LMFDB - Embedded newform 448.2.ba.c.81.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(81,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			81.11
Character	$\chi$	$=$	448.81
Dual form			448.2.ba.c.177.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.46036 - 0.659252i) q^{3} +(1.87532 + 0.502490i) q^{5} +(-0.364450 - 2.62053i) q^{7} +(3.02070 - 1.74400i) q^{9} +(1.37168 + 5.11917i) q^{11} +(-3.61173 - 3.61173i) q^{13} +4.94523 q^{15} +(-0.294815 + 0.510634i) q^{17} +(0.137946 - 0.514822i) q^{19} +(-2.62427 - 6.20719i) q^{21} +(-0.378033 + 0.218258i) q^{23} +(-1.06581 - 0.615344i) q^{25} +(0.878939 - 0.878939i) q^{27} +(2.68976 + 2.68976i) q^{29} +(-3.94118 + 6.82633i) q^{31} +(6.74965 + 11.6907i) q^{33} +(0.633329 - 5.09746i) q^{35} +(-2.90863 - 0.779365i) q^{37} +(-11.2672 - 6.50513i) q^{39} +2.95135i q^{41} +(7.67329 - 7.67329i) q^{43} +(6.54110 - 1.75268i) q^{45} +(-2.01771 - 3.49478i) q^{47} +(-6.73435 + 1.91011i) q^{49} +(-0.388715 + 1.45070i) q^{51} +(0.244374 + 0.912017i) q^{53} +10.2893i q^{55} -1.35759i q^{57} +(-0.00753382 - 0.0281166i) q^{59} +(0.529990 - 1.97795i) q^{61} +(-5.67110 - 7.28022i) q^{63} +(-4.95829 - 8.58801i) q^{65} +(6.24795 - 1.67413i) q^{67} +(-0.786212 + 0.786212i) q^{69} +2.05630i q^{71} +(6.85664 + 3.95868i) q^{73} +(-3.02794 - 0.811334i) q^{75} +(12.9150 - 5.46021i) q^{77} +(6.53028 + 11.3108i) q^{79} +(-3.64893 + 6.32013i) q^{81} +(-10.1551 - 10.1551i) q^{83} +(-0.809460 + 0.809460i) q^{85} +(8.39101 + 4.84455i) q^{87} +(-3.35262 + 1.93564i) q^{89} +(-8.14836 + 10.7810i) q^{91} +(-5.19647 + 19.3935i) q^{93} +(0.517385 - 0.896137i) q^{95} -12.0556 q^{97} +(13.0712 + 13.0712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.46036	−	0.659252i	1.42049	−	0.380619i	0.534833	−	0.844958i	$-0.320374\pi$
$3$	2.46036	−	0.659252i	1.42049	−	0.380619i	0.885658	+	0.464338i	$0.153708\pi$
$4$		0			0
$5$	1.87532	+	0.502490i	0.838668	+	0.224720i	0.652491	−	0.757796i	$-0.273724\pi$
$5$	1.87532	+	0.502490i	0.838668	+	0.224720i	0.186176	+	0.982516i	$0.440391\pi$
$6$		0			0
$7$	−0.364450	−	2.62053i	−0.137749	−	0.990467i
$7$	−0.364450	−	2.62053i	−0.137749	−	0.990467i
$8$		0			0
$9$	3.02070	−	1.74400i	1.00690	−	0.581333i
$10$		0			0
$11$	1.37168	+	5.11917i	0.413576	+	1.54349i	0.787670	+	0.616097i	$0.211287\pi$
$11$	1.37168	+	5.11917i	0.413576	+	1.54349i	−0.374094	+	0.927391i	$0.622046\pi$
$12$		0			0
$13$	−3.61173	−	3.61173i	−1.00171	−	1.00171i	−0.999999	−	0.00171617i	$-0.999454\pi$
$13$	−3.61173	−	3.61173i	−1.00171	−	1.00171i	−0.00171617	−	0.999999i	$-0.500546\pi$
$14$		0			0
$15$	4.94523			1.27685
$16$		0			0
$17$	−0.294815	+	0.510634i	−0.0715031	+	0.123847i	−0.899560	−	0.436797i	$-0.856113\pi$
$17$	−0.294815	+	0.510634i	−0.0715031	+	0.123847i	0.828057	+	0.560644i	$0.189446\pi$
$18$		0			0
$19$	0.137946	−	0.514822i	0.0316470	−	0.118108i	−0.948295	−	0.317389i	$-0.897194\pi$
$19$	0.137946	−	0.514822i	0.0316470	−	0.118108i	0.979942	+	0.199281i	$0.0638606\pi$
$20$		0			0
$21$	−2.62427	−	6.20719i	−0.572663	−	1.35452i
$22$		0			0
$23$	−0.378033	+	0.218258i	−0.0788254	+	0.0455098i	−0.538895	−	0.842373i	$-0.681158\pi$
$23$	−0.378033	+	0.218258i	−0.0788254	+	0.0455098i	0.460069	+	0.887883i	$0.347825\pi$
$24$		0			0
$25$	−1.06581	−	0.615344i	−0.213161	−	0.123069i
$26$		0			0
$27$	0.878939	−	0.878939i	0.169152	−	0.169152i
$28$		0			0
$29$	2.68976	+	2.68976i	0.499476	+	0.499476i	0.911275	−	0.411799i	$-0.135099\pi$
$29$	2.68976	+	2.68976i	0.499476	+	0.499476i	−0.411799	+	0.911275i	$0.635099\pi$
$30$		0			0
$31$	−3.94118	+	6.82633i	−0.707857	+	1.22605i	0.257793	+	0.966200i	$0.417005\pi$
$31$	−3.94118	+	6.82633i	−0.707857	+	1.22605i	−0.965650	+	0.259845i	$0.916329\pi$
$32$		0			0
$33$	6.74965	+	11.6907i	1.17496	+	2.03510i
$34$		0			0
$35$	0.633329	−	5.09746i	0.107052	−	0.861628i
$36$		0			0
$37$	−2.90863	−	0.779365i	−0.478176	−	0.128127i	0.0116774	−	0.999932i	$-0.496283\pi$
$37$	−2.90863	−	0.779365i	−0.478176	−	0.128127i	−0.489853	+	0.871805i	$0.662950\pi$
$38$		0			0
$39$	−11.2672	−	6.50513i	−1.80420	−	1.04165i
$40$		0			0
$41$			2.95135i			0.460923i	0.973081	+	0.230461i	$0.0740235\pi$
$41$			2.95135i			0.460923i	−0.973081	+	0.230461i	$0.925976\pi$
$42$		0			0
$43$	7.67329	−	7.67329i	1.17017	−	1.17017i	0.187996	−	0.982170i	$-0.439801\pi$
$43$	7.67329	−	7.67329i	1.17017	−	1.17017i	0.982170	−	0.187996i	$-0.0601993\pi$
$44$		0			0
$45$	6.54110	−	1.75268i	0.975090	−	0.261275i
$46$		0			0
$47$	−2.01771	−	3.49478i	−0.294314	−	0.509766i	0.680511	−	0.732738i	$-0.261758\pi$
$47$	−2.01771	−	3.49478i	−0.294314	−	0.509766i	−0.974825	+	0.222971i	$0.928424\pi$
$48$		0			0
$49$	−6.73435	+	1.91011i	−0.962050	+	0.272872i
$50$		0			0
$51$	−0.388715	+	1.45070i	−0.0544310	+	0.203139i
$52$		0			0
$53$	0.244374	+	0.912017i	0.0335674	+	0.125275i	0.980676	−	0.195637i	$-0.0626773\pi$
$53$	0.244374	+	0.912017i	0.0335674	+	0.125275i	−0.947109	+	0.320912i	$0.896011\pi$
$54$		0			0
$55$			10.2893i			1.38741i
$56$		0			0
$57$		−	1.35759i		−	0.179817i
$58$		0			0
$59$	−0.00753382	−	0.0281166i	−0.000980820	−	0.00366047i	0.965434	−	0.260649i	$-0.0839365\pi$
$59$	−0.00753382	−	0.0281166i	−0.000980820	−	0.00366047i	−0.966415	+	0.256988i	$0.917270\pi$
$60$		0			0
$61$	0.529990	−	1.97795i	0.0678583	−	0.253251i	−0.923661	−	0.383211i	$-0.874818\pi$
$61$	0.529990	−	1.97795i	0.0678583	−	0.253251i	0.991519	+	0.129960i	$0.0414850\pi$
$62$		0			0
$63$	−5.67110	−	7.28022i	−0.714491	−	0.917222i
$64$		0			0
$65$	−4.95829	−	8.58801i	−0.615000	−	1.06521i
$66$		0			0
$67$	6.24795	−	1.67413i	0.763309	−	0.204528i	0.143895	−	0.989593i	$-0.454037\pi$
$67$	6.24795	−	1.67413i	0.763309	−	0.204528i	0.619414	+	0.785065i	$0.287370\pi$
$68$		0			0
$69$	−0.786212	+	0.786212i	−0.0946488	+	0.0946488i
$70$		0			0
$71$			2.05630i			0.244037i	0.992528	+	0.122019i	$0.0389368\pi$
$71$			2.05630i			0.244037i	−0.992528	+	0.122019i	$0.961063\pi$
$72$		0			0
$73$	6.85664	+	3.95868i	0.802509	+	0.463329i	0.844348	−	0.535796i	$-0.179988\pi$
$73$	6.85664	+	3.95868i	0.802509	+	0.463329i	−0.0418389	+	0.999124i	$0.513322\pi$
$74$		0			0
$75$	−3.02794	−	0.811334i	−0.349636	−	0.0936847i
$76$		0			0
$77$	12.9150	−	5.46021i	1.47180	−	0.622248i
$78$		0			0
$79$	6.53028	+	11.3108i	0.734714	+	1.27256i	0.954849	+	0.297092i	$0.0960169\pi$
$79$	6.53028	+	11.3108i	0.734714	+	1.27256i	−0.220135	+	0.975469i	$0.570650\pi$
$80$		0			0
$81$	−3.64893	+	6.32013i	−0.405437	+	0.702237i
$82$		0			0
$83$	−10.1551	−	10.1551i	−1.11467	−	1.11467i	−0.992510	−	0.122161i	$-0.961018\pi$
$83$	−10.1551	−	10.1551i	−1.11467	−	1.11467i	−0.122161	−	0.992510i	$-0.538982\pi$
$84$		0			0
$85$	−0.809460	+	0.809460i	−0.0877983	+	0.0877983i
$86$		0			0
$87$	8.39101	+	4.84455i	0.899611	+	0.519391i
$88$		0			0
$89$	−3.35262	+	1.93564i	−0.355377	+	0.205177i	−0.667051	−	0.745012i	$-0.732444\pi$
$89$	−3.35262	+	1.93564i	−0.355377	+	0.205177i	0.311674	+	0.950189i	$0.399110\pi$
$90$		0			0
$91$	−8.14836	+	10.7810i	−0.854180	+	1.13015i
$92$		0			0
$93$	−5.19647	+	19.3935i	−0.538849	+	2.01101i
$94$		0			0
$95$	0.517385	−	0.896137i	0.0530826	−	0.0919418i
$96$		0			0
$97$	−12.0556			−1.22406			−0.612029	−	0.790836i	$-0.709646\pi$
$97$	−12.0556			−1.22406			−0.612029	+	0.790836i	$0.709646\pi$
$98$		0			0
$99$	13.0712	+	13.0712i	1.31371	+	1.31371i
$100$		0			0
$101$	−0.694969	−	2.59366i	−0.0691520	−	0.258079i	0.922692	−	0.385539i	$-0.125984\pi$
$101$	−0.694969	−	2.59366i	−0.0691520	−	0.258079i	−0.991844	+	0.127460i	$0.959318\pi$
$102$		0			0
$103$	−0.0773103	+	0.0446351i	−0.00761761	+	0.00439803i	−0.503804	−	0.863818i	$-0.668067\pi$
$103$	−0.0773103	+	0.0446351i	−0.00761761	+	0.00439803i	0.496186	+	0.868216i	$0.334733\pi$
$104$		0			0
$105$	−1.80229	−	12.9591i	−0.175886	−	1.26468i
$106$		0			0
$107$	−14.0802	−	3.77279i	−1.36119	−	0.364729i	−0.496935	−	0.867788i	$-0.665541\pi$
$107$	−14.0802	−	3.77279i	−1.36119	−	0.364729i	−0.864252	+	0.503059i	$0.832208\pi$
$108$		0			0
$109$	−6.68404	+	1.79098i	−0.640215	+	0.171545i	−0.564301	−	0.825569i	$-0.690854\pi$
$109$	−6.68404	+	1.79098i	−0.640215	+	0.171545i	−0.0759141	+	0.997114i	$0.524187\pi$
$110$		0			0
$111$	−7.67008			−0.728012
$112$		0			0
$113$	7.51142			0.706615			0.353307	−	0.935507i	$-0.385057\pi$
$113$	7.51142			0.706615			0.353307	+	0.935507i	$0.385057\pi$
$114$		0			0
$115$	−0.818604	+	0.219344i	−0.0763353	+	0.0204540i
$116$		0			0
$117$	−17.2088	−	4.61109i	−1.59095	−	0.426295i
$118$		0			0
$119$	1.44558	+	0.586470i	0.132516	+	0.0537616i
$120$		0			0
$121$	−14.7981	+	8.54370i	−1.34528	+	0.776700i
$122$		0			0
$123$	1.94568	+	7.26138i	0.175436	+	0.654737i
$124$		0			0
$125$	−8.55366	−	8.55366i	−0.765063	−	0.765063i
$126$		0			0
$127$	−4.25202			−0.377306			−0.188653	−	0.982044i	$-0.560412\pi$
$127$	−4.25202			−0.377306			−0.188653	+	0.982044i	$0.560412\pi$
$128$		0			0
$129$	13.8204	−	23.9377i	1.21682	−	2.10760i
$130$		0			0
$131$	−1.31046	+	4.89071i	−0.114496	+	0.427304i	−0.999249	−	0.0387565i	$-0.987660\pi$
$131$	−1.31046	+	4.89071i	−0.114496	+	0.427304i	0.884753	+	0.466060i	$0.154327\pi$
$132$		0			0
$133$	−1.39938	−	0.173865i	−0.121342	−	0.0150760i
$134$		0			0
$135$	2.08995	−	1.20663i	0.179874	−	0.103850i
$136$		0			0
$137$	0.241507	+	0.139434i	0.0206333	+	0.0119127i	0.510281	−	0.860008i	$-0.329541\pi$
$137$	0.241507	+	0.139434i	0.0206333	+	0.0119127i	−0.489648	+	0.871920i	$0.662875\pi$
$138$		0			0
$139$	12.1095	−	12.1095i	1.02712	−	1.02712i	0.0274943	−	0.999622i	$-0.491247\pi$
$139$	12.1095	−	12.1095i	1.02712	−	1.02712i	0.999622	−	0.0274943i	$-0.00875280\pi$
$140$		0			0
$141$	−7.26825	−	7.26825i	−0.612097	−	0.612097i
$142$		0			0
$143$	13.5349	−	23.4432i	1.13185	−	1.96042i
$144$		0			0
$145$	3.69258	+	6.39573i	0.306652	+	0.531136i
$146$		0			0
$147$	−15.3097	+	9.13919i	−1.26272	+	0.753788i
$148$		0			0
$149$	21.1901	+	5.67786i	1.73596	+	0.465149i	0.981542	−	0.191247i	$-0.0612532\pi$
$149$	21.1901	+	5.67786i	1.73596	+	0.465149i	0.754417	+	0.656396i	$0.227920\pi$
$150$		0			0
$151$	−8.08773	−	4.66946i	−0.658170	−	0.379995i	0.133409	−	0.991061i	$-0.457408\pi$
$151$	−8.08773	−	4.66946i	−0.658170	−	0.379995i	−0.791580	+	0.611066i	$0.790741\pi$
$152$		0			0
$153$			2.05663i			0.166269i
$154$		0			0
$155$	−10.8211	+	10.8211i	−0.869174	+	0.869174i
$156$		0			0
$157$	−11.2775	+	3.02179i	−0.900040	+	0.241165i	−0.679034	−	0.734107i	$-0.737601\pi$
$157$	−11.2775	+	3.02179i	−0.900040	+	0.241165i	−0.221007	+	0.975272i	$0.570934\pi$
$158$		0			0
$159$	1.20250	+	2.08279i	0.0953643	+	0.165176i
$160$		0			0
$161$	0.709725	+	0.911103i	0.0559341	+	0.0718050i
$162$		0			0
$163$	−3.82793	+	14.2860i	−0.299826	+	1.11897i	0.637482	+	0.770466i	$0.279976\pi$
$163$	−3.82793	+	14.2860i	−0.299826	+	1.11897i	−0.937308	+	0.348502i	$0.886690\pi$
$164$		0			0
$165$	6.78326	+	25.3155i	0.528076	+	1.97081i
$166$		0			0
$167$			0.426814i			0.0330279i	0.999864	+	0.0165139i	$0.00525679\pi$
$167$			0.426814i			0.0330279i	−0.999864	+	0.0165139i	$0.994743\pi$
$168$		0			0
$169$			13.0892i			1.00686i
$170$		0			0
$171$	−0.481156	−	1.79570i	−0.0367949	−	0.137320i
$172$		0			0
$173$	1.08986	−	4.06740i	0.0828603	−	0.309239i	−0.912040	−	0.410101i	$-0.865493\pi$
$173$	1.08986	−	4.06740i	0.0828603	−	0.309239i	0.994900	+	0.100862i	$0.0321601\pi$
$174$		0			0
$175$	−1.22409	+	3.01724i	−0.0925327	+	0.228082i
$176$		0			0
$177$	−0.0370719	−	0.0642104i	−0.00278649	−	0.00482635i
$178$		0			0
$179$	13.5720	−	3.63660i	1.01442	−	0.271812i	0.286943	−	0.957948i	$-0.407361\pi$
$179$	13.5720	−	3.63660i	1.01442	−	0.271812i	0.727474	+	0.686135i	$0.240694\pi$
$180$		0			0
$181$	10.0681	−	10.0681i	0.748356	−	0.748356i	−0.225814	−	0.974170i	$-0.572504\pi$
$181$	10.0681	−	10.0681i	0.748356	−	0.748356i	0.974170	+	0.225814i	$0.0725042\pi$
$182$		0			0
$183$		−	5.21587i		−	0.385568i
$184$		0			0
$185$	−5.06298	−	2.92311i	−0.372238	−	0.214911i
$186$		0			0
$187$	−3.01842	−	0.808782i	−0.220728	−	0.0591440i
$188$		0			0
$189$	−2.62362	−	1.98296i	−0.190840	−	0.144239i
$190$		0			0
$191$	4.82250	+	8.35282i	0.348944	+	0.604389i	0.986062	−	0.166377i	$-0.0532070\pi$
$191$	4.82250	+	8.35282i	0.348944	+	0.604389i	−0.637118	+	0.770766i	$0.719874\pi$
$192$		0			0
$193$	9.77970	−	16.9389i	0.703959	−	1.21929i	−0.263108	−	0.964767i	$-0.584747\pi$
$193$	9.77970	−	16.9389i	0.703959	−	1.21929i	0.967066	−	0.254525i	$-0.0819193\pi$
$194$		0			0
$195$	−17.8609	−	17.8609i	−1.27904	−	1.27904i
$196$		0			0
$197$	−8.33252	+	8.33252i	−0.593668	+	0.593668i	−0.938620	−	0.344953i	$-0.887895\pi$
$197$	−8.33252	+	8.33252i	−0.593668	+	0.593668i	0.344953	+	0.938620i	$0.387895\pi$
$198$		0			0
$199$	2.34374	+	1.35316i	0.166144	+	0.0959230i	0.580766	−	0.814070i	$-0.302753\pi$
$199$	2.34374	+	1.35316i	0.166144	+	0.0959230i	−0.414623	+	0.909993i	$0.636086\pi$
$200$		0			0
$201$	14.2686	−	8.23795i	1.00643	−	0.581060i
$202$		0			0
$203$	6.06831	−	8.02888i	0.425912	−	0.563517i
$204$		0			0
$205$	−1.48302	+	5.53471i	−0.103579	+	0.386561i
$206$		0			0
$207$	−0.761282	+	1.31858i	−0.0529128	+	0.0916476i
$208$		0			0
$209$	2.82468			0.195387
$210$		0			0
$211$	−11.9853	−	11.9853i	−0.825100	−	0.825100i	0.161734	−	0.986834i	$-0.448291\pi$
$211$	−11.9853	−	11.9853i	−0.825100	−	0.825100i	−0.986834	+	0.161734i	$0.948291\pi$
$212$		0			0
$213$	1.35562	+	5.05923i	0.0928854	+	0.346653i
$214$		0			0
$215$	18.2456	−	10.5341i	1.24434	−	0.718420i
$216$		0			0
$217$	19.3250	+	7.84013i	1.31186	+	0.532223i
$218$		0			0
$219$	19.4796	+	5.21954i	1.31631	+	0.352704i
$220$		0			0
$221$	2.90907	−	0.779483i	0.195685	−	0.0524337i
$222$		0			0
$223$	−2.50874			−0.167998			−0.0839988	−	0.996466i	$-0.526769\pi$
$223$	−2.50874			−0.167998			−0.0839988	+	0.996466i	$0.526769\pi$
$224$		0			0
$225$	−4.29264			−0.286176
$226$		0			0
$227$	18.3064	−	4.90519i	1.21504	−	0.325569i	0.406303	−	0.913739i	$-0.366818\pi$
$227$	18.3064	−	4.90519i	1.21504	−	0.325569i	0.808738	+	0.588170i	$0.200151\pi$
$228$		0			0
$229$	25.1003	+	6.72559i	1.65867	+	0.444440i	0.962022	−	0.272972i	$-0.0880066\pi$
$229$	25.1003	+	6.72559i	1.65867	+	0.444440i	0.696650	+	0.717412i	$0.254673\pi$
$230$		0			0
$231$	28.1760	−	21.9483i	1.85385	−	1.44410i
$232$		0			0
$233$	12.2405	−	7.06704i	0.801900	−	0.462977i	−0.0422348	−	0.999108i	$-0.513448\pi$
$233$	12.2405	−	7.06704i	0.801900	−	0.462977i	0.844135	+	0.536130i	$0.180114\pi$
$234$		0			0
$235$	−2.02776	−	7.56771i	−0.132277	−	0.493663i
$236$		0			0
$237$	23.5235	+	23.5235i	1.52802	+	1.52802i
$238$		0			0
$239$	2.15987			0.139710			0.0698550	−	0.997557i	$-0.477746\pi$
$239$	2.15987			0.139710			0.0698550	+	0.997557i	$0.477746\pi$
$240$		0			0
$241$	4.85611	−	8.41103i	0.312809	−	0.541802i	−0.666160	−	0.745809i	$-0.732063\pi$
$241$	4.85611	−	8.41103i	0.312809	−	0.541802i	0.978969	+	0.204007i	$0.0653966\pi$
$242$		0			0
$243$	−5.77627	+	21.5573i	−0.370548	+	1.38290i
$244$		0			0
$245$	−13.5889	+	0.198113i	−0.868160	+	0.0126570i
$246$		0			0
$247$	−2.35762	+	1.36117i	−0.150012	+	0.0866094i
$248$		0			0
$249$	−31.6801	−	18.2905i	−2.00765	−	1.15912i
$250$		0			0
$251$	10.1748	−	10.1748i	0.642228	−	0.642228i	−0.308875	−	0.951103i	$-0.599952\pi$
$251$	10.1748	−	10.1748i	0.642228	−	0.642228i	0.951103	+	0.308875i	$0.0999525\pi$
$252$		0			0
$253$	−1.63584	−	1.63584i	−0.102844	−	0.102844i
$254$		0			0
$255$	−1.45793	+	2.52520i	−0.0912990	+	0.158134i
$256$		0			0
$257$	−13.2555	−	22.9591i	−0.826853	−	1.43215i	−0.900495	−	0.434867i	$-0.856795\pi$
$257$	−13.2555	−	22.9591i	−0.826853	−	1.43215i	0.0736418	−	0.997285i	$-0.476538\pi$
$258$		0			0
$259$	−0.982297	+	7.90619i	−0.0610370	+	0.491267i
$260$		0			0
$261$	12.8159	+	3.43401i	0.793283	+	0.212560i
$262$		0			0
$263$	17.9812	+	10.3814i	1.10877	+	0.640146i	0.938509	−	0.345254i	$-0.112207\pi$
$263$	17.9812	+	10.3814i	1.10877	+	0.640146i	0.170256	+	0.985400i	$0.445540\pi$
$264$		0			0
$265$			1.83312i			0.112607i
$266$		0			0
$267$	−6.97259	+	6.97259i	−0.426716	+	0.426716i
$268$		0			0
$269$	24.1792	−	6.47880i	1.47423	−	0.395019i	0.569852	−	0.821747i	$-0.307000\pi$
$269$	24.1792	−	6.47880i	1.47423	−	0.395019i	0.904380	+	0.426728i	$0.140334\pi$
$270$		0			0
$271$	−2.82072	−	4.88563i	−0.171347	−	0.296781i	0.767544	−	0.640996i	$-0.221478\pi$
$271$	−2.82072	−	4.88563i	−0.171347	−	0.296781i	−0.938891	+	0.344215i	$0.888145\pi$
$272$		0			0
$273$	−12.9405	+	31.8969i	−0.783198	+	1.93049i
$274$		0			0
$275$	1.68811	−	6.30010i	0.101797	−	0.379910i
$276$		0			0
$277$	−4.95063	−	18.4760i	−0.297455	−	1.11012i	−0.939248	−	0.343239i	$-0.888476\pi$
$277$	−4.95063	−	18.4760i	−0.297455	−	1.11012i	0.641793	−	0.766878i	$-0.278191\pi$
$278$		0			0
$279$			27.4937i			1.64600i
$280$		0			0
$281$		−	20.6400i		−	1.23128i	−0.788029	−	0.615639i	$-0.788898\pi$
$281$		−	20.6400i		−	1.23128i	0.788029	−	0.615639i	$-0.211102\pi$
$282$		0			0
$283$	−6.14544	−	22.9351i	−0.365309	−	1.36335i	−0.867002	−	0.498305i	$-0.833956\pi$
$283$	−6.14544	−	22.9351i	−0.365309	−	1.36335i	0.501693	−	0.865046i	$-0.332711\pi$
$284$		0			0
$285$	0.682175	−	2.54591i	0.0404085	−	0.150807i
$286$		0			0
$287$	7.73409	−	1.07562i	0.456529	−	0.0634918i
$288$		0			0
$289$	8.32617	+	14.4213i	0.489775	+	0.848315i
$290$		0			0
$291$	−29.6611	+	7.94766i	−1.73876	+	0.465900i
$292$		0			0
$293$	20.5268	−	20.5268i	1.19919	−	1.19919i	0.224778	−	0.974410i	$-0.427834\pi$
$293$	20.5268	−	20.5268i	1.19919	−	1.19919i	0.974410	−	0.224778i	$-0.0721656\pi$
$294$		0			0
$295$		−	0.0565132i		−	0.00329033i
$296$		0			0
$297$	5.70506	+	3.29382i	0.331041	+	0.191127i
$298$		0			0
$299$	2.15364	+	0.577067i	0.124548	+	0.0333726i
$300$		0			0
$301$	−22.9046	−	17.3116i	−1.32020	−	0.997822i
$302$		0			0
$303$	−3.41975	−	5.92318i	−0.196460	−	0.340278i
$304$		0			0
$305$	1.98780	−	3.44297i	0.113821	−	0.197144i
$306$		0			0
$307$	6.03127	+	6.03127i	0.344223	+	0.344223i	0.857952	−	0.513730i	$-0.171737\pi$
$307$	6.03127	+	6.03127i	0.344223	+	0.344223i	−0.513730	+	0.857952i	$0.671737\pi$
$308$		0			0
$309$	−0.160786	+	0.160786i	−0.00914677	+	0.00914677i
$310$		0			0
$311$	−13.8721	−	8.00907i	−0.786616	−	0.454153i	0.0521541	−	0.998639i	$-0.483391\pi$
$311$	−13.8721	−	8.00907i	−0.786616	−	0.454153i	−0.838770	+	0.544486i	$0.816725\pi$
$312$		0			0
$313$	−15.3757	+	8.87715i	−0.869085	+	0.501766i	−0.867044	−	0.498232i	$-0.833983\pi$
$313$	−15.3757	+	8.87715i	−0.869085	+	0.501766i	−0.00204070	+	0.999998i	$0.500650\pi$
$314$		0			0
$315$	−6.97687	−	16.5024i	−0.393102	−	0.929805i
$316$		0			0
$317$	−4.02311	+	15.0144i	−0.225960	+	0.843295i	0.756057	+	0.654505i	$0.227123\pi$
$317$	−4.02311	+	15.0144i	−0.225960	+	0.843295i	−0.982018	+	0.188790i	$0.939544\pi$
$318$		0			0
$319$	−10.0799	+	17.4588i	−0.564364	+	0.977506i
$320$		0			0
$321$	−37.1297			−2.07238
$322$		0			0
$323$	0.222217	+	0.222217i	0.0123645	+	0.0123645i
$324$		0			0
$325$	1.62695	+	6.07187i	0.0902471	+	0.336807i
$326$		0			0
$327$	−15.2645	+	8.81294i	−0.844126	+	0.487356i
$328$		0			0
$329$	−8.42282	+	6.56115i	−0.464365	+	0.361728i
$330$		0			0
$331$	14.6818	+	3.93399i	0.806987	+	0.216232i	0.638649	−	0.769498i	$-0.279493\pi$
$331$	14.6818	+	3.93399i	0.806987	+	0.216232i	0.168338	+	0.985729i	$0.446160\pi$
$332$		0			0
$333$	−10.1453	+	2.71842i	−0.555959	+	0.148969i
$334$		0			0
$335$	12.5581			0.686124
$336$		0			0
$337$	18.9202			1.03065			0.515325	−	0.856995i	$-0.327671\pi$
$337$	18.9202			1.03065			0.515325	+	0.856995i	$0.327671\pi$
$338$		0			0
$339$	18.4808	−	4.95192i	1.00374	−	0.268951i
$340$		0			0
$341$	−40.3512	−	10.8121i	−2.18514	−	0.585506i
$342$		0			0
$343$	7.45983	+	16.9514i	0.402793	+	0.915291i
$344$		0			0
$345$	−1.86946	+	1.07933i	−0.100648	+	0.0581094i
$346$		0			0
$347$	1.58787	+	5.92600i	0.0852412	+	0.318125i	0.995360	−	0.0962234i	$-0.0306763\pi$
$347$	1.58787	+	5.92600i	0.0852412	+	0.318125i	−0.910119	+	0.414348i	$0.864010\pi$
$348$		0			0
$349$	−2.94202	−	2.94202i	−0.157483	−	0.157483i	0.623968	−	0.781450i	$-0.285520\pi$
$349$	−2.94202	−	2.94202i	−0.157483	−	0.157483i	−0.781450	+	0.623968i	$0.785520\pi$
$350$		0			0
$351$	−6.34899			−0.338884
$352$		0			0
$353$	−13.0287	+	22.5663i	−0.693446	+	1.20108i	0.277256	+	0.960796i	$0.410575\pi$
$353$	−13.0287	+	22.5663i	−0.693446	+	1.20108i	−0.970702	+	0.240288i	$0.922758\pi$
$354$		0			0
$355$	−1.03327	+	3.85621i	−0.0548402	+	0.204666i
$356$		0			0
$357$	3.94328	+	0.489929i	0.208700	+	0.0259298i
$358$		0			0
$359$	−25.7055	+	14.8411i	−1.35668	+	0.783282i	−0.989175	−	0.146739i	$-0.953122\pi$
$359$	−25.7055	+	14.8411i	−1.35668	+	0.783282i	−0.367508	+	0.930020i	$0.619789\pi$
$360$		0			0
$361$	16.2085	+	9.35796i	0.853077	+	0.492524i
$362$		0			0
$363$	−30.7763	+	30.7763i	−1.61534	+	1.61534i
$364$		0			0
$365$	10.8692	+	10.8692i	0.568919	+	0.568919i
$366$		0			0
$367$	−2.21998	+	3.84511i	−0.115882	+	0.200713i	−0.918132	−	0.396275i	$-0.870303\pi$
$367$	−2.21998	+	3.84511i	−0.115882	+	0.200713i	0.802250	+	0.596988i	$0.203636\pi$
$368$		0			0
$369$	5.14714	+	8.91512i	0.267950	+	0.464102i
$370$		0			0
$371$	2.30090	−	0.972775i	0.119457	−	0.0505039i
$372$		0			0
$373$	−17.6779	−	4.73679i	−0.915328	−	0.245261i	−0.229741	−	0.973252i	$-0.573788\pi$
$373$	−17.6779	−	4.73679i	−0.915328	−	0.245261i	−0.685587	+	0.727990i	$0.740455\pi$
$374$		0			0
$375$	−26.6841	−	15.4061i	−1.37796	−	0.795567i
$376$		0			0
$377$		−	19.4294i		−	1.00066i
$378$		0			0
$379$	−1.71717	+	1.71717i	−0.0882050	+	0.0882050i	−0.749833	−	0.661628i	$-0.769866\pi$
$379$	−1.71717	+	1.71717i	−0.0882050	+	0.0882050i	0.661628	+	0.749833i	$0.269866\pi$
$380$		0			0
$381$	−10.4615	+	2.80315i	−0.535960	+	0.143610i
$382$		0			0
$383$	−5.88728	−	10.1971i	−0.300826	−	0.521046i	0.675497	−	0.737363i	$-0.263929\pi$
$383$	−5.88728	−	10.1971i	−0.300826	−	0.521046i	−0.976323	+	0.216316i	$0.930596\pi$
$384$		0			0
$385$	26.9635	−	3.74995i	1.37419	−	0.191115i
$386$		0			0
$387$	9.79646	−	36.5609i	0.497982	−	1.85849i
$388$		0			0
$389$	4.04561	+	15.0984i	0.205120	+	0.765520i	0.989413	+	0.145128i	$0.0463595\pi$
$389$	4.04561	+	15.0984i	0.205120	+	0.765520i	−0.784292	+	0.620391i	$0.786974\pi$
$390$		0			0
$391$		−	0.257382i		−	0.0130164i
$392$		0			0
$393$			12.8969i			0.650560i
$394$		0			0
$395$	6.56280	+	24.4927i	0.330210	+	1.23236i
$396$		0			0
$397$	−0.836855	+	3.12318i	−0.0420005	+	0.156748i	−0.983741	−	0.179592i	$-0.942522\pi$
$397$	−0.836855	+	3.12318i	−0.0420005	+	0.156748i	0.941741	+	0.336340i	$0.109189\pi$
$398$		0			0
$399$	−3.55760	+	0.494774i	−0.178103	+	0.0247697i
$400$		0			0
$401$	−2.37385	−	4.11163i	−0.118544	−	0.205325i	0.800647	−	0.599137i	$-0.204489\pi$
$401$	−2.37385	−	4.11163i	−0.118544	−	0.205325i	−0.919191	+	0.393812i	$0.871156\pi$
$402$		0			0
$403$	38.8894	−	10.4204i	1.93722	−	0.519076i
$404$		0			0
$405$	−10.0187	+	10.0187i	−0.497834	+	0.497834i
$406$		0			0
$407$		−	15.9588i		−	0.791048i
$408$		0			0
$409$	−2.68361	−	1.54938i	−0.132696	−	0.0766121i	0.432182	−	0.901786i	$-0.357744\pi$
$409$	−2.68361	−	1.54938i	−0.132696	−	0.0766121i	−0.564879	+	0.825174i	$0.691077\pi$
$410$		0			0
$411$	0.686118	+	0.183845i	0.0338437	+	0.00906839i
$412$		0			0
$413$	−0.0709347	+	0.0299897i	−0.00349047	+	0.00147570i
$414$		0			0
$415$	−13.9413	−	24.1470i	−0.684349	−	1.18533i
$416$		0			0
$417$	21.8106	−	37.7770i	1.06807	−	1.84995i
$418$		0			0
$419$	−2.62329	−	2.62329i	−0.128156	−	0.128156i	0.640119	−	0.768276i	$-0.278885\pi$
$419$	−2.62329	−	2.62329i	−0.128156	−	0.128156i	−0.768276	+	0.640119i	$0.778885\pi$
$420$		0			0
$421$	−3.44059	+	3.44059i	−0.167684	+	0.167684i	−0.785961	−	0.618276i	$-0.787831\pi$
$421$	−3.44059	+	3.44059i	−0.167684	+	0.167684i	0.618276	+	0.785961i	$0.287831\pi$
$422$		0			0
$423$	−12.1898	−	7.03778i	−0.592688	−	0.342189i
$424$		0			0
$425$	0.628432	−	0.362825i	0.0304834	−	0.0175996i
$426$		0			0
$427$	−5.37643	−	0.667990i	−0.260184	−	0.0323263i
$428$		0			0
$429$	17.8459	−	66.6018i	0.861608	−	3.21556i
$430$		0			0
$431$	−11.3945	+	19.7358i	−0.548853	+	0.950642i	0.449500	+	0.893280i	$0.351602\pi$
$431$	−11.3945	+	19.7358i	−0.548853	+	0.950642i	−0.998353	+	0.0573616i	$0.981731\pi$
$432$		0			0
$433$	−16.6448			−0.799899			−0.399950	−	0.916537i	$-0.630972\pi$
$433$	−16.6448			−0.799899			−0.399950	+	0.916537i	$0.630972\pi$
$434$		0			0
$435$	13.3015	+	13.3015i	0.637757	+	0.637757i
$436$		0			0
$437$	0.0602155	+	0.224727i	0.00288050	+	0.0107502i
$438$		0			0
$439$	26.7406	−	15.4387i	1.27626	−	0.736847i	0.300099	−	0.953908i	$-0.402980\pi$
$439$	26.7406	−	15.4387i	1.27626	−	0.736847i	0.976158	+	0.217061i	$0.0696469\pi$
$440$		0			0
$441$	−17.0112	+	17.5146i	−0.810057	+	0.834026i
$442$		0			0
$443$	13.7414	+	3.68200i	0.652874	+	0.174937i	0.570028	−	0.821625i	$-0.306932\pi$
$443$	13.7414	+	3.68200i	0.652874	+	0.174937i	0.0828461	+	0.996562i	$0.473599\pi$
$444$		0			0
$445$	−7.25987	+	1.94528i	−0.344151	+	0.0922149i
$446$		0			0
$447$	55.8784			2.64296
$448$		0			0
$449$	14.7633			0.696725			0.348363	−	0.937360i	$-0.386738\pi$
$449$	14.7633			0.696725			0.348363	+	0.937360i	$0.386738\pi$
$450$		0			0
$451$	−15.1084	+	4.04830i	−0.711429	+	0.190627i
$452$		0			0
$453$	−22.9771	−	6.15670i	−1.07956	−	0.289267i
$454$		0			0
$455$	−20.6981	+	16.1232i	−0.970341	+	0.755869i
$456$		0			0
$457$	−1.80328	+	1.04112i	−0.0843539	+	0.0487017i	−0.541584	−	0.840647i	$-0.682175\pi$
$457$	−1.80328	+	1.04112i	−0.0843539	+	0.0487017i	0.457230	+	0.889349i	$0.348842\pi$
$458$		0			0
$459$	0.189692	+	0.707941i	0.00885407	+	0.0330439i
$460$		0			0
$461$	10.5211	+	10.5211i	0.490015	+	0.490015i	0.908311	−	0.418296i	$-0.137372\pi$
$461$	10.5211	+	10.5211i	0.490015	+	0.490015i	−0.418296	+	0.908311i	$0.637372\pi$
$462$		0			0
$463$	−26.5483			−1.23380			−0.616902	−	0.787040i	$-0.711613\pi$
$463$	−26.5483			−1.23380			−0.616902	+	0.787040i	$0.711613\pi$
$464$		0			0
$465$	−19.4901	+	33.7578i	−0.903830	+	1.56548i
$466$		0			0
$467$	−2.50402	+	9.34512i	−0.115872	+	0.432440i	−0.999351	−	0.0360311i	$-0.988528\pi$
$467$	−2.50402	+	9.34512i	−0.115872	+	0.432440i	0.883479	+	0.468472i	$0.155195\pi$
$468$		0			0
$469$	−6.66419	−	15.7628i	−0.307724	−	0.727859i
$470$		0			0
$471$	−25.7546	+	14.8694i	−1.18671	+	0.685146i
$472$		0			0
$473$	49.8062	+	28.7556i	2.29009	+	1.32218i
$474$		0			0
$475$	−0.463816	+	0.463816i	−0.0212813	+	0.0212813i
$476$		0			0
$477$	2.32874	+	2.32874i	0.106626	+	0.106626i
$478$		0			0
$479$	−1.94642	+	3.37130i	−0.0889342	+	0.154039i	−0.907061	−	0.420999i	$-0.861679\pi$
$479$	−1.94642	+	3.37130i	−0.0889342	+	0.154039i	0.818127	+	0.575038i	$0.195013\pi$
$480$		0			0
$481$	7.69033	+	13.3200i	0.350649	+	0.607342i
$482$		0			0
$483$	2.34683	+	1.77376i	0.106784	+	0.0807087i
$484$		0			0
$485$	−22.6080	−	6.05780i	−1.02658	−	0.275070i
$486$		0			0
$487$	2.49944	+	1.44305i	0.113260	+	0.0653909i	0.555560	−	0.831476i	$-0.312504\pi$
$487$	2.49944	+	1.44305i	0.113260	+	0.0653909i	−0.442300	+	0.896867i	$0.645837\pi$
$488$		0			0
$489$			37.6724i			1.70360i
$490$		0			0
$491$	−10.1200	+	10.1200i	−0.456710	+	0.456710i	−0.897574	−	0.440864i	$-0.854672\pi$
$491$	−10.1200	+	10.1200i	−0.456710	+	0.456710i	0.440864	+	0.897574i	$0.354672\pi$
$492$		0			0
$493$	−2.16647	+	0.580503i	−0.0975727	+	0.0261445i
$494$		0			0
$495$	17.9446	+	31.0809i	0.806549	+	1.39698i
$496$		0			0
$497$	5.38858	−	0.749418i	0.241711	−	0.0336160i
$498$		0			0
$499$	4.96424	−	18.5268i	0.222230	−	0.829373i	−0.761265	−	0.648440i	$-0.775422\pi$
$499$	4.96424	−	18.5268i	0.222230	−	0.829373i	0.983495	−	0.180933i	$-0.0579117\pi$
$500$		0			0
$501$	0.281378	+	1.05012i	0.0125710	+	0.0469158i
$502$		0			0
$503$		−	25.3179i		−	1.12887i	−0.825477	−	0.564436i	$-0.809094\pi$
$503$		−	25.3179i		−	1.12887i	0.825477	−	0.564436i	$-0.190906\pi$
$504$		0			0
$505$		−	5.21315i		−	0.231982i
$506$		0			0
$507$	8.62911	+	32.2043i	0.383232	+	1.43024i
$508$		0			0
$509$	−0.572369	+	2.13611i	−0.0253698	+	0.0946814i	−0.977450	−	0.211167i	$-0.932274\pi$
$509$	−0.572369	+	2.13611i	−0.0253698	+	0.0946814i	0.952080	+	0.305849i	$0.0989402\pi$
$510$		0			0
$511$	7.87494	−	19.4108i	0.348367	−	0.858682i
$512$		0			0
$513$	−0.331251	−	0.573743i	−0.0146251	−	0.0253314i
$514$		0			0
$515$	−0.167410	+	0.0448574i	−0.00737697	+	0.00197665i
$516$		0			0
$517$	15.1227	−	15.1227i	0.665097	−	0.665097i
$518$		0			0
$519$		−	10.7258i		−	0.470809i
$520$		0			0
$521$	−8.90915	−	5.14370i	−0.390317	−	0.225349i	0.291981	−	0.956424i	$-0.405686\pi$
$521$	−8.90915	−	5.14370i	−0.390317	−	0.225349i	−0.682297	+	0.731075i	$0.739019\pi$
$522$		0			0
$523$	6.30777	+	1.69016i	0.275819	+	0.0739056i	0.394077	−	0.919077i	$-0.371064\pi$
$523$	6.30777	+	1.69016i	0.275819	+	0.0739056i	−0.118258	+	0.992983i	$0.537731\pi$
$524$		0			0
$525$	−1.02259	+	8.23049i	−0.0446295	+	0.359208i
$526$		0			0
$527$	−2.32384	−	4.02501i	−0.101228	−	0.175332i
$528$		0			0
$529$	−11.4047	+	19.7536i	−0.495858	+	0.858851i
$530$		0			0
$531$	−0.0717927	−	0.0717927i	−0.00311554	−	0.00311554i
$532$		0			0
$533$	10.6595	−	10.6595i	0.461713	−	0.461713i
$534$		0			0
$535$	−24.5091	−	14.1503i	−1.05962	−	0.611773i
$536$		0			0
$537$	30.9946	−	17.8947i	1.33751	−	0.772214i
$538$		0			0
$539$	−19.0155	−	31.8542i	−0.819056	−	1.37206i
$540$		0			0
$541$	−1.75097	+	6.53469i	−0.0752799	+	0.280948i	−0.993297	−	0.115593i	$-0.963123\pi$
$541$	−1.75097	+	6.53469i	−0.0752799	+	0.280948i	0.918017	+	0.396542i	$0.129790\pi$
$542$		0			0
$543$	18.1338	−	31.4086i	0.778195	−	1.34787i
$544$		0			0
$545$	−13.4346			−0.575477
$546$		0			0
$547$	1.78581	+	1.78581i	0.0763555	+	0.0763555i	0.744253	−	0.667898i	$-0.232806\pi$
$547$	1.78581	+	1.78581i	0.0763555	+	0.0763555i	−0.667898	+	0.744253i	$0.732806\pi$
$548$		0			0
$549$	−1.84860	−	6.89909i	−0.0788965	−	0.294446i
$550$		0			0
$551$	1.75579	−	1.01370i	0.0747991	−	0.0431853i
$552$		0			0
$553$	27.2603	−	21.2350i	1.15922	−	0.903004i
$554$		0			0
$555$	−14.3838	−	3.85414i	−0.610560	−	0.163599i
$556$		0			0
$557$	3.36982	−	0.902940i	0.142784	−	0.0382588i	−0.186719	−	0.982413i	$-0.559785\pi$
$557$	3.36982	−	0.902940i	0.142784	−	0.0382588i	0.329503	+	0.944155i	$0.393119\pi$
$558$		0			0
$559$	−55.4278			−2.34435
$560$		0			0
$561$	−7.95959			−0.336054
$562$		0			0
$563$	−38.4688	+	10.3077i	−1.62127	+	0.434417i	−0.951373	−	0.308041i	$-0.900327\pi$
$563$	−38.4688	+	10.3077i	−1.62127	+	0.434417i	−0.669893	+	0.742458i	$0.733660\pi$
$564$		0			0
$565$	14.0863	+	3.77441i	0.592615	+	0.158791i
$566$		0			0
$567$	17.8920	+	7.25876i	0.751391	+	0.304839i
$568$		0			0
$569$	−39.1325	+	22.5931i	−1.64052	+	0.947153i	−0.659868	+	0.751381i	$0.729388\pi$
$569$	−39.1325	+	22.5931i	−1.64052	+	0.947153i	−0.980649	+	0.195772i	$0.937279\pi$
$570$		0			0
$571$	−6.44226	−	24.0429i	−0.269600	−	1.00616i	−0.959374	−	0.282137i	$-0.908957\pi$
$571$	−6.44226	−	24.0429i	−0.269600	−	1.00616i	0.689774	−	0.724025i	$-0.257710\pi$
$572$		0			0
$573$	17.3717	+	17.3717i	0.725714	+	0.725714i
$574$		0			0
$575$	0.537214			0.0224034
$576$		0			0
$577$	−5.46579	+	9.46703i	−0.227544	+	0.394118i	−0.957080	−	0.289825i	$-0.906403\pi$
$577$	−5.46579	+	9.46703i	−0.227544	+	0.394118i	0.729536	+	0.683943i	$0.239736\pi$
$578$		0			0
$579$	12.8946	−	48.1232i	0.535881	−	1.99993i
$580$		0			0
$581$	−22.9108	+	30.3129i	−0.950500	+	1.25759i
$582$		0			0
$583$	−4.33357	+	2.50199i	−0.179478	+	0.103622i
$584$		0			0
$585$	−29.9550	−	17.2945i	−1.23848	−	0.715040i
$586$		0			0
$587$	7.44744	−	7.44744i	0.307389	−	0.307389i	−0.536507	−	0.843896i	$-0.680256\pi$
$587$	7.44744	−	7.44744i	0.307389	−	0.307389i	0.843896	+	0.536507i	$0.180256\pi$
$588$		0			0
$589$	2.97067	+	2.97067i	0.122404	+	0.122404i
$590$		0			0
$591$	−15.0078	+	25.9943i	−0.617338	+	1.06926i
$592$		0			0
$593$	12.6447	+	21.9013i	0.519256	+	0.899377i	0.999750	+	0.0223792i	$0.00712412\pi$
$593$	12.6447	+	21.9013i	0.519256	+	0.899377i	−0.480494	+	0.876998i	$0.659543\pi$
$594$		0			0
$595$	2.41622	+	1.82621i	0.0990555	+	0.0748672i
$596$		0			0
$597$	6.65853	+	1.78415i	0.272516	+	0.0730203i
$598$		0			0
$599$	−15.4613	−	8.92656i	−0.631730	−	0.364729i	0.149692	−	0.988733i	$-0.452172\pi$
$599$	−15.4613	−	8.92656i	−0.631730	−	0.364729i	−0.781422	+	0.624003i	$0.785505\pi$
$600$		0			0
$601$		−	15.3921i		−	0.627855i	−0.949447	−	0.313928i	$-0.898355\pi$
$601$		−	15.3921i		−	0.627855i	0.949447	−	0.313928i	$-0.101645\pi$
$602$		0			0
$603$	15.9535	−	15.9535i	0.649676	−	0.649676i
$604$		0			0
$605$	−32.0443	+	8.58625i	−1.30279	+	0.349081i
$606$		0			0
$607$	15.1434	+	26.2292i	0.614652	+	1.06461i	0.990445	+	0.137905i	$0.0440370\pi$
$607$	15.1434	+	26.2292i	0.614652	+	1.06461i	−0.375793	+	0.926704i	$0.622630\pi$
$608$		0			0
$609$	9.63719	−	23.7545i	0.390519	−	0.962581i
$610$		0			0
$611$	−5.33478	+	19.9097i	−0.215822	+	0.805459i
$612$		0			0
$613$	3.95872	+	14.7741i	0.159891	+	0.596722i	0.998637	+	0.0521982i	$0.0166228\pi$
$613$	3.95872	+	14.7741i	0.159891	+	0.596722i	−0.838746	+	0.544523i	$0.816711\pi$
$614$		0			0
$615$			14.5951i			0.588531i
$616$		0			0
$617$		−	39.3266i		−	1.58323i	−0.611020	−	0.791615i	$-0.709241\pi$
$617$		−	39.3266i		−	1.58323i	0.611020	−	0.791615i	$-0.290759\pi$
$618$		0			0
$619$	1.39109	+	5.19162i	0.0559127	+	0.208669i	0.988231	−	0.152970i	$-0.0488839\pi$
$619$	1.39109	+	5.19162i	0.0559127	+	0.208669i	−0.932318	+	0.361639i	$0.882217\pi$
$620$		0			0
$621$	−0.140433	+	0.524103i	−0.00563538	+	0.0210315i
$622$		0			0
$623$	6.29426	+	8.08020i	0.252174	+	0.323726i
$624$		0			0
$625$	−8.66598	−	15.0099i	−0.346639	−	0.600397i
$626$		0			0
$627$	6.94973	−	1.86217i	0.277545	−	0.0743681i
$628$		0			0
$629$	1.25548	−	1.25548i	0.0500592	−	0.0500592i
$630$		0			0
$631$			7.48252i			0.297875i	0.988847	+	0.148937i	$0.0475853\pi$
$631$			7.48252i			0.297875i	−0.988847	+	0.148937i	$0.952415\pi$
$632$		0			0
$633$	−37.3894	−	21.5868i	−1.48610	−	0.857998i
$634$		0			0
$635$	−7.97389	−	2.13660i	−0.316434	−	0.0847883i
$636$		0			0
$637$	31.2215	+	17.4239i	1.23704	+	0.690360i
$638$		0			0
$639$	3.58618	+	6.21144i	0.141867	+	0.245721i
$640$		0			0
$641$	−4.73385	+	8.19927i	−0.186976	+	0.323852i	−0.944241	−	0.329256i	$-0.893202\pi$
$641$	−4.73385	+	8.19927i	−0.186976	+	0.323852i	0.757265	+	0.653108i	$0.226535\pi$
$642$		0			0
$643$	20.6140	+	20.6140i	0.812939	+	0.812939i	0.985073	−	0.172135i	$-0.0550665\pi$
$643$	20.6140	+	20.6140i	0.812939	+	0.812939i	−0.172135	+	0.985073i	$0.555066\pi$
$644$		0			0
$645$	37.9462	−	37.9462i	1.49413	−	1.49413i
$646$		0			0
$647$	30.2216	+	17.4485i	1.18813	+	0.685970i	0.957882	−	0.287161i	$-0.0927115\pi$
$647$	30.2216	+	17.4485i	1.18813	+	0.685970i	0.230252	+	0.973131i	$0.426045\pi$
$648$		0			0
$649$	0.133600	−	0.0771338i	0.00524425	−	0.00302777i
$650$		0			0
$651$	52.7151	+	6.54954i	2.06607	+	0.256697i
$652$		0			0
$653$	10.3267	−	38.5399i	0.404117	−	1.50818i	−0.401562	−	0.915832i	$-0.631533\pi$
$653$	10.3267	−	38.5399i	0.404117	−	1.50818i	0.805679	−	0.592353i	$-0.201801\pi$
$654$		0			0
$655$	−4.91507	+	8.51315i	−0.192048	+	0.332636i
$656$		0			0
$657$	27.6157			1.07739
$658$		0			0
$659$	6.66795	+	6.66795i	0.259746	+	0.259746i	0.824951	−	0.565205i	$-0.191203\pi$
$659$	6.66795	+	6.66795i	0.259746	+	0.259746i	−0.565205	+	0.824951i	$0.691203\pi$
$660$		0			0
$661$	0.649564	+	2.42421i	0.0252651	+	0.0942907i	0.977407	−	0.211365i	$-0.0677909\pi$
$661$	0.649564	+	2.42421i	0.0252651	+	0.0942907i	−0.952142	+	0.305656i	$0.901124\pi$
$662$		0			0
$663$	6.64349	−	3.83562i	0.258012	−	0.148963i
$664$		0			0
$665$	−2.53692	−	1.02923i	−0.0983774	−	0.0399117i
$666$		0			0
$667$	−1.60388	−	0.429758i	−0.0621024	−	0.0166403i
$668$		0			0
$669$	−6.17241	+	1.65389i	−0.238639	+	0.0639432i
$670$		0			0
$671$	10.8524			0.418954
$672$		0			0
$673$	−36.8448			−1.42026			−0.710131	−	0.704070i	$-0.751364\pi$
$673$	−36.8448			−1.42026			−0.710131	+	0.704070i	$0.751364\pi$
$674$		0			0
$675$	−1.47763	+	0.395930i	−0.0568740	+	0.0152393i
$676$		0			0
$677$	16.8935	+	4.52660i	0.649270	+	0.173971i	0.568399	−	0.822753i	$-0.307563\pi$
$677$	16.8935	+	4.52660i	0.649270	+	0.173971i	0.0808713	+	0.996725i	$0.474230\pi$
$678$		0			0
$679$	4.39366	+	31.5920i	0.168613	+	1.21239i
$680$		0			0
$681$	41.8067	−	24.1371i	1.60204	−	0.924936i
$682$		0			0
$683$	8.60472	+	32.1132i	0.329250	+	1.22878i	0.909970	+	0.414675i	$0.136105\pi$
$683$	8.60472	+	32.1132i	0.329250	+	1.22878i	−0.580719	+	0.814104i	$0.697229\pi$
$684$		0			0
$685$	0.382838	+	0.382838i	0.0146275	+	0.0146275i
$686$		0			0
$687$	66.1896			2.52529
$688$		0			0
$689$	2.41135	−	4.17658i	0.0918650	−	0.159115i
$690$		0			0
$691$	−3.84416	+	14.3466i	−0.146239	+	0.545771i	0.853458	+	0.521161i	$0.174501\pi$
$691$	−3.84416	+	14.3466i	−0.146239	+	0.545771i	−0.999697	+	0.0246098i	$0.992166\pi$
$692$		0			0
$693$	29.4898	−	39.0174i	1.12022	−	1.48215i
$694$		0			0
$695$	28.7941	−	16.6243i	1.09222	−	0.630595i
$696$		0			0
$697$	−1.50706	−	0.870101i	−0.0570839	−	0.0329574i
$698$		0			0
$699$	25.4571	−	25.4571i	0.962874	−	0.962874i
$700$		0			0
$701$	−21.3787	−	21.3787i	−0.807464	−	0.807464i	0.176785	−	0.984249i	$-0.443430\pi$
$701$	−21.3787	−	21.3787i	−0.807464	−	0.807464i	−0.984249	+	0.176785i	$0.943430\pi$
$702$		0			0
$703$	−0.802467	+	1.38991i	−0.0302656	+	0.0524216i
$704$		0			0
$705$	−9.97805	−	17.2825i	−0.375795	−	0.650897i
$706$		0			0
$707$	−6.54348	+	2.76645i	−0.246093	+	0.104043i
$708$		0			0
$709$	−13.3395	−	3.57430i	−0.500974	−	0.134236i	−0.000522056	−	1.00000i	$-0.500166\pi$
$709$	−13.3395	−	3.57430i	−0.500974	−	0.134236i	−0.500452	+	0.865764i	$0.666833\pi$
$710$		0			0
$711$	39.4520	+	22.7776i	1.47956	+	0.854227i
$712$		0			0
$713$		−	3.44077i		−	0.128858i
$714$		0			0
$715$	37.1623	−	37.1623i	1.38979	−	1.38979i
$716$		0			0
$717$	5.31405	−	1.42390i	0.198457	−	0.0531764i
$718$		0			0
$719$	−22.1881	−	38.4309i	−0.827477	−	1.43323i	−0.900011	−	0.435866i	$-0.856442\pi$
$719$	−22.1881	−	38.4309i	−0.827477	−	1.43323i	0.0725344	−	0.997366i	$-0.476891\pi$
$720$		0			0
$721$	0.145143	+	0.186327i	0.00540542	+	0.00693917i
$722$		0			0
$723$	6.40280	−	23.8956i	0.238123	−	0.888686i
$724$		0			0
$725$	−1.21164	−	4.52189i	−0.0449991	−	0.167939i
$726$		0			0
$727$			1.44539i			0.0536067i	0.999641	+	0.0268033i	$0.00853279\pi$
$727$			1.44539i			0.0536067i	−0.999641	+	0.0268033i	$0.991467\pi$
$728$		0			0
$729$			34.9533i			1.29457i
$730$		0			0
$731$	1.65605	+	6.18045i	0.0612511	+	0.228592i
$732$		0			0
$733$	10.5622	−	39.4186i	0.390123	−	1.45596i	−0.439807	−	0.898093i	$-0.644953\pi$
$733$	10.5622	−	39.4186i	0.390123	−	1.45596i	0.829930	−	0.557868i	$-0.188380\pi$
$734$		0			0
$735$	−33.3029	+	9.44591i	−1.22840	+	0.348418i
$736$		0			0
$737$	17.1404	+	29.6880i	0.631373	+	1.09357i
$738$		0			0
$739$	10.9326	−	2.92937i	0.402161	−	0.107759i	−0.0520685	−	0.998644i	$-0.516581\pi$
$739$	10.9326	−	2.92937i	0.402161	−	0.107759i	0.454229	+	0.890885i	$0.349915\pi$
$740$		0			0
$741$	−4.90325	+	4.90325i	−0.180125	+	0.180125i
$742$		0			0
$743$			9.66874i			0.354712i	0.984147	+	0.177356i	$0.0567544\pi$
$743$			9.66874i			0.354712i	−0.984147	+	0.177356i	$0.943246\pi$
$744$		0			0
$745$	36.8851	+	21.2956i	1.35136	+	0.780210i
$746$		0			0
$747$	−48.3861	−	12.9650i	−1.77036	−	0.474365i
$748$		0			0
$749$	−4.75515	+	38.2727i	−0.173749	+	1.39845i
$750$		0			0
$751$	−25.8756	−	44.8178i	−0.944213	−	1.63542i	−0.757319	−	0.653045i	$-0.773491\pi$
$751$	−25.8756	−	44.8178i	−0.944213	−	1.63542i	−0.186893	−	0.982380i	$-0.559842\pi$
$752$		0			0
$753$	18.3259	−	31.7415i	0.667834	−	1.15672i
$754$		0			0
$755$	−12.8207	−	12.8207i	−0.466594	−	0.466594i
$756$		0			0
$757$	−28.2783	+	28.2783i	−1.02779	+	1.02779i	−0.0281911	+	0.999603i	$0.508975\pi$
$757$	−28.2783	+	28.2783i	−1.02779	+	1.02779i	−0.999603	+	0.0281911i	$0.991025\pi$
$758$		0			0
$759$	−5.10318	−	2.94632i	−0.185234	−	0.106945i
$760$		0			0
$761$	−4.94191	+	2.85321i	−0.179144	+	0.103429i	−0.586891	−	0.809666i	$-0.699648\pi$
$761$	−4.94191	+	2.85321i	−0.179144	+	0.103429i	0.407746	+	0.913095i	$0.366315\pi$
$762$		0			0
$763$	7.12933	+	16.8630i	0.258099	+	0.610482i
$764$		0			0
$765$	−1.03343	+	3.85683i	−0.0373639	+	0.139444i
$766$		0			0
$767$	−0.0743395	+	0.128760i	−0.00268425	+	0.00464925i
$768$		0			0
$769$	39.6503			1.42983			0.714914	−	0.699212i	$-0.246466\pi$
$769$	39.6503			1.42983			0.714914	+	0.699212i	$0.246466\pi$
$770$		0			0
$771$	−47.7491	−	47.7491i	−1.71964	−	1.71964i
$772$		0			0
$773$	5.74604	+	21.4445i	0.206671	+	0.771305i	0.988934	+	0.148357i	$0.0473985\pi$
$773$	5.74604	+	21.4445i	0.206671	+	0.771305i	−0.782263	+	0.622948i	$0.785935\pi$
$774$		0			0
$775$	8.40108	−	4.85037i	0.301776	−	0.174230i
$776$		0			0
$777$	2.79536	+	20.0997i	0.100283	+	0.721072i
$778$		0			0
$779$	1.51942	+	0.407126i	0.0544387	+	0.0145868i
$780$		0			0
$781$	−10.5265	+	2.82057i	−0.376669	+	0.100928i
$782$		0			0
$783$	4.72827			0.168975
$784$		0			0
$785$	−22.6673			−0.809029
$786$		0			0
$787$	−18.8470	+	5.05004i	−0.671823	+	0.180014i	−0.578576	−	0.815629i	$-0.696391\pi$
$787$	−18.8470	+	5.05004i	−0.671823	+	0.180014i	−0.0932471	+	0.995643i	$0.529725\pi$
$788$		0			0
$789$	51.0841	+	13.6880i	1.81864	+	0.487304i
$790$		0			0
$791$	−2.73754	−	19.6839i	−0.0973357	−	0.699879i
$792$		0			0
$793$	−9.05801	+	5.22965i	−0.321659	+	0.185710i
$794$		0			0
$795$	1.20849	+	4.51013i	0.0428606	+	0.159958i
$796$		0			0
$797$	−2.54421	−	2.54421i	−0.0901206	−	0.0901206i	0.660609	−	0.750730i	$-0.270298\pi$
$797$	−2.54421	−	2.54421i	−0.0901206	−	0.0901206i	−0.750730	+	0.660609i	$0.770298\pi$
$798$		0			0
$799$	2.37941			0.0841774
$800$		0			0
$801$	−6.75150	+	11.6939i	−0.238553	+	0.413185i
$802$		0			0
$803$	−10.8601	+	40.5303i	−0.383244	+	1.43028i
$804$		0			0
$805$	0.873139	+	2.06524i	0.0307741	+	0.0727900i
$806$		0			0
$807$	55.2185	−	31.8804i	1.94378	−	1.12224i
$808$		0			0
$809$	−19.3519	−	11.1728i	−0.680378	−	0.392816i	0.119620	−	0.992820i	$-0.461832\pi$
$809$	−19.3519	−	11.1728i	−0.680378	−	0.392816i	−0.799997	+	0.600004i	$0.795166\pi$
$810$		0			0
$811$	−31.7484	+	31.7484i	−1.11484	+	1.11484i	−0.122349	+	0.992487i	$0.539043\pi$
$811$	−31.7484	+	31.7484i	−1.11484	+	1.11484i	−0.992487	+	0.122349i	$0.960957\pi$
$812$		0			0
$813$	−10.1609	−	10.1609i	−0.356357	−	0.356357i
$814$		0			0
$815$	−14.3572	+	24.8673i	−0.502909	+	0.871065i
$816$		0			0
$817$	−2.89188	−	5.00888i	−0.101174	−	0.175238i
$818$		0			0
$819$	−5.81173	+	46.7767i	−0.203078	+	1.63451i
$820$		0			0
$821$	46.9829	+	12.5890i	1.63972	+	0.439361i	0.956708	−	0.291050i	$-0.0940047\pi$
$821$	46.9829	+	12.5890i	1.63972	+	0.439361i	0.683008	+	0.730411i	$0.260671\pi$
$822$		0			0
$823$	16.7248	+	9.65608i	0.582991	+	0.336590i	0.762321	−	0.647199i	$-0.224060\pi$
$823$	16.7248	+	9.65608i	0.582991	+	0.336590i	−0.179330	+	0.983789i	$0.557393\pi$
$824$		0			0
$825$		−	16.6134i		−	0.578405i
$826$		0			0
$827$	−14.4794	+	14.4794i	−0.503498	+	0.503498i	−0.912523	−	0.409025i	$-0.865869\pi$
$827$	−14.4794	+	14.4794i	−0.503498	+	0.503498i	0.409025	+	0.912523i	$0.365869\pi$
$828$		0			0
$829$	−1.38085	+	0.369998i	−0.0479589	+	0.0128505i	−0.282719	−	0.959203i	$-0.591236\pi$
$829$	−1.38085	+	0.369998i	−0.0479589	+	0.0128505i	0.234760	+	0.972053i	$0.424570\pi$
$830$		0			0
$831$	−24.3607	−	42.1940i	−0.845064	−	1.46369i
$832$		0			0
$833$	1.01002	−	4.00192i	0.0349952	−	0.138658i
$834$		0			0
$835$	−0.214470	+	0.800412i	−0.00742203	+	0.0276994i
$836$		0			0
$837$	2.53587	+	9.46399i	0.0876524	+	0.327123i
$838$		0			0
$839$		−	41.9512i		−	1.44832i	−0.689634	−	0.724158i	$-0.742228\pi$
$839$		−	41.9512i		−	1.44832i	0.689634	−	0.724158i	$-0.257772\pi$
$840$		0			0
$841$		−	14.5304i		−	0.501048i
$842$		0			0
$843$	−13.6069	−	50.7818i	−0.468648	−	1.74902i
$844$		0			0
$845$	−6.57721	+	24.5465i	−0.226263	+	0.844425i
$846$		0			0
$847$	27.7822	+	35.6652i	0.954608	+	1.22547i
$848$		0			0
$849$	−30.2400	−	52.3773i	−1.03784	−	1.79758i
$850$		0			0
$851$	1.26966	−	0.340204i	0.0435234	−	0.0116621i
$852$		0			0
$853$	−34.5722	+	34.5722i	−1.18373	+	1.18373i	−0.204960	+	0.978770i	$0.565706\pi$
$853$	−34.5722	+	34.5722i	−1.18373	+	1.18373i	−0.978770	+	0.204960i	$0.934294\pi$
$854$		0			0
$855$		−	3.60928i		−	0.123435i
$856$		0			0
$857$	−7.21992	−	4.16842i	−0.246628	−	0.142391i	0.371591	−	0.928396i	$-0.378812\pi$
$857$	−7.21992	−	4.16842i	−0.246628	−	0.142391i	−0.618219	+	0.786006i	$0.712146\pi$
$858$		0			0
$859$	−12.6163	−	3.38053i	−0.430463	−	0.115342i	0.0370807	−	0.999312i	$-0.488194\pi$
$859$	−12.6163	−	3.38053i	−0.430463	−	0.115342i	−0.467543	+	0.883970i	$0.654861\pi$
$860$		0			0
$861$	18.3196	−	7.74513i	0.624329	−	0.263953i
$862$		0			0
$863$	24.7192	+	42.8148i	0.841450	+	1.45743i	0.888669	+	0.458549i	$0.151631\pi$
$863$	24.7192	+	42.8148i	0.841450	+	1.45743i	−0.0472194	+	0.998885i	$0.515036\pi$
$864$		0			0
$865$	4.08766	−	7.08003i	0.138985	−	0.240728i
$866$		0			0
$867$	29.9927	+	29.9927i	1.01861	+	1.01861i
$868$		0			0
$869$	−48.9443	+	48.9443i	−1.66032	+	1.66032i
$870$		0			0
$871$	−28.6125	−	16.5194i	−0.969497	−	0.559739i
$872$		0			0
$873$	−36.4162	+	21.0249i	−1.23250	+	0.711585i
$874$		0			0
$875$	−19.2977	+	25.5325i	−0.652383	+	0.863156i
$876$		0			0
$877$	−13.9238	+	51.9644i	−0.470174	+	1.75471i	0.168966	+	0.985622i	$0.445957\pi$
$877$	−13.9238	+	51.9644i	−0.470174	+	1.75471i	−0.639140	+	0.769091i	$0.720709\pi$
$878$		0			0
$879$	36.9710	−	64.0357i	1.24700	−	2.15987i
$880$		0			0
$881$	26.2319			0.883776			0.441888	−	0.897070i	$-0.354309\pi$
$881$	26.2319			0.883776			0.441888	+	0.897070i	$0.354309\pi$
$882$		0			0
$883$	12.8278	+	12.8278i	0.431688	+	0.431688i	0.889202	−	0.457514i	$-0.151260\pi$
$883$	12.8278	+	12.8278i	0.431688	+	0.431688i	−0.457514	+	0.889202i	$0.651260\pi$
$884$		0			0
$885$	−0.0372565	−	0.139043i	−0.00125236	−	0.00467388i
$886$		0			0
$887$	−46.3646	+	26.7686i	−1.55677	+	0.898801i	−0.559207	+	0.829028i	$0.688894\pi$
$887$	−46.3646	+	26.7686i	−1.55677	+	0.898801i	−0.997563	+	0.0697733i	$0.977772\pi$
$888$		0			0
$889$	1.54965	+	11.1425i	0.0519736	+	0.373709i
$890$		0			0
$891$	−37.3590	−	10.0103i	−1.25157	−	0.335358i
$892$		0			0
$893$	−2.07752	+	0.556671i	−0.0695217	+	0.0186283i
$894$		0			0
$895$	27.2791			0.911841
$896$		0			0
$897$	5.67918			0.189622
$898$		0			0
$899$	−28.9620	+	7.76035i	−0.965937	+	0.258822i
$900$		0			0
$901$	−0.537752	−	0.144090i	−0.0179151	−	0.00480034i
$902$		0			0
$903$	−67.7664	−	27.4928i	−2.25512	−	0.914903i
$904$		0			0
$905$	23.9400	−	13.8218i	0.795793	−	0.459451i
$906$		0			0
$907$	−9.73321	−	36.3248i	−0.323186	−	1.20615i	−0.916123	−	0.400897i	$-0.868698\pi$
$907$	−9.73321	−	36.3248i	−0.323186	−	1.20615i	0.592937	−	0.805249i	$-0.297968\pi$
$908$		0			0
$909$	−6.62263	−	6.62263i	−0.219659	−	0.219659i
$910$		0			0
$911$	−18.6202			−0.616914			−0.308457	−	0.951238i	$-0.599813\pi$
$911$	−18.6202			−0.616914			−0.308457	+	0.951238i	$0.599813\pi$
$912$		0			0
$913$	38.0563	−	65.9155i	1.25948	−	2.18148i
$914$		0			0
$915$	2.62092	−	9.78142i	0.0866450	−	0.323364i
$916$		0			0
$917$	13.2939	+	1.65168i	0.439002	+	0.0545434i
$918$		0			0
$919$	15.5605	−	8.98389i	0.513295	−	0.296351i	−0.220892	−	0.975298i	$-0.570897\pi$
$919$	15.5605	−	8.98389i	0.513295	−	0.296351i	0.734187	+	0.678947i	$0.237563\pi$
$920$		0			0
$921$	18.8152	+	10.8630i	0.619983	+	0.357947i
$922$		0			0
$923$	7.42679	−	7.42679i	0.244456	−	0.244456i
$924$		0			0
$925$	2.62046	+	2.62046i	0.0861602	+	0.0861602i
$926$		0			0
$927$	−0.155687	+	0.269658i	−0.00511344	+	0.00885674i
$928$		0			0
$929$	−13.1258	−	22.7345i	−0.430642	−	0.745894i	0.566286	−	0.824209i	$-0.308380\pi$
$929$	−13.1258	−	22.7345i	−0.430642	−	0.745894i	−0.996929	+	0.0783141i	$0.975046\pi$
$930$		0			0
$931$	0.0543870	+	3.73048i	0.00178246	+	0.122262i
$932$		0			0
$933$	−39.4104	−	10.5600i	−1.29024	−	0.345719i
$934$		0			0
$935$	−5.25408	−	3.03345i	−0.171827	−	0.0992043i
$936$		0			0
$937$			47.7798i			1.56090i	0.625219	+	0.780449i	$0.285010\pi$
$937$			47.7798i			1.56090i	−0.625219	+	0.780449i	$0.714990\pi$
$938$		0			0
$939$	−31.9775	+	31.9775i	−1.04355	+	1.04355i
$940$		0			0
$941$	−41.8248	+	11.2069i	−1.36345	+	0.365335i	−0.865082	−	0.501630i	$-0.832734\pi$
$941$	−41.8248	+	11.2069i	−1.36345	+	0.365335i	−0.498368	+	0.866966i	$0.666067\pi$
$942$		0			0
$943$	−0.644154	−	1.11571i	−0.0209765	−	0.0363324i
$944$		0			0
$945$	−3.92370	−	5.03701i	−0.127638	−	0.163854i
$946$		0			0
$947$	−4.82935	+	18.0234i	−0.156933	+	0.585681i	0.841999	+	0.539478i	$0.181379\pi$
$947$	−4.82935	+	18.0234i	−0.156933	+	0.585681i	−0.998932	+	0.0462023i	$0.985288\pi$
$948$		0			0
$949$	−10.4666	−	39.0620i	−0.339762	−	1.26801i
$950$		0			0
$951$			39.5932i			1.28390i
$952$		0			0
$953$			33.1972i			1.07536i	0.843148	+	0.537681i	$0.180700\pi$
$953$			33.1972i			1.07536i	−0.843148	+	0.537681i	$0.819300\pi$
$954$		0			0
$955$	4.84652	+	18.0875i	0.156830	+	0.585296i
$956$		0			0
$957$	−13.2903	+	49.6002i	−0.429615	+	1.60335i
$958$		0			0
$959$	0.277374	−	0.683694i	0.00895688	−	0.0220776i
$960$		0			0
$961$	−15.5659	−	26.9609i	−0.502124	−	0.869705i
$962$		0			0
$963$	−49.1118	+	13.1595i	−1.58261	+	0.424058i
$964$		0			0
$965$	26.8517	−	26.8517i	0.864387	−	0.864387i
$966$		0			0
$967$		−	13.2736i		−	0.426850i	−0.976959	−	0.213425i	$-0.931538\pi$
$967$		−	13.2736i		−	0.426850i	0.976959	−	0.213425i	$-0.0684619\pi$
$968$		0			0
$969$	0.693232	+	0.400238i	0.0222698	+	0.0128575i
$970$		0			0
$971$	41.1279	+	11.0202i	1.31986	+	0.353655i	0.848925	−	0.528514i	$-0.177250\pi$
$971$	41.1279	+	11.0202i	1.31986	+	0.353655i	0.470934	+	0.882169i	$0.343917\pi$
$972$		0			0
$973$	−36.1467	−	27.3200i	−1.15881	−	0.875840i
$974$		0			0
$975$	8.00579	+	13.8664i	0.256390	+	0.444081i
$976$		0			0
$977$	−24.4001	+	42.2622i	−0.780628	+	1.35209i	0.150949	+	0.988542i	$0.451767\pi$
$977$	−24.4001	+	42.2622i	−0.780628	+	1.35209i	−0.931577	+	0.363545i	$0.881566\pi$
$978$		0			0
$979$	−14.5076	−	14.5076i	−0.463664	−	0.463664i
$980$		0			0
$981$	−17.0670	+	17.0670i	−0.544907	+	0.544907i
$982$		0			0
$983$	45.9141	+	26.5085i	1.46443	+	0.845491i	0.999212	−	0.0397033i	$-0.0126413\pi$
$983$	45.9141	+	26.5085i	1.46443	+	0.845491i	0.465222	+	0.885194i	$0.345975\pi$
$984$		0			0
$985$	−19.8131	+	11.4391i	−0.631299	+	0.364481i
$986$		0			0
$987$	−16.3977	+	21.6956i	−0.521946	+	0.690578i
$988$		0			0
$989$	−1.22601	+	4.57551i	−0.0389847	+	0.145493i
$990$		0			0
$991$	−6.92839	+	12.0003i	−0.220088	+	0.381203i	−0.954834	−	0.297139i	$-0.903968\pi$
$991$	−6.92839	+	12.0003i	−0.220088	+	0.381203i	0.734747	+	0.678341i	$0.237301\pi$
$992$		0			0
$993$	38.7162			1.22862
$994$		0			0
$995$	3.71531	+	3.71531i	0.117783	+	0.117783i
$996$		0			0
$997$	−6.93196	−	25.8704i	−0.219537	−	0.819325i	−0.984520	−	0.175273i	$-0.943919\pi$
$997$	−6.93196	−	25.8704i	−0.219537	−	0.819325i	0.764982	−	0.644051i	$-0.222748\pi$
$998$		0			0
$999$	−3.24152	+	1.87149i	−0.102557	+	0.0592114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.ba.c.81.11		48
4.3	odd	2		112.2.w.c.109.11	yes	48
7.2	even	3	inner	448.2.ba.c.401.2		48
8.3	odd	2		896.2.ba.f.417.11		48
8.5	even	2		896.2.ba.e.417.2		48
16.3	odd	4		896.2.ba.f.865.2		48
16.5	even	4	inner	448.2.ba.c.305.2		48
16.11	odd	4		112.2.w.c.53.6	yes	48
16.13	even	4		896.2.ba.e.865.11		48
28.3	even	6		784.2.m.k.589.3		24
28.11	odd	6		784.2.m.j.589.3		24
28.19	even	6		784.2.x.o.765.6		48
28.23	odd	6		112.2.w.c.93.6	yes	48
28.27	even	2		784.2.x.o.557.11		48
56.37	even	6		896.2.ba.e.289.11		48
56.51	odd	6		896.2.ba.f.289.2		48
112.11	odd	12		784.2.m.j.197.3		24
112.27	even	4		784.2.x.o.165.6		48
112.37	even	12	inner	448.2.ba.c.177.11		48
112.51	odd	12		896.2.ba.f.737.11		48
112.59	even	12		784.2.m.k.197.3		24
112.75	even	12		784.2.x.o.373.11		48
112.93	even	12		896.2.ba.e.737.2		48
112.107	odd	12		112.2.w.c.37.11	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.11	✓	48	112.107	odd	12
112.2.w.c.53.6	yes	48	16.11	odd	4
112.2.w.c.93.6	yes	48	28.23	odd	6
112.2.w.c.109.11	yes	48	4.3	odd	2
448.2.ba.c.81.11		48	1.1	even	1	trivial
448.2.ba.c.177.11		48	112.37	even	12	inner
448.2.ba.c.305.2		48	16.5	even	4	inner
448.2.ba.c.401.2		48	7.2	even	3	inner
784.2.m.j.197.3		24	112.11	odd	12
784.2.m.j.589.3		24	28.11	odd	6
784.2.m.k.197.3		24	112.59	even	12
784.2.m.k.589.3		24	28.3	even	6
784.2.x.o.165.6		48	112.27	even	4
784.2.x.o.373.11		48	112.75	even	12
784.2.x.o.557.11		48	28.27	even	2
784.2.x.o.765.6		48	28.19	even	6
896.2.ba.e.289.11		48	56.37	even	6
896.2.ba.e.417.2		48	8.5	even	2
896.2.ba.e.737.2		48	112.93	even	12
896.2.ba.e.865.11		48	16.13	even	4
896.2.ba.f.289.2		48	56.51	odd	6
896.2.ba.f.417.11		48	8.3	odd	2
896.2.ba.f.737.11		48	112.51	odd	12
896.2.ba.f.865.2		48	16.3	odd	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.46036 - 0.659252i) q^{3} +(1.87532 + 0.502490i) q^{5} +(-0.364450 - 2.62053i) q^{7} +(3.02070 - 1.74400i) q^{9} +(1.37168 + 5.11917i) q^{11} +(-3.61173 - 3.61173i) q^{13} +4.94523 q^{15} +(-0.294815 + 0.510634i) q^{17} +(0.137946 - 0.514822i) q^{19} +(-2.62427 - 6.20719i) q^{21} +(-0.378033 + 0.218258i) q^{23} +(-1.06581 - 0.615344i) q^{25} +(0.878939 - 0.878939i) q^{27} +(2.68976 + 2.68976i) q^{29} +(-3.94118 + 6.82633i) q^{31} +(6.74965 + 11.6907i) q^{33} +(0.633329 - 5.09746i) q^{35} +(-2.90863 - 0.779365i) q^{37} +(-11.2672 - 6.50513i) q^{39} +2.95135i q^{41} +(7.67329 - 7.67329i) q^{43} +(6.54110 - 1.75268i) q^{45} +(-2.01771 - 3.49478i) q^{47} +(-6.73435 + 1.91011i) q^{49} +(-0.388715 + 1.45070i) q^{51} +(0.244374 + 0.912017i) q^{53} +10.2893i q^{55} -1.35759i q^{57} +(-0.00753382 - 0.0281166i) q^{59} +(0.529990 - 1.97795i) q^{61} +(-5.67110 - 7.28022i) q^{63} +(-4.95829 - 8.58801i) q^{65} +(6.24795 - 1.67413i) q^{67} +(-0.786212 + 0.786212i) q^{69} +2.05630i q^{71} +(6.85664 + 3.95868i) q^{73} +(-3.02794 - 0.811334i) q^{75} +(12.9150 - 5.46021i) q^{77} +(6.53028 + 11.3108i) q^{79} +(-3.64893 + 6.32013i) q^{81} +(-10.1551 - 10.1551i) q^{83} +(-0.809460 + 0.809460i) q^{85} +(8.39101 + 4.84455i) q^{87} +(-3.35262 + 1.93564i) q^{89} +(-8.14836 + 10.7810i) q^{91} +(-5.19647 + 19.3935i) q^{93} +(0.517385 - 0.896137i) q^{95} -12.0556 q^{97} +(13.0712 + 13.0712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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