LMFDB - Embedded newform 896.2.ba.e.417.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(289,896)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("896.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.15459602111$
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			417.2
Character	$\chi$	$=$	896.417
Dual form			896.2.ba.e.737.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46036 + 0.659252i) q^{3} +(-1.87532 - 0.502490i) q^{5} +(-0.364450 - 2.62053i) q^{7} +(3.02070 - 1.74400i) q^{9} +O(q^{10})$	\(q+(-2.46036 + 0.659252i) q^{3} +(-1.87532 - 0.502490i) q^{5} +(-0.364450 - 2.62053i) q^{7} +(3.02070 - 1.74400i) q^{9} +(-1.37168 - 5.11917i) q^{11} +(3.61173 + 3.61173i) q^{13} +4.94523 q^{15} +(-0.294815 + 0.510634i) q^{17} +(-0.137946 + 0.514822i) q^{19} +(2.62427 + 6.20719i) q^{21} +(-0.378033 + 0.218258i) q^{23} +(-1.06581 - 0.615344i) q^{25} +(-0.878939 + 0.878939i) q^{27} +(-2.68976 - 2.68976i) q^{29} +(-3.94118 + 6.82633i) q^{31} +(6.74965 + 11.6907i) q^{33} +(-0.633329 + 5.09746i) q^{35} +(2.90863 + 0.779365i) q^{37} +(-11.2672 - 6.50513i) q^{39} +2.95135i q^{41} +(-7.67329 + 7.67329i) q^{43} +(-6.54110 + 1.75268i) q^{45} +(-2.01771 - 3.49478i) q^{47} +(-6.73435 + 1.91011i) q^{49} +(0.388715 - 1.45070i) q^{51} +(-0.244374 - 0.912017i) q^{53} +10.2893i q^{55} -1.35759i q^{57} +(0.00753382 + 0.0281166i) q^{59} +(-0.529990 + 1.97795i) q^{61} +(-5.67110 - 7.28022i) q^{63} +(-4.95829 - 8.58801i) q^{65} +(-6.24795 + 1.67413i) q^{67} +(0.786212 - 0.786212i) q^{69} +2.05630i q^{71} +(6.85664 + 3.95868i) q^{73} +(3.02794 + 0.811334i) q^{75} +(-12.9150 + 5.46021i) q^{77} +(6.53028 + 11.3108i) q^{79} +(-3.64893 + 6.32013i) q^{81} +(10.1551 + 10.1551i) q^{83} +(0.809460 - 0.809460i) q^{85} +(8.39101 + 4.84455i) q^{87} +(-3.35262 + 1.93564i) q^{89} +(8.14836 - 10.7810i) q^{91} +(5.19647 - 19.3935i) q^{93} +(0.517385 - 0.896137i) q^{95} -12.0556 q^{97} +(-13.0712 - 13.0712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5}+O(q^{10}) $ 48 * q - 4 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.885658	−	0.464338i	$-0.846292\pi$
$3$	−2.46036	+	0.659252i	−1.42049	+	0.380619i	−0.534833	+	0.844958i	$0.679626\pi$
$4$		0			0
$5$	−1.87532	−	0.502490i	−0.838668	−	0.224720i	−0.186176	−	0.982516i	$-0.559609\pi$
$5$	−1.87532	−	0.502490i	−0.838668	−	0.224720i	−0.652491	+	0.757796i	$0.726276\pi$
$6$		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	$-0.788713\pi$
$11$	−1.37168	−	5.11917i	−0.413576	−	1.54349i	0.374094	−	0.927391i	$-0.377954\pi$
$12$		0			0
$13$	3.61173	+	3.61173i	1.00171	+	1.00171i	0.999999	+	0.00171617i	$0.000546274\pi$
$13$	3.61173	+	3.61173i	1.00171	+	1.00171i	0.00171617	+	0.999999i	$0.499454\pi$
$14$		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	−0.979942	−	0.199281i	$-0.936139\pi$
$19$	−0.137946	+	0.514822i	−0.0316470	+	0.118108i	0.948295	+	0.317389i	$0.102806\pi$
$20$		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	0.411799	−	0.911275i	$-0.364901\pi$
$29$	−2.68976	−	2.68976i	−0.499476	−	0.499476i	−0.911275	+	0.411799i	$0.864901\pi$
$30$		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	0.489853	−	0.871805i	$-0.337050\pi$
$37$	2.90863	+	0.779365i	0.478176	+	0.128127i	−0.0116774	+	0.999932i	$0.503717\pi$
$38$		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	$0.560199\pi$
$43$	−7.67329	+	7.67329i	−1.17017	+	1.17017i	−0.982170	+	0.187996i	$0.939801\pi$
$44$		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	0.947109	−	0.320912i	$-0.103989\pi$
$53$	−0.244374	−	0.912017i	−0.0335674	−	0.125275i	−0.980676	+	0.195637i	$0.937323\pi$
$54$		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	0.966415	−	0.256988i	$-0.0827302\pi$
$59$	0.00753382	+	0.0281166i	0.000980820	+	0.00366047i	−0.965434	+	0.260649i	$0.916064\pi$
$60$		0			0
$61$	−0.529990	+	1.97795i	−0.0678583	+	0.253251i	−0.991519	−	0.129960i	$-0.958515\pi$
$61$	−0.529990	+	1.97795i	−0.0678583	+	0.253251i	0.923661	+	0.383211i	$0.125182\pi$
$62$		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	−0.619414	−	0.785065i	$-0.712630\pi$
$67$	−6.24795	+	1.67413i	−0.763309	+	0.204528i	−0.143895	+	0.989593i	$0.545963\pi$
$68$		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	$0.0389824\pi$
$83$	10.1551	+	10.1551i	1.11467	+	1.11467i	0.122161	+	0.992510i	$0.461018\pi$
$84$		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	0.991844	−	0.127460i	$-0.0406824\pi$
$101$	0.694969	+	2.59366i	0.0691520	+	0.258079i	−0.922692	+	0.385539i	$0.874016\pi$
$102$		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	0.864252	−	0.503059i	$-0.167792\pi$
$107$	14.0802	+	3.77279i	1.36119	+	0.364729i	0.496935	+	0.867788i	$0.334459\pi$
$108$		0			0
$109$	6.68404	−	1.79098i	0.640215	−	0.171545i	0.0759141	−	0.997114i	$-0.475813\pi$
$109$	6.68404	−	1.79098i	0.640215	−	0.171545i	0.564301	+	0.825569i	$0.309146\pi$
$110$		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	−0.884753	−	0.466060i	$-0.845673\pi$
$131$	1.31046	−	4.89071i	0.114496	−	0.427304i	0.999249	+	0.0387565i	$0.0123397\pi$
$132$		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	$0.508753\pi$
$139$	−12.1095	+	12.1095i	−1.02712	+	1.02712i	−0.999622	+	0.0274943i	$0.991247\pi$
$140$		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	−0.754417	−	0.656396i	$-0.772080\pi$
$149$	−21.1901	−	5.67786i	−1.73596	−	0.465149i	−0.981542	+	0.191247i	$0.938747\pi$
$150$		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	0.221007	−	0.975272i	$-0.429066\pi$
$157$	11.2775	−	3.02179i	0.900040	−	0.241165i	0.679034	+	0.734107i	$0.262399\pi$
$158$		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	$-0.720024\pi$
$163$	3.82793	−	14.2860i	0.299826	−	1.11897i	0.937308	−	0.348502i	$-0.113310\pi$
$164$		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	−0.994900	−	0.100862i	$-0.967840\pi$
$173$	−1.08986	+	4.06740i	−0.0828603	+	0.309239i	0.912040	+	0.410101i	$0.134507\pi$
$174$		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	−0.727474	−	0.686135i	$-0.759306\pi$
$179$	−13.5720	+	3.63660i	−1.01442	+	0.271812i	−0.286943	+	0.957948i	$0.592639\pi$
$180$		0			0
$181$	−10.0681	+	10.0681i	−0.748356	+	0.748356i	−0.974170	−	0.225814i	$-0.927496\pi$
$181$	−10.0681	+	10.0681i	−0.748356	+	0.748356i	0.225814	+	0.974170i	$0.427496\pi$
$182$		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	−0.344953	−	0.938620i	$-0.612105\pi$
$197$	8.33252	−	8.33252i	0.593668	−	0.593668i	0.938620	+	0.344953i	$0.112105\pi$
$198$		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	0.986834	−	0.161734i	$-0.0517087\pi$
$211$	11.9853	+	11.9853i	0.825100	+	0.825100i	−0.161734	+	0.986834i	$0.551709\pi$
$212$		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	−0.808738	−	0.588170i	$-0.799849\pi$
$227$	−18.3064	+	4.90519i	−1.21504	+	0.325569i	−0.406303	+	0.913739i	$0.633182\pi$
$228$		0			0
$229$	−25.1003	−	6.72559i	−1.65867	−	0.444440i	−0.696650	−	0.717412i	$-0.745327\pi$
$229$	−25.1003	−	6.72559i	−1.65867	−	0.444440i	−0.962022	+	0.272972i	$0.911993\pi$
$230$		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	−0.951103	−	0.308875i	$-0.900048\pi$
$251$	−10.1748	+	10.1748i	−0.642228	+	0.642228i	0.308875	+	0.951103i	$0.400048\pi$
$252$		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	−0.904380	−	0.426728i	$-0.859666\pi$
$269$	−24.1792	+	6.47880i	−1.47423	+	0.395019i	−0.569852	+	0.821747i	$0.693000\pi$
$270$		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	$0.111524\pi$
$277$	4.95063	+	18.4760i	0.297455	+	1.11012i	−0.641793	+	0.766878i	$0.721809\pi$
$278$		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	$0.166044\pi$
$283$	6.14544	+	22.9351i	0.365309	+	1.36335i	−0.501693	+	0.865046i	$0.667289\pi$
$284$		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	$0.572166\pi$
$293$	−20.5268	+	20.5268i	−1.19919	+	1.19919i	−0.974410	+	0.224778i	$0.927834\pi$
$294$		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	0.513730	−	0.857952i	$-0.328263\pi$
$307$	−6.03127	−	6.03127i	−0.344223	−	0.344223i	−0.857952	+	0.513730i	$0.828263\pi$
$308$		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	$-0.772877\pi$
$317$	4.02311	−	15.0144i	0.225960	−	0.843295i	0.982018	−	0.188790i	$-0.0604565\pi$
$318$		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	−0.168338	−	0.985729i	$-0.553840\pi$
$331$	−14.6818	−	3.93399i	−0.806987	−	0.216232i	−0.638649	+	0.769498i	$0.720507\pi$
$332$		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	0.910119	−	0.414348i	$-0.135990\pi$
$347$	−1.58787	−	5.92600i	−0.0852412	−	0.318125i	−0.995360	+	0.0962234i	$0.969324\pi$
$348$		0			0
$349$	2.94202	+	2.94202i	0.157483	+	0.157483i	0.781450	−	0.623968i	$-0.214480\pi$
$349$	2.94202	+	2.94202i	0.157483	+	0.157483i	−0.623968	+	0.781450i	$0.714480\pi$
$350$		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	0.685587	−	0.727990i	$-0.259545\pi$
$373$	17.6779	+	4.73679i	0.915328	+	0.245261i	0.229741	+	0.973252i	$0.426212\pi$
$374$		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	−0.661628	−	0.749833i	$-0.730134\pi$
$379$	1.71717	−	1.71717i	0.0882050	−	0.0882050i	0.749833	+	0.661628i	$0.230134\pi$
$380$		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	$-0.953640\pi$
$389$	−4.04561	−	15.0984i	−0.205120	−	0.765520i	0.784292	−	0.620391i	$-0.213026\pi$
$390$		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	−0.941741	−	0.336340i	$-0.890811\pi$
$397$	0.836855	−	3.12318i	0.0420005	−	0.156748i	0.983741	+	0.179592i	$0.0574776\pi$
$398$		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	0.768276	−	0.640119i	$-0.221115\pi$
$419$	2.62329	+	2.62329i	0.128156	+	0.128156i	−0.640119	+	0.768276i	$0.721115\pi$
$420$		0			0
$421$	3.44059	−	3.44059i	0.167684	−	0.167684i	−0.618276	−	0.785961i	$-0.712169\pi$
$421$	3.44059	−	3.44059i	0.167684	−	0.167684i	0.785961	+	0.618276i	$0.212169\pi$
$422$		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	−0.0828461	−	0.996562i	$-0.526401\pi$
$443$	−13.7414	−	3.68200i	−0.652874	−	0.174937i	−0.570028	+	0.821625i	$0.693068\pi$
$444$		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	0.418296	−	0.908311i	$-0.362628\pi$
$461$	−10.5211	−	10.5211i	−0.490015	−	0.490015i	−0.908311	+	0.418296i	$0.862628\pi$
$462$		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	−0.883479	−	0.468472i	$-0.844805\pi$
$467$	2.50402	−	9.34512i	0.115872	−	0.432440i	0.999351	+	0.0360311i	$0.0114715\pi$
$468$		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	−0.440864	−	0.897574i	$-0.645328\pi$
$491$	10.1200	−	10.1200i	0.456710	−	0.456710i	0.897574	+	0.440864i	$0.145328\pi$
$492$		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	$0.224578\pi$
$499$	−4.96424	+	18.5268i	−0.222230	+	0.829373i	−0.983495	+	0.180933i	$0.942088\pi$
$500$		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	−0.952080	−	0.305849i	$-0.901060\pi$
$509$	0.572369	−	2.13611i	0.0253698	−	0.0946814i	0.977450	+	0.211167i	$0.0677265\pi$
$510$		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	0.118258	−	0.992983i	$-0.462269\pi$
$523$	−6.30777	−	1.69016i	−0.275819	−	0.0739056i	−0.394077	+	0.919077i	$0.628936\pi$
$524$		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	−0.918017	−	0.396542i	$-0.870210\pi$
$541$	1.75097	−	6.53469i	0.0752799	−	0.280948i	0.993297	+	0.115593i	$0.0368769\pi$
$542$		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	0.667898	−	0.744253i	$-0.267194\pi$
$547$	−1.78581	−	1.78581i	−0.0763555	−	0.0763555i	−0.744253	+	0.667898i	$0.767194\pi$
$548$		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	−0.329503	−	0.944155i	$-0.606881\pi$
$557$	−3.36982	+	0.902940i	−0.142784	+	0.0382588i	0.186719	+	0.982413i	$0.440215\pi$
$558$		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	0.669893	−	0.742458i	$-0.266340\pi$
$563$	38.4688	−	10.3077i	1.62127	−	0.434417i	0.951373	+	0.308041i	$0.0996734\pi$
$564$		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	$0.0910433\pi$
$571$	6.44226	+	24.0429i	0.269600	+	1.00616i	−0.689774	+	0.724025i	$0.742290\pi$
$572$		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	−0.843896	−	0.536507i	$-0.819744\pi$
$587$	−7.44744	+	7.44744i	−0.307389	+	0.307389i	0.536507	+	0.843896i	$0.319744\pi$
$588$		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	$-0.983377\pi$
$613$	−3.95872	−	14.7741i	−0.159891	−	0.596722i	0.838746	−	0.544523i	$-0.183289\pi$
$614$		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	0.932318	−	0.361639i	$-0.117783\pi$
$619$	−1.39109	−	5.19162i	−0.0559127	−	0.208669i	−0.988231	+	0.152970i	$0.951116\pi$
$620$		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	0.172135	−	0.985073i	$-0.444934\pi$
$643$	−20.6140	−	20.6140i	−0.812939	−	0.812939i	−0.985073	+	0.172135i	$0.944934\pi$
$644$		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	$0.368467\pi$
$653$	−10.3267	+	38.5399i	−0.404117	+	1.50818i	−0.805679	+	0.592353i	$0.798199\pi$
$654$		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	0.565205	−	0.824951i	$-0.308797\pi$
$659$	−6.66795	−	6.66795i	−0.259746	−	0.259746i	−0.824951	+	0.565205i	$0.808797\pi$
$660$		0			0
$661$	−0.649564	−	2.42421i	−0.0252651	−	0.0942907i	0.952142	−	0.305656i	$-0.0988757\pi$
$661$	−0.649564	−	2.42421i	−0.0252651	−	0.0942907i	−0.977407	+	0.211365i	$0.932209\pi$
$662$		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	−0.0808713	−	0.996725i	$-0.525770\pi$
$677$	−16.8935	−	4.52660i	−0.649270	−	0.173971i	−0.568399	+	0.822753i	$0.692437\pi$
$678$		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	$-0.863895\pi$
$683$	−8.60472	−	32.1132i	−0.329250	−	1.22878i	0.580719	−	0.814104i	$-0.302771\pi$
$684$		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	$-0.825499\pi$
$691$	3.84416	−	14.3466i	0.146239	−	0.545771i	0.999697	−	0.0246098i	$-0.00783432\pi$
$692$		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	0.984249	−	0.176785i	$-0.0565698\pi$
$701$	21.3787	+	21.3787i	0.807464	+	0.807464i	−0.176785	+	0.984249i	$0.556570\pi$
$702$		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	0.500452	−	0.865764i	$-0.333167\pi$
$709$	13.3395	+	3.57430i	0.500974	+	0.134236i	0.000522056		1.00000i	$0.499834\pi$
$710$		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	$0.355047\pi$
$733$	−10.5622	+	39.4186i	−0.390123	+	1.45596i	−0.829930	+	0.557868i	$0.811620\pi$
$734$		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	−0.454229	−	0.890885i	$-0.650085\pi$
$739$	−10.9326	+	2.92937i	−0.402161	+	0.107759i	0.0520685	+	0.998644i	$0.483419\pi$
$740$		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	$-0.491025\pi$
$757$	28.2783	−	28.2783i	1.02779	−	1.02779i	0.999603	−	0.0281911i	$-0.00897468\pi$
$758$		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	$-0.952601\pi$
$773$	−5.74604	−	21.4445i	−0.206671	−	0.771305i	0.782263	−	0.622948i	$-0.214065\pi$
$774$		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	0.0932471	−	0.995643i	$-0.470275\pi$
$787$	18.8470	−	5.05004i	0.671823	−	0.180014i	0.578576	+	0.815629i	$0.303609\pi$
$788$		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	0.750730	−	0.660609i	$-0.229702\pi$
$797$	2.54421	+	2.54421i	0.0901206	+	0.0901206i	−0.660609	+	0.750730i	$0.729702\pi$
$798$		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	$-0.460957\pi$
$811$	31.7484	−	31.7484i	1.11484	−	1.11484i	0.992487	−	0.122349i	$-0.0390426\pi$
$812$		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	−0.683008	−	0.730411i	$-0.739329\pi$
$821$	−46.9829	−	12.5890i	−1.63972	−	0.439361i	−0.956708	+	0.291050i	$0.905995\pi$
$822$		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	−0.409025	−	0.912523i	$-0.634131\pi$
$827$	14.4794	−	14.4794i	0.503498	−	0.503498i	0.912523	+	0.409025i	$0.134131\pi$
$828$		0			0
$829$	1.38085	−	0.369998i	0.0479589	−	0.0128505i	−0.234760	−	0.972053i	$-0.575430\pi$
$829$	1.38085	−	0.369998i	0.0479589	−	0.0128505i	0.282719	+	0.959203i	$0.408764\pi$
$830$		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	$-0.434294\pi$
$853$	34.5722	−	34.5722i	1.18373	−	1.18373i	0.978770	−	0.204960i	$-0.0657064\pi$
$854$		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	0.467543	−	0.883970i	$-0.345139\pi$
$859$	12.6163	+	3.38053i	0.430463	+	0.115342i	−0.0370807	+	0.999312i	$0.511806\pi$
$860$		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	$-0.554043\pi$
$877$	13.9238	−	51.9644i	0.470174	−	1.75471i	0.639140	−	0.769091i	$-0.279291\pi$
$878$		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	0.457514	−	0.889202i	$-0.348740\pi$
$883$	−12.8278	−	12.8278i	−0.431688	−	0.431688i	−0.889202	+	0.457514i	$0.848740\pi$
$884$		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	$0.131302\pi$
$907$	9.73321	+	36.3248i	0.323186	+	1.20615i	−0.592937	+	0.805249i	$0.702032\pi$
$908$		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	0.498368	−	0.866966i	$-0.333933\pi$
$941$	41.8248	−	11.2069i	1.36345	−	0.365335i	0.865082	+	0.501630i	$0.167266\pi$
$942$		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	$-0.818621\pi$
$947$	4.82935	−	18.0234i	0.156933	−	0.585681i	0.998932	−	0.0462023i	$-0.0147119\pi$
$948$		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	−0.470934	−	0.882169i	$-0.656083\pi$
$971$	−41.1279	−	11.0202i	−1.31986	−	0.353655i	−0.848925	+	0.528514i	$0.822750\pi$
$972$		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	$0.0560809\pi$
$997$	6.93196	+	25.8704i	0.219537	+	0.819325i	−0.764982	+	0.644051i	$0.777252\pi$
$998$		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	896.2.ba.e.417.2		48
4.3	odd	2		896.2.ba.f.417.11		48
7.2	even	3	inner	896.2.ba.e.289.11		48
8.3	odd	2		112.2.w.c.109.11	yes	48
8.5	even	2		448.2.ba.c.81.11		48
16.3	odd	4		112.2.w.c.53.6	yes	48
16.5	even	4	inner	896.2.ba.e.865.11		48
16.11	odd	4		896.2.ba.f.865.2		48
16.13	even	4		448.2.ba.c.305.2		48
28.23	odd	6		896.2.ba.f.289.2		48
56.3	even	6		784.2.m.k.589.3		24
56.11	odd	6		784.2.m.j.589.3		24
56.19	even	6		784.2.x.o.765.6		48
56.27	even	2		784.2.x.o.557.11		48
56.37	even	6		448.2.ba.c.401.2		48
56.51	odd	6		112.2.w.c.93.6	yes	48
112.3	even	12		784.2.m.k.197.3		24
112.19	even	12		784.2.x.o.373.11		48
112.37	even	12	inner	896.2.ba.e.737.2		48
112.51	odd	12		112.2.w.c.37.11	✓	48
112.67	odd	12		784.2.m.j.197.3		24
112.83	even	4		784.2.x.o.165.6		48
112.93	even	12		448.2.ba.c.177.11		48
112.107	odd	12		896.2.ba.f.737.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.11	✓	48	112.51	odd	12
112.2.w.c.53.6	yes	48	16.3	odd	4
112.2.w.c.93.6	yes	48	56.51	odd	6
112.2.w.c.109.11	yes	48	8.3	odd	2
448.2.ba.c.81.11		48	8.5	even	2
448.2.ba.c.177.11		48	112.93	even	12
448.2.ba.c.305.2		48	16.13	even	4
448.2.ba.c.401.2		48	56.37	even	6
784.2.m.j.197.3		24	112.67	odd	12
784.2.m.j.589.3		24	56.11	odd	6
784.2.m.k.197.3		24	112.3	even	12
784.2.m.k.589.3		24	56.3	even	6
784.2.x.o.165.6		48	112.83	even	4
784.2.x.o.373.11		48	112.19	even	12
784.2.x.o.557.11		48	56.27	even	2
784.2.x.o.765.6		48	56.19	even	6
896.2.ba.e.289.11		48	7.2	even	3	inner
896.2.ba.e.417.2		48	1.1	even	1	trivial
896.2.ba.e.737.2		48	112.37	even	12	inner
896.2.ba.e.865.11		48	16.5	even	4	inner
896.2.ba.f.289.2		48	28.23	odd	6
896.2.ba.f.417.11		48	4.3	odd	2
896.2.ba.f.737.11		48	112.107	odd	12
896.2.ba.f.865.2		48	16.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.46036 + 0.659252i) q^{3} +(-1.87532 - 0.502490i) q^{5} +(-0.364450 - 2.62053i) q^{7} +(3.02070 - 1.74400i) q^{9} +O(q^{10})\)	\(q+(-2.46036 + 0.659252i) q^{3} +(-1.87532 - 0.502490i) q^{5} +(-0.364450 - 2.62053i) q^{7} +(3.02070 - 1.74400i) q^{9} +(-1.37168 - 5.11917i) q^{11} +(3.61173 + 3.61173i) q^{13} +4.94523 q^{15} +(-0.294815 + 0.510634i) q^{17} +(-0.137946 + 0.514822i) q^{19} +(2.62427 + 6.20719i) q^{21} +(-0.378033 + 0.218258i) q^{23} +(-1.06581 - 0.615344i) q^{25} +(-0.878939 + 0.878939i) q^{27} +(-2.68976 - 2.68976i) q^{29} +(-3.94118 + 6.82633i) q^{31} +(6.74965 + 11.6907i) q^{33} +(-0.633329 + 5.09746i) q^{35} +(2.90863 + 0.779365i) q^{37} +(-11.2672 - 6.50513i) q^{39} +2.95135i q^{41} +(-7.67329 + 7.67329i) q^{43} +(-6.54110 + 1.75268i) q^{45} +(-2.01771 - 3.49478i) q^{47} +(-6.73435 + 1.91011i) q^{49} +(0.388715 - 1.45070i) q^{51} +(-0.244374 - 0.912017i) q^{53} +10.2893i q^{55} -1.35759i q^{57} +(0.00753382 + 0.0281166i) q^{59} +(-0.529990 + 1.97795i) q^{61} +(-5.67110 - 7.28022i) q^{63} +(-4.95829 - 8.58801i) q^{65} +(-6.24795 + 1.67413i) q^{67} +(0.786212 - 0.786212i) q^{69} +2.05630i q^{71} +(6.85664 + 3.95868i) q^{73} +(3.02794 + 0.811334i) q^{75} +(-12.9150 + 5.46021i) q^{77} +(6.53028 + 11.3108i) q^{79} +(-3.64893 + 6.32013i) q^{81} +(10.1551 + 10.1551i) q^{83} +(0.809460 - 0.809460i) q^{85} +(8.39101 + 4.84455i) q^{87} +(-3.35262 + 1.93564i) q^{89} +(8.14836 - 10.7810i) q^{91} +(5.19647 - 19.3935i) q^{93} +(0.517385 - 0.896137i) q^{95} -12.0556 q^{97} +(-13.0712 - 13.0712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5}+O(q^{10}) \) 48 * q - 4 * q^5	\( 48 q - 4 q^{5} - 4 q^{11} + 24 q^{13} + 40 q^{15} + 8 q^{17} - 4 q^{19} + 8 q^{21} - 24 q^{27} - 24 q^{29} - 28 q^{31} + 16 q^{33} + 28 q^{35} + 24 q^{37} - 40 q^{43} + 28 q^{45} + 20 q^{47} + 24 q^{51} + 16 q^{53} - 20 q^{59} - 8 q^{61} + 16 q^{63} + 8 q^{65} + 48 q^{67} + 40 q^{69} - 4 q^{75} + 20 q^{77} + 36 q^{79} - 8 q^{83} + 64 q^{91} - 8 q^{93} + 4 q^{95} - 48 q^{97} - 24 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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