664i	$0.868084\pi$
$788$		0			0
$789$	−35.8004	+	62.0080i	−1.27453	+	2.20754i
$790$		0			0
$791$	2.15960	−	1.24684i	0.0767864	−	0.0443327i
$792$		0			0
$793$	−24.8373	+	9.91950i	−0.881998	+	0.352252i
$794$		0			0
$795$	−37.5665	+	21.6890i	−1.33235	+	0.769231i
$796$		0			0
$797$	−14.5892	+	25.2693i	−0.516777	+	0.895085i	0.483033	+	0.875602i	$0.339535\pi$
$797$	−14.5892	+	25.2693i	−0.516777	+	0.895085i	−0.999810	+	0.0194825i	$0.993798\pi$
$798$		0			0
$799$	−26.9875	−	15.5812i	−0.954748	−	0.551224i
$800$		0			0
$801$		−	56.7658i		−	2.00572i
$802$		0			0
$803$	13.7985	+	23.8997i	0.486938	+	0.843401i
$804$		0			0
$805$	4.43365			0.156266
$806$		0			0
$807$	30.1665			1.06191
$808$		0			0
$809$	8.08358	+	14.0012i	0.284204	+	0.492255i	0.972416	−	0.233255i	$-0.0749375\pi$
$809$	8.08358	+	14.0012i	0.284204	+	0.492255i	−0.688212	+	0.725509i	$0.741604\pi$
$810$		0			0
$811$			3.45855i			0.121446i	0.998155	+	0.0607230i	$0.0193406\pi$
$811$			3.45855i			0.121446i	−0.998155	+	0.0607230i	$0.980659\pi$
$812$		0			0
$813$	42.4070	+	24.4837i	1.48728	+	0.858681i
$814$		0			0
$815$	11.3132	−	19.5950i	0.396283	−	0.686382i
$816$		0			0
$817$	−35.0662	+	20.2455i	−1.22681	+	0.708300i
$818$		0			0
$819$	−24.3217	−	3.51749i	−0.849871	−	0.122911i
$820$		0			0
$821$	−5.78541	+	3.34021i	−0.201912	+	0.116574i	−0.597547	−	0.801834i	$-0.703858\pi$
$821$	−5.78541	+	3.34021i	−0.201912	+	0.116574i	0.395635	+	0.918408i	$0.370525\pi$
$822$		0			0
$823$	−5.43236	+	9.40912i	−0.189360	+	0.327981i	−0.945037	−	0.326963i	$-0.893975\pi$
$823$	−5.43236	+	9.40912i	−0.189360	+	0.327981i	0.755677	+	0.654945i	$0.227308\pi$
$824$		0			0
$825$	3.12868	+	1.80635i	0.108927	+	0.0628889i
$826$		0			0
$827$		−	48.6460i		−	1.69159i	−0.533512	−	0.845793i	$-0.679128\pi$
$827$		−	48.6460i		−	1.69159i	0.533512	−	0.845793i	$-0.320872\pi$
$828$		0			0
$829$	3.45723	+	5.98809i	0.120074	+	0.207975i	0.919797	−	0.392395i	$-0.128353\pi$
$829$	3.45723	+	5.98809i	0.120074	+	0.207975i	−0.799722	+	0.600370i	$0.795020\pi$
$830$		0			0
$831$	13.1042			0.454581
$832$		0			0
$833$	5.60774			0.194297
$834$		0			0
$835$	−10.9743	−	19.0081i	−0.379783	−	0.657803i
$836$		0			0
$837$		−	8.23940i		−	0.284795i
$838$		0			0
$839$	−19.7284	−	11.3902i	−0.681101	−	0.393234i	0.119169	−	0.992874i	$-0.461977\pi$
$839$	−19.7284	−	11.3902i	−0.681101	−	0.393234i	−0.800270	+	0.599640i	$0.795310\pi$
$840$		0			0
$841$	7.29857	−	12.6415i	0.251675	−	0.435913i
$842$		0			0
$843$	−13.9224	+	8.03812i	−0.479514	+	0.276848i
$844$		0			0
$845$	−28.8452	+	6.94724i	−0.992307	+	0.238992i
$846$		0			0
$847$	−16.8485	+	9.72751i	−0.578923	+	0.334241i
$848$		0			0
$849$	9.76061	−	16.9059i	0.334983	−	0.580208i
$850$		0			0
$851$	−10.5059	−	6.06558i	−0.360138	−	0.207926i
$852$		0			0
$853$			11.9607i			0.409527i	0.978811	+	0.204764i	$0.0656426\pi$
$853$			11.9607i			0.409527i	−0.978811	+	0.204764i	$0.934357\pi$
$854$		0			0
$855$	−38.2592	−	66.2668i	−1.30844	−	2.26628i
$856$		0			0
$857$	10.3815			0.354627			0.177313	−	0.984154i	$-0.443259\pi$
$857$	10.3815			0.354627			0.177313	+	0.984154i	$0.443259\pi$
$858$		0			0
$859$	−10.0436			−0.342683			−0.171341	−	0.985212i	$-0.554810\pi$
$859$	−10.0436			−0.342683			−0.171341	+	0.985212i	$0.554810\pi$
$860$		0			0
$861$	6.54519	+	11.3366i	0.223060	+	0.386351i
$862$		0			0
$863$			30.1151i			1.02513i	0.858648	+	0.512565i	$0.171305\pi$
$863$			30.1151i			1.02513i	−0.858648	+	0.512565i	$0.828695\pi$
$864$		0			0
$865$	6.37532	+	3.68079i	0.216767	+	0.125151i
$866$		0			0
$867$	22.6309	−	39.1979i	0.768587	−	1.33123i
$868$		0			0
$869$	32.9873	−	19.0452i	1.11902	−	0.646066i
$870$		0			0
$871$	32.5889	+	4.71311i	1.10423	+	0.159698i
$872$		0			0
$873$	−24.4173	+	14.0974i	−0.826402	+	0.477123i
$874$		0			0
$875$	5.46734	−	9.46971i	0.184830	−	0.320135i
$876$		0			0
$877$	−41.0471	−	23.6986i	−1.38606	−	0.800244i	−0.393194	−	0.919456i	$-0.628630\pi$
$877$	−41.0471	−	23.6986i	−1.38606	−	0.800244i	−0.992869	+	0.119212i	$0.961963\pi$
$878$		0			0
$879$			22.0268i			0.742945i
$880$		0			0
$881$	−14.0650	−	24.3614i	−0.473863	−	0.820755i	0.525689	−	0.850677i	$-0.323808\pi$
$881$	−14.0650	−	24.3614i	−0.473863	−	0.820755i	−0.999552	+	0.0299215i	$0.990474\pi$
$882$		0			0
$883$	9.73484			0.327604			0.163802	−	0.986493i	$-0.447624\pi$
$883$	9.73484			0.327604			0.163802	+	0.986493i	$0.447624\pi$
$884$		0			0
$885$	−106.601			−3.58337
$886$		0			0
$887$	8.88854	+	15.3954i	0.298448	+	0.516927i	0.975781	−	0.218749i	$-0.0701977\pi$
$887$	8.88854	+	15.3954i	0.298448	+	0.516927i	−0.677333	+	0.735676i	$0.736864\pi$
$888$		0			0
$889$		−	3.18900i		−	0.106956i
$890$		0			0
$891$	81.2853	+	46.9301i	2.72316	+	1.57222i
$892$		0			0
$893$	13.6674	−	23.6726i	0.457362	−	0.792175i
$894$		0			0
$895$	31.2551	−	18.0451i	1.04474	−	0.603182i
$896$		0			0
$897$	20.3791	−	8.13901i	0.680439	−	0.271754i
$898$		0			0
$899$	2.26516	−	1.30779i	0.0755474	−	0.0436173i
$900$		0			0
$901$	17.0094	−	29.4612i	0.566666	−	0.981494i
$902$		0			0
$903$	22.3347	+	12.8949i	0.743252	+	0.429116i
$904$		0			0
$905$		−	53.4618i		−	1.77713i
$906$		0			0
$907$	18.8071	+	32.5748i	0.624478	+	1.08163i	0.988642	+	0.150293i	$0.0480217\pi$
$907$	18.8071	+	32.5748i	0.624478	+	1.08163i	−0.364163	+	0.931335i	$0.618645\pi$
$908$		0			0
$909$	−24.3781			−0.808569
$910$		0			0
$911$	−55.1136			−1.82599			−0.912997	−	0.407966i	$-0.866238\pi$
$911$	−55.1136			−1.82599			−0.912997	+	0.407966i	$0.866238\pi$
$912$		0			0
$913$	−43.7623	−	75.7986i	−1.44832	−	2.50857i
$914$		0			0
$915$			53.0404i			1.75346i
$916$		0			0
$917$	−5.41675	−	3.12736i	−0.178877	−	0.103275i
$918$		0			0
$919$	−10.3413	+	17.9117i	−0.341129	+	0.590853i	−0.984643	−	0.174582i	$-0.944143\pi$
$919$	−10.3413	+	17.9117i	−0.341129	+	0.590853i	0.643514	+	0.765435i	$0.277476\pi$
$920$		0			0
$921$	−18.5555	+	10.7130i	−0.611426	+	0.353007i
$922$		0			0
$923$	−16.6479	−	41.6845i	−0.547973	−	1.37206i
$924$		0			0
$925$	1.13002	−	0.652415i	0.0371547	−	0.0214513i
$926$		0			0
$927$	48.8052	−	84.5331i	1.60297	−	2.77643i
$928$		0			0
$929$	25.5240	+	14.7363i	0.837415	+	0.483482i	0.856385	−	0.516338i	$-0.172705\pi$
$929$	25.5240	+	14.7363i	0.837415	+	0.483482i	−0.0189695	+	0.999820i	$0.506039\pi$
$930$		0			0
$931$			4.91895i			0.161212i
$932$		0			0
$933$	−22.7425	−	39.3912i	−0.744557	−	1.28961i
$934$		0			0
$935$	−70.6305			−2.30986
$936$		0			0
$937$	46.0479			1.50432			0.752160	−	0.658980i	$-0.229012\pi$
$937$	46.0479			1.50432			0.752160	+	0.658980i	$0.229012\pi$
$938$		0			0
$939$	48.2642	+	83.5960i	1.57504	+	2.72805i
$940$		0			0
$941$			11.1787i			0.364414i	0.983260	+	0.182207i	$0.0583241\pi$
$941$			11.1787i			0.364414i	−0.983260	+	0.182207i	$0.941676\pi$
$942$		0			0
$943$	−7.02921	−	4.05832i	−0.228903	−	0.132157i
$944$		0			0
$945$	−13.6426	+	23.6296i	−0.443793	+	0.768672i
$946$		0			0
$947$	−15.3118	+	8.84027i	−0.497567	+	0.287270i	−0.727708	−	0.685887i	$-0.759414\pi$
$947$	−15.3118	+	8.84027i	−0.497567	+	0.287270i	0.230142	+	0.973157i	$0.426081\pi$
$948$		0			0
$949$	−11.1573	+	14.1636i	−0.362182	+	0.459769i
$950$		0			0
$951$	18.4023	−	10.6246i	0.596736	−	0.344525i
$952$		0			0
$953$	7.74718	−	13.4185i	0.250956	−	0.434668i	−0.712833	−	0.701333i	$-0.752588\pi$
$953$	7.74718	−	13.4185i	0.250956	−	0.434668i	0.963789	+	0.266665i	$0.0859218\pi$
$954$		0			0
$955$	46.9369	+	27.0990i	1.51884	+	0.876903i
$956$		0			0
$957$			65.6171i			2.12110i
$958$		0			0
$959$	6.14108	+	10.6367i	0.198306	+	0.343476i
$960$		0			0
$961$	30.5250			0.984678
$962$		0			0
$963$	23.0253			0.741980
$964$		0			0
$965$	−17.7539	−	30.7506i	−0.571518	−	0.989898i
$966$		0			0
$967$		−	10.9723i		−	0.352847i	−0.984314	−	0.176423i	$-0.943547\pi$
$967$		−	10.9723i		−	0.352847i	0.984314	−	0.176423i	$-0.0564528\pi$
$968$		0			0
$969$	74.8434	+	43.2109i	2.40432	+	1.38813i
$970$		0			0
$971$	−26.9868	+	46.7425i	−0.866048	+	1.50004i	−4.43892e−5		1.00000i	$0.500014\pi$
$971$	−26.9868	+	46.7425i	−0.866048	+	1.50004i	−0.866003	+	0.500038i	$0.833319\pi$
$972$		0			0
$973$	13.8347	−	7.98744i	0.443519	−	0.256066i
$974$		0			0
$975$	−0.337844	+	2.33603i	−0.0108197	+	0.0748128i
$976$		0			0
$977$	51.6726	−	29.8332i	1.65315	−	0.954448i	0.677387	−	0.735627i	$-0.263112\pi$
$977$	51.6726	−	29.8332i	1.65315	−	0.954448i	0.975765	−	0.218820i	$-0.0702209\pi$
$978$		0			0
$979$	22.9809	−	39.8042i	0.734474	−	1.27215i
$980$		0			0
$981$	−26.4415	−	15.2660i	−0.844212	−	0.487406i
$982$		0			0
$983$		−	21.2863i		−	0.678926i	−0.940619	−	0.339463i	$-0.889755\pi$
$983$		−	21.2863i		−	0.678926i	0.940619	−	0.339463i	$-0.110245\pi$
$984$		0			0
$985$	18.2501	+	31.6101i	0.581497	+	1.00718i
$986$		0			0
$987$	−17.4103			−0.554177
$988$		0			0
$989$	−15.9909			−0.508481
$990$		0			0
$991$	−1.48951	−	2.57991i	−0.0473160	−	0.0819537i	0.841397	−	0.540417i	$-0.181733\pi$
$991$	−1.48951	−	2.57991i	−0.0473160	−	0.0819537i	−0.888713	+	0.458463i	$0.848400\pi$
$992$		0			0
$993$			12.7907i			0.405900i
$994$		0			0
$995$	−19.4915	−	11.2534i	−0.617923	−	0.356758i
$996$		0			0
$997$	1.10898	−	1.92081i	0.0351217	−	0.0608326i	−0.847930	−	0.530108i	$-0.822151\pi$
$997$	1.10898	−	1.92081i	0.0351217	−	0.0608326i	0.883052	+	0.469275i	$0.155485\pi$
$998$		0			0
$999$	64.6543	−	37.3282i	2.04557	−	1.18101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.g.673.12		24
4.3	odd	2		728.2.bm.c.673.1	yes	24
13.4	even	6	inner	1456.2.cc.g.225.12		24
52.11	even	12		9464.2.a.bl.1.12		12
52.15	even	12		9464.2.a.bm.1.12		12
52.43	odd	6		728.2.bm.c.225.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.1	✓	24	52.43	odd	6
728.2.bm.c.673.1	yes	24	4.3	odd	2
1456.2.cc.g.225.12		24	13.4	even	6	inner
1456.2.cc.g.673.12		24	1.1	even	1	trivial
9464.2.a.bl.1.12		12	52.11	even	12
9464.2.a.bm.1.12		12	52.15	even	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.56651 + 2.71328i) q^{3} +2.28231i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-3.40791 + 5.90267i) q^{9} +(-4.77925 + 2.75930i) q^{11} +(-2.83231 - 2.23115i) q^{13} +(-6.19254 + 3.57527i) q^{15} +(2.80387 - 4.85644i) q^{17} +(4.25993 + 2.45947i) q^{19} -3.13302i q^{21} +(0.971308 + 1.68235i) q^{23} -0.208948 q^{25} -11.9550 q^{27} +(-1.89756 - 3.28666i) q^{29} +0.689198i q^{31} +(-14.9735 - 8.64496i) q^{33} +(1.14116 - 1.97654i) q^{35} +(-5.40812 + 3.12238i) q^{37} +(1.61688 - 11.1800i) q^{39} +(-3.61843 + 2.08910i) q^{41} +(-4.11581 + 7.12880i) q^{43} +(-13.4717 - 7.77791i) q^{45} -5.55704i q^{47} +(0.500000 + 0.866025i) q^{49} +17.5692 q^{51} +6.06641 q^{53} +(-6.29759 - 10.9077i) q^{55} +15.4112i q^{57} +(12.9109 + 7.45409i) q^{59} +(3.70884 - 6.42391i) q^{61} +(5.90267 - 3.40791i) q^{63} +(5.09218 - 6.46421i) q^{65} +(-7.90904 + 4.56629i) q^{67} +(-3.04313 + 5.27085i) q^{69} +(10.7813 + 6.22456i) q^{71} -5.00071i q^{73} +(-0.327319 - 0.566933i) q^{75} +5.51861 q^{77} -6.90219 q^{79} +(-8.50397 - 14.7293i) q^{81} +15.8599i q^{83} +(11.0839 + 6.39930i) q^{85} +(5.94508 - 10.2972i) q^{87} +(-7.21272 + 4.16427i) q^{89} +(1.33728 + 3.34839i) q^{91} +(-1.86999 + 1.07964i) q^{93} +(-5.61329 + 9.72250i) q^{95} +(3.58245 + 2.06833i) q^{97} -37.6138i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) \) 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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