LMFDB - Embedded newform 912.2.cc.d.737.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))

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

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

chi := DirichletCharacter("912.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			737.3
Root			$-0.363139 + 1.69356i$ of defining polynomial
Character	$\chi$	$=$	912.737
Dual form			912.2.cc.d.641.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64823 + 0.532290i) q^{3} +(2.20556 + 2.62849i) q^{5} +(-1.68651 + 2.92113i) q^{7} +(2.43333 + 1.75467i) q^{9} +O(q^{10})$	\(q+(1.64823 + 0.532290i) q^{3} +(2.20556 + 2.62849i) q^{5} +(-1.68651 + 2.92113i) q^{7} +(2.43333 + 1.75467i) q^{9} +(2.33635 - 1.34889i) q^{11} +(-5.05419 - 0.891189i) q^{13} +(2.23616 + 5.50635i) q^{15} +(1.44531 - 3.97095i) q^{17} +(2.73048 + 3.39772i) q^{19} +(-4.33465 + 3.91698i) q^{21} +(1.69398 - 2.01881i) q^{23} +(-1.17620 + 6.67054i) q^{25} +(3.07670 + 4.18735i) q^{27} +(-3.54249 + 1.28936i) q^{29} +(-4.78254 - 2.76120i) q^{31} +(4.56886 - 0.979673i) q^{33} +(-11.3979 + 2.00975i) q^{35} -5.17636i q^{37} +(-7.85610 - 4.15918i) q^{39} +(-0.289735 - 1.64317i) q^{41} +(-1.85806 + 1.55910i) q^{43} +(0.754733 + 10.2660i) q^{45} +(0.0440069 + 0.120908i) q^{47} +(-2.18866 - 3.79087i) q^{49} +(4.49590 - 5.77572i) q^{51} +(6.53342 + 5.48219i) q^{53} +(8.69853 + 3.16600i) q^{55} +(2.69188 + 7.05363i) q^{57} +(3.87665 + 1.41099i) q^{59} +(3.53369 + 2.96512i) q^{61} +(-9.22948 + 4.14880i) q^{63} +(-8.80484 - 15.2504i) q^{65} +(-3.81629 - 10.4852i) q^{67} +(3.86667 - 2.42578i) q^{69} +(9.91131 - 8.31658i) q^{71} +(-0.414656 - 2.35163i) q^{73} +(-5.48930 + 10.3685i) q^{75} +9.09972i q^{77} +(-2.22246 + 0.391880i) q^{79} +(2.84224 + 8.53942i) q^{81} +(6.27861 + 3.62496i) q^{83} +(13.6253 - 4.95920i) q^{85} +(-6.52515 + 0.239533i) q^{87} +(-0.209662 + 1.18905i) q^{89} +(11.1272 - 13.2609i) q^{91} +(-6.41298 - 7.09680i) q^{93} +(-2.90863 + 14.6709i) q^{95} +(3.13271 - 8.60706i) q^{97} +(8.05200 + 0.817228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) $ 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.64823	+	0.532290i	0.951607	+	0.307318i
$3$	1.64823	+	0.532290i	0.951607	+	0.307318i
$4$		0			0
$5$	2.20556	+	2.62849i	0.986357	+	1.17549i	0.984480	+	0.175496i	$0.0561531\pi$
$5$	2.20556	+	2.62849i	0.986357	+	1.17549i	0.00187711	+	0.999998i	$0.499402\pi$
$6$		0			0
$7$	−1.68651	+	2.92113i	−0.637442	+	1.10408i	0.348550	+	0.937290i	$0.386674\pi$
$7$	−1.68651	+	2.92113i	−0.637442	+	1.10408i	−0.985992	+	0.166792i	$0.946659\pi$
$8$		0			0
$9$	2.43333	+	1.75467i	0.811112	+	0.584891i
$10$		0			0
$11$	2.33635	−	1.34889i	0.704437	−	0.406707i	−0.104561	−	0.994519i	$-0.533344\pi$
$11$	2.33635	−	1.34889i	0.704437	−	0.406707i	0.808998	+	0.587811i	$0.200010\pi$
$12$		0			0
$13$	−5.05419	−	0.891189i	−1.40178	−	0.247171i	−0.578905	−	0.815395i	$-0.696520\pi$
$13$	−5.05419	−	0.891189i	−1.40178	−	0.247171i	−0.822874	+	0.568224i	$0.807631\pi$
$14$		0			0
$15$	2.23616	+	5.50635i	0.577374	+	1.42173i
$16$		0			0
$17$	1.44531	−	3.97095i	0.350538	−	0.963096i	−0.631659	−	0.775246i	$-0.717626\pi$
$17$	1.44531	−	3.97095i	0.350538	−	0.963096i	0.982198	−	0.187850i	$-0.0601520\pi$
$18$		0			0
$19$	2.73048	+	3.39772i	0.626414	+	0.779490i
$19$	2.73048	+	3.39772i	0.626414	+	0.779490i
$20$		0			0
$21$	−4.33465	+	3.91698i	−0.945899	+	0.854755i
$22$		0			0
$23$	1.69398	−	2.01881i	0.353220	−	0.420951i	−0.559952	−	0.828525i	$-0.689181\pi$
$23$	1.69398	−	2.01881i	0.353220	−	0.420951i	0.913172	+	0.407574i	$0.133625\pi$
$24$		0			0
$25$	−1.17620	+	6.67054i	−0.235239	+	1.33411i
$26$		0			0
$27$	3.07670	+	4.18735i	0.592112	+	0.805856i
$28$		0			0
$29$	−3.54249	+	1.28936i	−0.657823	+	0.239428i	−0.649296	−	0.760536i	$-0.724936\pi$
$29$	−3.54249	+	1.28936i	−0.657823	+	0.239428i	−0.00852691	+	0.999964i	$0.502714\pi$
$30$		0			0
$31$	−4.78254	−	2.76120i	−0.858970	−	0.495927i	0.00469717	−	0.999989i	$-0.498505\pi$
$31$	−4.78254	−	2.76120i	−0.858970	−	0.495927i	−0.863667	+	0.504062i	$0.831838\pi$
$32$		0			0
$33$	4.56886	−	0.979673i	0.795336	−	0.170539i
$34$		0			0
$35$	−11.3979	+	2.00975i	−1.92659	+	0.339710i
$36$		0			0
$37$		−	5.17636i		−	0.850989i	−0.904961	−	0.425494i	$-0.860100\pi$
$37$		−	5.17636i		−	0.850989i	0.904961	−	0.425494i	$-0.139900\pi$
$38$		0			0
$39$	−7.85610	−	4.15918i	−1.25798	−	0.666002i
$40$		0			0
$41$	−0.289735	−	1.64317i	−0.0452490	−	0.256620i	0.953789	−	0.300478i	$-0.0971462\pi$
$41$	−0.289735	−	1.64317i	−0.0452490	−	0.256620i	−0.999038	+	0.0438581i	$0.986035\pi$
$42$		0			0
$43$	−1.85806	+	1.55910i	−0.283351	+	0.237760i	−0.773374	−	0.633950i	$-0.781433\pi$
$43$	−1.85806	+	1.55910i	−0.283351	+	0.237760i	0.490023	+	0.871709i	$0.336988\pi$
$44$		0			0
$45$	0.754733	+	10.2660i	0.112509	+	1.53037i
$46$		0			0
$47$	0.0440069	+	0.120908i	0.00641906	+	0.0176362i	0.942861	−	0.333187i	$-0.108124\pi$
$47$	0.0440069	+	0.120908i	0.00641906	+	0.0176362i	−0.936442	+	0.350823i	$0.885902\pi$
$48$		0			0
$49$	−2.18866	−	3.79087i	−0.312665	−	0.541552i
$50$		0			0
$51$	4.49590	−	5.77572i	0.629551	−	0.808763i
$52$		0			0
$53$	6.53342	+	5.48219i	0.897434	+	0.753036i	0.969687	−	0.244350i	$-0.0785746\pi$
$53$	6.53342	+	5.48219i	0.897434	+	0.753036i	−0.0722533	+	0.997386i	$0.523019\pi$
$54$		0			0
$55$	8.69853	+	3.16600i	1.17291	+	0.426904i
$56$		0			0
$57$	2.69188	+	7.05363i	0.356549	+	0.934277i
$58$		0			0
$59$	3.87665	+	1.41099i	0.504697	+	0.183695i	0.581805	−	0.813328i	$-0.302347\pi$
$59$	3.87665	+	1.41099i	0.504697	+	0.183695i	−0.0771085	+	0.997023i	$0.524569\pi$
$60$		0			0
$61$	3.53369	+	2.96512i	0.452443	+	0.379645i	0.840342	−	0.542057i	$-0.182354\pi$
$61$	3.53369	+	2.96512i	0.452443	+	0.379645i	−0.387898	+	0.921702i	$0.626799\pi$
$62$		0			0
$63$	−9.22948	+	4.14880i	−1.16281	+	0.522700i
$64$		0			0
$65$	−8.80484	−	15.2504i	−1.09211	−	1.89158i
$66$		0			0
$67$	−3.81629	−	10.4852i	−0.466234	−	1.28097i	−0.920724	−	0.390215i	$-0.872401\pi$
$67$	−3.81629	−	10.4852i	−0.466234	−	1.28097i	0.454490	−	0.890752i	$-0.349821\pi$
$68$		0			0
$69$	3.86667	−	2.42578i	0.465492	−	0.292029i
$70$		0			0
$71$	9.91131	−	8.31658i	1.17626	−	0.986996i	0.176260	−	0.984344i	$-0.443600\pi$
$71$	9.91131	−	8.31658i	1.17626	−	0.986996i	0.999996	−	0.00265261i	$-0.000844352\pi$
$72$		0			0
$73$	−0.414656	−	2.35163i	−0.0485318	−	0.275238i	0.950879	−	0.309563i	$-0.100183\pi$
$73$	−0.414656	−	2.35163i	−0.0485318	−	0.275238i	−0.999411	+	0.0343255i	$0.989072\pi$
$74$		0			0
$75$	−5.48930	+	10.3685i	−0.633850	+	1.19725i
$76$		0			0
$77$			9.09972i			1.03701i
$78$		0			0
$79$	−2.22246	+	0.391880i	−0.250046	+	0.0440899i	−0.297266	−	0.954795i	$-0.596075\pi$
$79$	−2.22246	+	0.391880i	−0.250046	+	0.0440899i	0.0472200	+	0.998885i	$0.484964\pi$
$80$		0			0
$81$	2.84224	+	8.53942i	0.315804	+	0.948824i
$82$		0			0
$83$	6.27861	+	3.62496i	0.689167	+	0.397891i	0.803300	−	0.595575i	$-0.203076\pi$
$83$	6.27861	+	3.62496i	0.689167	+	0.397891i	−0.114133	+	0.993465i	$0.536409\pi$
$84$		0			0
$85$	13.6253	−	4.95920i	1.47787	−	0.537901i
$86$		0			0
$87$	−6.52515	+	0.239533i	−0.699570	+	0.0256807i
$88$		0			0
$89$	−0.209662	+	1.18905i	−0.0222241	+	0.126039i	−0.993901	−	0.110273i	$-0.964828\pi$
$89$	−0.209662	+	1.18905i	−0.0222241	+	0.126039i	0.971677	+	0.236312i	$0.0759387\pi$
$90$		0			0
$91$	11.1272	−	13.2609i	1.16645	−	1.39012i
$92$		0			0
$93$	−6.41298	−	7.09680i	−0.664995	−	0.735904i
$94$		0			0
$95$	−2.90863	+	14.6709i	−0.298419	+	1.50520i
$96$		0			0
$97$	3.13271	−	8.60706i	0.318079	−	0.873914i	−0.672880	−	0.739751i	$-0.734943\pi$
$97$	3.13271	−	8.60706i	0.318079	−	0.873914i	0.990959	−	0.134163i	$-0.0428346\pi$
$98$		0			0
$99$	8.05200	+	0.817228i	0.809257	+	0.0821345i
$100$		0			0
$101$	−5.56915	−	0.981991i	−0.554151	−	0.0977117i	−0.110442	−	0.993883i	$-0.535227\pi$
$101$	−5.56915	−	0.981991i	−0.554151	−	0.0977117i	−0.443709	+	0.896171i	$0.646338\pi$
$102$		0			0
$103$	−3.35680	+	1.93805i	−0.330755	+	0.190961i	−0.656176	−	0.754608i	$-0.727827\pi$
$103$	−3.35680	+	1.93805i	−0.330755	+	0.190961i	0.325421	+	0.945569i	$0.394494\pi$
$104$		0			0
$105$	−19.8561	−	2.75443i	−1.93775	−	0.268805i
$106$		0			0
$107$	−3.48940	+	6.04382i	−0.337333	+	0.584278i	−0.983930	−	0.178554i	$-0.942858\pi$
$107$	−3.48940	+	6.04382i	−0.337333	+	0.584278i	0.646597	+	0.762832i	$0.276191\pi$
$108$		0			0
$109$	3.68457	+	4.39110i	0.352918	+	0.420591i	0.913073	−	0.407797i	$-0.133703\pi$
$109$	3.68457	+	4.39110i	0.352918	+	0.420591i	−0.560155	+	0.828388i	$0.689258\pi$
$110$		0			0
$111$	2.75533	−	8.53184i	0.261524	−	0.809807i
$112$		0			0
$113$	16.8907			1.58895			0.794474	−	0.607298i	$-0.207747\pi$
$113$	16.8907			1.58895			0.794474	+	0.607298i	$0.207747\pi$
$114$		0			0
$115$	9.04260			0.843227
$116$		0			0
$117$	−10.7348	−	11.0370i	−0.992431	−	1.02037i
$118$		0			0
$119$	9.16212	+	10.9190i	0.839890	+	1.00094i
$120$		0			0
$121$	−1.86097	+	3.22329i	−0.169179	+	0.293026i
$122$		0			0
$123$	0.397092	−	2.86255i	0.0358046	−	0.258107i
$124$		0			0
$125$	−5.26986	+	3.04256i	−0.471351	+	0.272134i
$126$		0			0
$127$	−5.44679	−	0.960416i	−0.483324	−	0.0852231i	−0.0733234	−	0.997308i	$-0.523361\pi$
$127$	−5.44679	−	0.960416i	−0.483324	−	0.0852231i	−0.410001	+	0.912085i	$0.634472\pi$
$128$		0			0
$129$	−3.89240	+	1.58072i	−0.342707	+	0.139175i
$130$		0			0
$131$	5.04199	−	13.8528i	0.440521	−	1.21032i	−0.498629	−	0.866815i	$-0.666163\pi$
$131$	5.04199	−	13.8528i	0.440521	−	1.21032i	0.939150	−	0.343506i	$-0.111615\pi$
$132$		0			0
$133$	−14.5302	+	2.24577i	−1.25992	+	0.194733i
$134$		0			0
$135$	−4.22053	+	17.3225i	−0.363245	+	1.49089i
$136$		0			0
$137$	−12.8171	+	15.2748i	−1.09503	+	1.30501i	−0.146195	+	0.989256i	$0.546703\pi$
$137$	−12.8171	+	15.2748i	−1.09503	+	1.30501i	−0.948840	+	0.315756i	$0.897742\pi$
$138$		0			0
$139$	0.280984	−	1.59354i	0.0238328	−	0.135162i	−0.970570	−	0.240820i	$-0.922584\pi$
$139$	0.280984	−	1.59354i	0.0238328	−	0.135162i	0.994403	+	0.105658i	$0.0336948\pi$
$140$		0			0
$141$	0.00817546	+	0.222709i	0.000688498	+	0.0187554i
$142$		0			0
$143$	−13.0105	+	4.73543i	−1.08799	+	0.395997i
$144$		0			0
$145$	−11.2022	−	6.46761i	−0.930295	−	0.537106i
$146$		0			0
$147$	−1.58957	−	7.41322i	−0.131106	−	0.611432i
$148$		0			0
$149$	23.7332	−	4.18480i	1.94430	−	0.342832i	0.944394	−	0.328815i	$-0.106649\pi$
$149$	23.7332	−	4.18480i	1.94430	−	0.342832i	0.999902	−	0.0140170i	$-0.00446189\pi$
$150$		0			0
$151$			14.7053i			1.19670i	0.801235	+	0.598349i	$0.204176\pi$
$151$			14.7053i			1.19670i	−0.801235	+	0.598349i	$0.795824\pi$
$152$		0			0
$153$	10.4846	−	7.12660i	0.847633	−	0.576152i
$154$		0			0
$155$	−3.29041	−	18.6609i	−0.264292	−	1.49888i
$156$		0			0
$157$	11.7536	−	9.86243i	0.938038	−	0.787108i	−0.0392046	−	0.999231i	$-0.512482\pi$
$157$	11.7536	−	9.86243i	0.938038	−	0.787108i	0.977243	+	0.212124i	$0.0680380\pi$
$158$		0			0
$159$	7.85047	+	12.5136i	0.622583	+	0.992392i
$160$		0			0
$161$	3.04028	+	8.35309i	0.239607	+	0.658316i
$162$		0			0
$163$	−5.96235	−	10.3271i	−0.467007	−	0.808880i	0.532283	−	0.846567i	$-0.321334\pi$
$163$	−5.96235	−	10.3271i	−0.467007	−	0.808880i	−0.999290	+	0.0376868i	$0.988001\pi$
$164$		0			0
$165$	12.6520	+	9.84845i	0.984953	+	0.766701i
$166$		0			0
$167$	−1.37759	−	1.15593i	−0.106601	−	0.0894489i	0.587929	−	0.808912i	$-0.299943\pi$
$167$	−1.37759	−	1.15593i	−0.106601	−	0.0894489i	−0.694530	+	0.719463i	$0.744388\pi$
$168$		0			0
$169$	12.5346	+	4.56221i	0.964198	+	0.350939i
$170$		0			0
$171$	0.682271	+	13.0589i	0.0521746	+	0.998638i
$172$		0			0
$173$	−6.36766	−	2.31764i	−0.484124	−	0.176207i	0.0884156	−	0.996084i	$-0.471820\pi$
$173$	−6.36766	−	2.31764i	−0.484124	−	0.176207i	−0.572540	+	0.819877i	$0.694042\pi$
$174$		0			0
$175$	−17.5018	−	14.6858i	−1.32301	−	1.11014i
$176$		0			0
$177$	5.63856	+	4.38913i	0.423820	+	0.329907i
$178$		0			0
$179$	−7.17879	−	12.4340i	−0.536568	−	0.929363i	−0.999086	−	0.0427531i	$-0.986387\pi$
$179$	−7.17879	−	12.4340i	−0.536568	−	0.929363i	0.462518	−	0.886610i	$-0.346946\pi$
$180$		0			0
$181$	−4.09139	−	11.2410i	−0.304111	−	0.835537i	−0.993775	−	0.111408i	$-0.964464\pi$
$181$	−4.09139	−	11.2410i	−0.304111	−	0.835537i	0.689664	−	0.724129i	$-0.257758\pi$
$182$		0			0
$183$	4.24604	+	6.76816i	0.313876	+	0.500316i
$184$		0			0
$185$	13.6060	−	11.4168i	1.00033	−	0.839379i
$186$		0			0
$187$	−1.97964	−	11.2271i	−0.144766	−	0.821008i
$188$		0			0
$189$	−17.4207	+	1.92542i	−1.26717	+	0.140054i
$190$		0			0
$191$			10.1652i			0.735526i	0.929919	+	0.367763i	$0.119876\pi$
$191$			10.1652i			0.735526i	−0.929919	+	0.367763i	$0.880124\pi$
$192$		0			0
$193$	−12.3371	+	2.17537i	−0.888046	+	0.156587i	−0.599019	−	0.800734i	$-0.704443\pi$
$193$	−12.3371	+	2.17537i	−0.888046	+	0.156587i	−0.289027	+	0.957321i	$0.593332\pi$
$194$		0			0
$195$	−6.39477	−	29.8230i	−0.457939	−	2.13567i
$196$		0			0
$197$	−19.9041	−	11.4916i	−1.41811	−	0.818744i	−0.421974	−	0.906608i	$-0.638662\pi$
$197$	−19.9041	−	11.4916i	−1.41811	−	0.818744i	−0.996132	+	0.0878643i	$0.971996\pi$
$198$		0			0
$199$	23.8117	−	8.66676i	1.68797	−	0.614370i	0.693601	−	0.720360i	$-0.256023\pi$
$199$	23.8117	−	8.66676i	1.68797	−	0.614370i	0.994367	+	0.105990i	$0.0338011\pi$
$200$		0			0
$201$	−0.708978	−	19.3133i	−0.0500075	−	1.36226i
$202$		0			0
$203$	2.20807	−	12.5226i	0.154976	−	0.878913i
$204$		0			0
$205$	3.68002	−	4.38567i	0.257024	−	0.306309i
$206$		0			0
$207$	7.66438	−	1.94005i	0.532711	−	0.134843i
$208$		0			0
$209$	10.9625	+	4.25515i	0.758294	+	0.294335i
$210$		0			0
$211$	4.07273	−	11.1897i	0.280378	−	0.770333i	−0.716939	−	0.697136i	$-0.754458\pi$
$211$	4.07273	−	11.1897i	0.280378	−	0.770333i	0.997317	−	0.0731972i	$-0.0233202\pi$
$212$		0			0
$213$	20.7630	−	8.43196i	1.42266	−	0.577748i
$214$		0			0
$215$	−8.19612	−	1.44520i	−0.558971	−	0.0985616i
$216$		0			0
$217$	16.1316	−	9.31361i	1.09509	−	0.632249i
$218$		0			0
$219$	0.568301	−	4.09675i	0.0384022	−	0.276833i
$220$		0			0
$221$	−10.8437	+	18.7819i	−0.729427	+	1.26341i
$222$		0			0
$223$	−8.14222	−	9.70352i	−0.545243	−	0.649796i	0.421111	−	0.907009i	$-0.361640\pi$
$223$	−8.14222	−	9.70352i	−0.545243	−	0.649796i	−0.966355	+	0.257213i	$0.917196\pi$
$224$		0			0
$225$	−14.5667	+	14.1678i	−0.971113	+	0.944521i
$226$		0			0
$227$	−3.77953			−0.250857			−0.125428	−	0.992103i	$-0.540030\pi$
$227$	−3.77953			−0.250857			−0.125428	+	0.992103i	$0.540030\pi$
$228$		0			0
$229$	15.3222			1.01252			0.506259	−	0.862381i	$-0.331028\pi$
$229$	15.3222			1.01252			0.506259	+	0.862381i	$0.331028\pi$
$230$		0			0
$231$	−4.84369	+	14.9984i	−0.318691	+	0.986825i
$232$		0			0
$233$	−15.6260	−	18.6223i	−1.02369	−	1.21999i	−0.975236	−	0.221165i	$-0.929014\pi$
$233$	−15.6260	−	18.6223i	−1.02369	−	1.21999i	−0.0484572	−	0.998825i	$-0.515430\pi$
$234$		0			0
$235$	−0.220745	+	0.382341i	−0.0143998	+	0.0249412i
$236$		0			0
$237$	−3.87172	−	0.537085i	−0.251496	−	0.0348874i
$238$		0			0
$239$	−11.5689	+	6.67933i	−0.748332	+	0.432050i	−0.825091	−	0.565000i	$-0.808876\pi$
$239$	−11.5689	+	6.67933i	−0.748332	+	0.432050i	0.0767587	+	0.997050i	$0.475543\pi$
$240$		0			0
$241$	−21.6352	−	3.81487i	−1.39365	−	0.245737i	−0.574116	−	0.818774i	$-0.694654\pi$
$241$	−21.6352	−	3.81487i	−1.39365	−	0.245737i	−0.819530	+	0.573037i	$0.805765\pi$
$242$		0			0
$243$	0.139216	+	15.5878i	0.00893073	+	0.999960i
$244$		0			0
$245$	5.13702	−	14.1138i	0.328192	−	0.901700i
$246$		0			0
$247$	−10.7723	−	19.6061i	−0.685427	−	1.24751i
$248$		0			0
$249$	8.41908	+	9.31681i	0.533537	+	0.590429i
$250$		0			0
$251$	−4.35873	+	5.19453i	−0.275121	+	0.327876i	−0.885857	−	0.463958i	$-0.846429\pi$
$251$	−4.35873	+	5.19453i	−0.275121	+	0.327876i	0.610737	+	0.791834i	$0.290873\pi$
$252$		0			0
$253$	1.23458	−	7.00166i	0.0776175	−	0.440191i
$254$		0			0
$255$	25.0974	−	0.921305i	1.57166	−	0.0576944i
$256$		0			0
$257$	−16.7251	+	6.08743i	−1.04328	+	0.379724i	−0.806123	−	0.591747i	$-0.798438\pi$
$257$	−16.7251	+	6.08743i	−1.04328	+	0.379724i	−0.237158	+	0.971471i	$0.576216\pi$
$258$		0			0
$259$	15.1208	+	8.73000i	0.939561	+	0.542456i
$260$		0			0
$261$	−10.8825	−	3.07847i	−0.673607	−	0.190552i
$262$		0			0
$263$	3.78041	−	0.666587i	0.233110	−	0.0411035i	−0.0558728	−	0.998438i	$-0.517794\pi$
$263$	3.78041	−	0.666587i	0.233110	−	0.0411035i	0.288983	+	0.957334i	$0.406683\pi$
$264$		0			0
$265$			29.2643i			1.79769i
$266$		0			0
$267$	−0.978490	+	1.84823i	−0.0598826	+	0.113110i
$268$		0			0
$269$	−0.457985	−	2.59736i	−0.0279239	−	0.158364i	0.967657	−	0.252268i	$-0.0811765\pi$
$269$	−0.457985	−	2.59736i	−0.0279239	−	0.158364i	−0.995581	+	0.0939040i	$0.970065\pi$
$270$		0			0
$271$	−10.7222	+	8.99702i	−0.651329	+	0.546530i	−0.907474	−	0.420108i	$-0.861992\pi$
$271$	−10.7222	+	8.99702i	−0.651329	+	0.546530i	0.256145	+	0.966638i	$0.417548\pi$
$272$		0			0
$273$	25.3989	−	15.9342i	1.53721	−	0.964379i
$274$		0			0
$275$	6.24984	+	17.1713i	0.376880	+	1.03547i
$276$		0			0
$277$	−0.166629	−	0.288609i	−0.0100117	−	0.0173408i	0.860976	−	0.508645i	$-0.169854\pi$
$277$	−0.166629	−	0.288609i	−0.0100117	−	0.0173408i	−0.870988	+	0.491305i	$0.836520\pi$
$278$		0			0
$279$	−6.79252	−	15.1107i	−0.406657	−	0.904656i
$280$		0			0
$281$	−1.92247	−	1.61315i	−0.114685	−	0.0962323i	0.583642	−	0.812011i	$-0.301627\pi$
$281$	−1.92247	−	1.61315i	−0.114685	−	0.0962323i	−0.698327	+	0.715779i	$0.746072\pi$
$282$		0			0
$283$	24.7578	+	9.01110i	1.47170	+	0.535655i	0.948561	−	0.316594i	$-0.102539\pi$
$283$	24.7578	+	9.01110i	1.47170	+	0.535655i	0.523138	+	0.852248i	$0.324761\pi$
$284$		0			0
$285$	−12.6033	+	22.6328i	−0.746553	+	1.34065i
$286$		0			0
$287$	5.28855	+	1.92487i	0.312173	+	0.113622i
$288$		0			0
$289$	−0.656761	−	0.551088i	−0.0386330	−	0.0324169i
$290$		0			0
$291$	9.74489	−	12.5189i	0.571255	−	0.733872i
$292$		0			0
$293$	6.53329	+	11.3160i	0.381679	+	0.661087i	0.991302	−	0.131604i	$-0.0420127\pi$
$293$	6.53329	+	11.3160i	0.381679	+	0.661087i	−0.609624	+	0.792691i	$0.708679\pi$
$294$		0			0
$295$	4.84144	+	13.3017i	0.281879	+	0.774457i
$296$		0			0
$297$	12.8366	+	5.63298i	0.744853	+	0.326859i
$298$		0			0
$299$	−10.3608	+	8.69378i	−0.599183	+	0.502775i
$300$		0			0
$301$	−1.42068	−	8.05706i	−0.0818864	−	0.464401i
$302$		0			0
$303$	−8.65654	−	4.58295i	−0.497305	−	0.263284i
$304$		0			0
$305$			15.8280i			0.906310i
$306$		0			0
$307$	−7.06477	+	1.24571i	−0.403208	+	0.0710964i	−0.371575	−	0.928403i	$-0.621182\pi$
$307$	−7.06477	+	1.24571i	−0.403208	+	0.0710964i	−0.0316333	+	0.999500i	$0.510071\pi$
$308$		0			0
$309$	−6.56438	+	1.40756i	−0.373435	+	0.0800734i
$310$		0			0
$311$	−9.96292	−	5.75210i	−0.564945	−	0.326171i	0.190183	−	0.981749i	$-0.439092\pi$
$311$	−9.96292	−	5.75210i	−0.564945	−	0.326171i	−0.755128	+	0.655577i	$0.772425\pi$
$312$		0			0
$313$	16.6644	−	6.06533i	0.941925	−	0.342833i	0.174999	−	0.984569i	$-0.444008\pi$
$313$	16.6644	−	6.06533i	0.941925	−	0.342833i	0.766926	+	0.641736i	$0.221785\pi$
$314$		0			0
$315$	−31.2612	−	15.1091i	−1.76137	−	0.851303i
$316$		0			0
$317$	5.91797	−	33.5625i	0.332386	−	1.88506i	−0.119267	−	0.992862i	$-0.538054\pi$
$317$	5.91797	−	33.5625i	0.332386	−	1.88506i	0.451653	−	0.892194i	$-0.350835\pi$
$318$		0			0
$319$	−6.53729	+	7.79084i	−0.366018	+	0.436203i
$320$		0			0
$321$	−8.96840	+	8.10424i	−0.500567	+	0.452334i
$322$		0			0
$323$	17.4385	−	5.93183i	0.970307	−	0.330056i
$324$		0			0
$325$	11.8894	−	32.6659i	0.659507	−	1.81198i
$326$		0			0
$327$	3.73569	+	9.19881i	0.206584	+	0.508695i
$328$		0			0
$329$	−0.427405	−	0.0753631i	−0.0235636	−	0.00415490i
$330$		0			0
$331$	−18.0961	+	10.4478i	−0.994652	+	0.574263i	−0.906662	−	0.421858i	$-0.861378\pi$
$331$	−18.0961	+	10.4478i	−0.994652	+	0.574263i	−0.0879907	+	0.996121i	$0.528045\pi$
$332$		0			0
$333$	9.08283	−	12.5958i	0.497736	−	0.690247i
$334$		0			0
$335$	19.1430	−	33.1567i	1.04590	−	1.81155i
$336$		0			0
$337$	−19.1366	−	22.8061i	−1.04244	−	1.24233i	−0.969526	−	0.244988i	$-0.921216\pi$
$337$	−19.1366	−	22.8061i	−1.04244	−	1.24233i	−0.0729092	−	0.997339i	$-0.523228\pi$
$338$		0			0
$339$	27.8399	+	8.99077i	1.51205	+	0.488312i
$340$		0			0
$341$	−14.8983			−0.806788
$342$		0			0
$343$	−8.84639			−0.477660
$344$		0			0
$345$	14.9043	+	4.81329i	0.802420	+	0.259139i
$346$		0			0
$347$	3.49226	+	4.16191i	0.187474	+	0.223423i	0.851592	−	0.524204i	$-0.175637\pi$
$347$	3.49226	+	4.16191i	0.187474	+	0.223423i	−0.664118	+	0.747628i	$0.731193\pi$
$348$		0			0
$349$	−8.07643	+	13.9888i	−0.432322	+	0.748803i	−0.997073	−	0.0764582i	$-0.975639\pi$
$349$	−8.07643	+	13.9888i	−0.432322	+	0.748803i	0.564751	+	0.825261i	$0.308972\pi$
$350$		0			0
$351$	−11.8185	−	23.9056i	−0.630826	−	1.27598i
$352$		0			0
$353$	−18.1153	+	10.4589i	−0.964180	+	0.556670i	−0.897457	−	0.441102i	$-0.854588\pi$
$353$	−18.1153	+	10.4589i	−0.964180	+	0.556670i	−0.0667232	+	0.997772i	$0.521254\pi$
$354$		0			0
$355$	43.7200	+	7.70902i	2.32042	+	0.409152i
$356$		0			0
$357$	9.28922	+	22.8739i	0.491638	+	1.21062i
$358$		0			0
$359$	8.05343	−	22.1266i	0.425044	−	1.16780i	−0.523741	−	0.851877i	$-0.675464\pi$
$359$	8.05343	−	22.1266i	0.425044	−	1.16780i	0.948785	−	0.315921i	$-0.102314\pi$
$360$		0			0
$361$	−4.08900	+	18.5548i	−0.215211	+	0.976568i
$362$		0			0
$363$	−4.78302	+	4.32215i	−0.251044	+	0.226854i
$364$		0			0
$365$	5.26668	−	6.27659i	0.275671	−	0.328532i
$366$		0			0
$367$	−3.11469	+	17.6643i	−0.162586	+	0.922069i	0.788933	+	0.614479i	$0.210634\pi$
$367$	−3.11469	+	17.6643i	−0.162586	+	0.922069i	−0.951519	+	0.307590i	$0.900477\pi$
$368$		0			0
$369$	2.17820	−	4.50677i	0.113393	−	0.234613i
$370$		0			0
$371$	−27.0329	+	9.83916i	−1.40348	+	0.510824i
$372$		0			0
$373$	12.2615	+	7.07917i	0.634876	+	0.366546i	0.782638	−	0.622477i	$-0.213874\pi$
$373$	12.2615	+	7.07917i	0.634876	+	0.366546i	−0.147762	+	0.989023i	$0.547207\pi$
$374$		0			0
$375$	−10.3055	+	2.20974i	−0.532172	+	0.114111i
$376$		0			0
$377$	19.0534	−	3.35964i	0.981303	−	0.173030i
$378$		0			0
$379$		−	1.25595i		−	0.0645137i	−0.999480	−	0.0322569i	$-0.989731\pi$
$379$		−	1.25595i		−	0.0645137i	0.999480	−	0.0322569i	$-0.0102695\pi$
$380$		0			0
$381$	−8.46635	−	4.48226i	−0.433744	−	0.229633i
$382$		0			0
$383$	0.465296	+	2.63882i	0.0237755	+	0.134838i	0.994385	−	0.105822i	$-0.0337474\pi$
$383$	0.465296	+	2.63882i	0.0237755	+	0.134838i	−0.970610	+	0.240660i	$0.922636\pi$
$384$		0			0
$385$	−23.9185	+	20.0700i	−1.21900	+	1.02286i
$386$		0			0
$387$	−7.25698	+	0.533515i	−0.368893	+	0.0271201i
$388$		0			0
$389$	−11.2472	−	30.9013i	−0.570253	−	1.56676i	−0.804106	−	0.594486i	$-0.797355\pi$
$389$	−11.2472	−	30.9013i	−0.570253	−	1.56676i	0.233852	−	0.972272i	$-0.424867\pi$
$390$		0			0
$391$	−5.56827	−	9.64452i	−0.281599	−	0.487744i
$392$		0			0
$393$	15.6841	−	20.1488i	0.791156	−	1.01637i
$394$		0			0
$395$	−5.93183	−	4.97739i	−0.298463	−	0.250440i
$396$		0			0
$397$	−2.19998	−	0.800726i	−0.110414	−	0.0401873i	0.286223	−	0.958163i	$-0.407600\pi$
$397$	−2.19998	−	0.800726i	−0.110414	−	0.0401873i	−0.396636	+	0.917976i	$0.629823\pi$
$398$		0			0
$399$	−25.1445	−	4.03271i	−1.25880	−	0.201888i
$400$		0			0
$401$	−12.8782	−	4.68726i	−0.643104	−	0.234071i	−0.000179351	−	1.00000i	$-0.500057\pi$
$401$	−12.8782	−	4.68726i	−0.643104	−	0.234071i	−0.642925	+	0.765929i	$0.722279\pi$
$402$		0			0
$403$	21.7111	+	18.2178i	1.08151	+	0.907492i
$404$		0			0
$405$	−16.1770	+	26.3050i	−0.803843	+	1.30711i
$406$		0			0
$407$	−6.98237	−	12.0938i	−0.346103	−	0.599468i
$408$		0			0
$409$	7.27394	+	19.9850i	0.359673	+	0.988194i	0.979143	+	0.203173i	$0.0651254\pi$
$409$	7.27394	+	19.9850i	0.359673	+	0.988194i	−0.619470	+	0.785020i	$0.712652\pi$
$410$		0			0
$411$	−29.2561	+	18.3540i	−1.44310	+	0.905335i
$412$		0			0
$413$	−10.6597	+	8.94454i	−0.524529	+	0.440132i
$414$		0			0
$415$	4.31971	+	24.4983i	0.212046	+	1.20257i
$416$		0			0
$417$	1.31135	−	2.47696i	0.0642173	−	0.121297i
$418$		0			0
$419$			29.1990i			1.42646i	0.700928	+	0.713232i	$0.252770\pi$
$419$			29.1990i			1.42646i	−0.700928	+	0.713232i	$0.747230\pi$
$420$		0			0
$421$	7.45681	−	1.31484i	0.363423	−	0.0640812i	0.0110448	−	0.999939i	$-0.496484\pi$
$421$	7.45681	−	1.31484i	0.363423	−	0.0640812i	0.352378	+	0.935858i	$0.385373\pi$
$422$		0			0
$423$	−0.105070	+	0.371427i	−0.00510870	+	0.0180594i
$424$		0			0
$425$	24.7884	+	14.3116i	1.20241	+	0.694214i
$426$		0			0
$427$	−14.6211	+	5.32165i	−0.707565	+	0.257533i
$428$		0			0
$429$	−23.9649	+	0.879734i	−1.15704	+	0.0424740i
$430$		0			0
$431$	−4.16028	+	23.5941i	−0.200394	+	1.13649i	0.704132	+	0.710069i	$0.251336\pi$
$431$	−4.16028	+	23.5941i	−0.200394	+	1.13649i	−0.904526	+	0.426419i	$0.859775\pi$
$432$		0			0
$433$	−9.89407	+	11.7913i	−0.475479	+	0.566654i	−0.949463	−	0.313880i	$-0.898371\pi$
$433$	−9.89407	+	11.7913i	−0.475479	+	0.566654i	0.473984	+	0.880534i	$0.342816\pi$
$434$		0			0
$435$	−15.0212	−	16.6230i	−0.720213	−	0.797010i
$436$		0			0
$437$	11.4847	+	0.243366i	0.549389	+	0.0116418i
$438$		0			0
$439$	7.60564	−	20.8963i	0.362997	−	0.997327i	−0.614967	−	0.788553i	$-0.710831\pi$
$439$	7.60564	−	20.8963i	0.362997	−	0.997327i	0.977964	−	0.208774i	$-0.0669472\pi$
$440$		0			0
$441$	1.32600	−	13.0648i	0.0631428	−	0.622134i
$442$		0			0
$443$	30.8547	+	5.44051i	1.46595	+	0.258486i	0.848948	−	0.528476i	$-0.177236\pi$
$443$	30.8547	+	5.44051i	1.46595	+	0.258486i	0.617001	+	0.786963i	$0.288348\pi$
$444$		0			0
$445$	−3.58782	+	2.07143i	−0.170079	+	0.0981952i
$446$		0			0
$447$	41.3453	+	5.73541i	1.95556	+	0.271276i
$448$		0			0
$449$	6.15216	−	10.6559i	0.290338	−	0.502881i	−0.683551	−	0.729902i	$-0.739565\pi$
$449$	6.15216	−	10.6559i	0.290338	−	0.502881i	0.973890	+	0.227022i	$0.0728988\pi$
$450$		0			0
$451$	−2.89339	−	3.44820i	−0.136244	−	0.162370i
$452$		0			0
$453$	−7.82747	+	24.2377i	−0.367767	+	1.13879i
$454$		0			0
$455$	59.3979			2.78462
$456$		0			0
$457$	−37.8216			−1.76922			−0.884609	−	0.466334i	$-0.845575\pi$
$457$	−37.8216			−1.76922			−0.884609	+	0.466334i	$0.845575\pi$
$458$		0			0
$459$	21.0745	−	6.16543i	0.983675	−	0.287777i
$460$		0			0
$461$	24.9818	+	29.7722i	1.16352	+	1.38663i	0.907550	+	0.419945i	$0.137950\pi$
$461$	24.9818	+	29.7722i	1.16352	+	1.38663i	0.255970	+	0.966685i	$0.417605\pi$
$462$		0			0
$463$	−12.3259	+	21.3492i	−0.572835	+	0.992180i	0.423438	+	0.905925i	$0.360823\pi$
$463$	−12.3259	+	21.3492i	−0.572835	+	0.992180i	−0.996273	+	0.0862548i	$0.972510\pi$
$464$		0			0
$465$	4.50962	−	32.5089i	0.209129	−	1.50756i
$466$		0			0
$467$	3.17931	−	1.83558i	0.147121	−	0.0849404i	−0.424632	−	0.905366i	$-0.639597\pi$
$467$	3.17931	−	1.83558i	0.147121	−	0.0849404i	0.571754	+	0.820425i	$0.306263\pi$
$468$		0			0
$469$	37.0647	+	6.53551i	1.71149	+	0.301782i
$470$		0			0
$471$	24.6223	−	9.99925i	1.13454	−	0.460741i
$472$		0			0
$473$	−2.23803	+	6.14892i	−0.102905	+	0.282728i
$474$		0			0
$475$	−25.8762	+	14.2174i	−1.18728	+	0.652337i
$476$		0			0
$477$	6.27854	+	24.8040i	0.287474	+	1.13570i
$478$		0			0
$479$	−16.6874	+	19.8872i	−0.762465	+	0.908670i	−0.998001	−	0.0631952i	$-0.979871\pi$
$479$	−16.6874	+	19.8872i	−0.762465	+	0.908670i	0.235536	+	0.971866i	$0.424315\pi$
$480$		0			0
$481$	−4.61312	+	26.1623i	−0.210340	+	1.19290i
$482$		0			0
$483$	0.564813	+	15.3861i	0.0256999	+	0.700094i
$484$		0			0
$485$	29.5329	−	10.7491i	1.34102	−	0.488092i
$486$		0			0
$487$	−8.59327	−	4.96133i	−0.389398	−	0.224819i	0.292501	−	0.956265i	$-0.405512\pi$
$487$	−8.59327	−	4.96133i	−0.389398	−	0.224819i	−0.681899	+	0.731446i	$0.738846\pi$
$488$		0			0
$489$	−4.33032	−	20.1951i	−0.195824	−	0.913255i
$490$		0			0
$491$	14.8971	−	2.62676i	0.672296	−	0.118544i	0.172929	−	0.984934i	$-0.444677\pi$
$491$	14.8971	−	2.62676i	0.672296	−	0.118544i	0.499367	+	0.866391i	$0.333566\pi$
$492$		0			0
$493$			15.9305i			0.717476i
$494$		0			0
$495$	15.6111	+	22.9670i	0.701668	+	1.03229i
$496$		0			0
$497$	7.57822	+	42.9782i	0.339930	+	1.92784i
$498$		0			0
$499$	−16.3136	+	13.6887i	−0.730296	+	0.612791i	−0.930212	−	0.367022i	$-0.880377\pi$
$499$	−16.3136	+	13.6887i	−0.730296	+	0.612791i	0.199917	+	0.979813i	$0.435933\pi$
$500$		0			0
$501$	−1.65529	−	2.63853i	−0.0739531	−	0.117881i
$502$		0			0
$503$	−1.99181	−	5.47245i	−0.0888104	−	0.244004i	0.887334	−	0.461128i	$-0.152555\pi$
$503$	−1.99181	−	5.47245i	−0.0888104	−	0.244004i	−0.976144	+	0.217123i	$0.930333\pi$
$504$		0			0
$505$	−9.70195	−	16.8043i	−0.431731	−	0.747780i
$506$		0			0
$507$	18.2315	+	14.1916i	0.809688	+	0.630272i
$508$		0			0
$509$	10.9586	+	9.19535i	0.485731	+	0.407577i	0.852493	−	0.522738i	$-0.175089\pi$
$509$	10.9586	+	9.19535i	0.485731	+	0.407577i	−0.366763	+	0.930315i	$0.619534\pi$
$510$		0			0
$511$	7.56874	+	2.75480i	0.334821	+	0.121865i
$512$		0			0
$513$	−5.82657	+	21.8872i	−0.257249	+	0.966345i
$514$		0			0
$515$	−12.4977	−	4.54881i	−0.550717	−	0.200444i
$516$		0			0
$517$	0.265908	+	0.223123i	0.0116946	+	0.00981294i
$518$		0			0
$519$	−9.26173	−	7.20945i	−0.406545	−	0.316460i
$520$		0			0
$521$	5.93133	+	10.2734i	0.259856	+	0.450084i	0.966203	−	0.257781i	$-0.0829914\pi$
$521$	5.93133	+	10.2734i	0.259856	+	0.450084i	−0.706347	+	0.707866i	$0.749658\pi$
$522$		0			0
$523$	−10.6971	−	29.3899i	−0.467750	−	1.28513i	−0.919536	−	0.393005i	$-0.871435\pi$
$523$	−10.6971	−	29.3899i	−0.467750	−	1.28513i	0.451787	−	0.892126i	$-0.350787\pi$
$524$		0			0
$525$	−21.0300	−	33.5216i	−0.917823	−	1.46300i
$526$		0			0
$527$	−17.8768	+	15.0004i	−0.778727	+	0.653430i
$528$		0			0
$529$	2.78789	+	15.8109i	0.121213	+	0.687431i
$530$		0			0
$531$	6.95737	+	10.2357i	0.301924	+	0.444190i
$532$		0			0
$533$			8.56309i			0.370909i
$534$		0			0
$535$	−23.5822	+	4.15817i	−1.01955	+	0.179774i
$536$		0			0
$537$	−5.21380	−	24.3154i	−0.224992	−	1.04929i
$538$		0			0
$539$	−10.2270	−	5.90454i	−0.440506	−	0.254326i
$540$		0			0
$541$	−26.2388	+	9.55016i	−1.12810	+	0.410593i	−0.837601	−	0.546283i	$-0.816042\pi$
$541$	−26.2388	+	9.55016i	−1.12810	+	0.410593i	−0.290495	+	0.956876i	$0.593820\pi$
$542$		0			0
$543$	−0.760086	−	20.7056i	−0.0326184	−	0.888561i
$544$		0			0
$545$	−3.41540	+	19.3697i	−0.146300	+	0.829706i
$546$		0			0
$547$	−12.0859	+	14.4034i	−0.516757	+	0.615847i	−0.959811	−	0.280648i	$-0.909451\pi$
$547$	−12.0859	+	14.4034i	−0.516757	+	0.615847i	0.443054	+	0.896495i	$0.353895\pi$
$548$		0			0
$549$	3.39584	+	13.4156i	0.144931	+	0.572564i
$550$		0			0
$551$	−14.0536	−	8.51581i	−0.598702	−	0.362786i
$552$		0			0
$553$	2.60348	−	7.15300i	0.110711	−	0.304177i
$554$		0			0
$555$	28.5029	−	11.5752i	1.20988	−	0.491339i
$556$		0			0
$557$	22.6372	+	3.99155i	0.959170	+	0.169128i	0.631251	−	0.775578i	$-0.282542\pi$
$557$	22.6372	+	3.99155i	0.959170	+	0.169128i	0.327919	+	0.944706i	$0.393653\pi$
$558$		0			0
$559$	10.7804	−	6.22408i	0.455963	−	0.263250i
$560$		0			0
$561$	2.71317	−	19.5586i	0.114550	−	0.825766i
$562$		0			0
$563$	6.45057	−	11.1727i	0.271859	−	0.470874i	−0.697479	−	0.716605i	$-0.745695\pi$
$563$	6.45057	−	11.1727i	0.271859	−	0.470874i	0.969338	+	0.245732i	$0.0790282\pi$
$564$		0			0
$565$	37.2536	+	44.3971i	1.56727	+	1.86780i
$566$		0			0
$567$	−29.7382	−	6.09931i	−1.24889	−	0.256147i
$568$		0			0
$569$	37.8380			1.58625			0.793125	−	0.609059i	$-0.208453\pi$
$569$	37.8380			1.58625			0.793125	+	0.609059i	$0.208453\pi$
$570$		0			0
$571$	−20.7087			−0.866632			−0.433316	−	0.901242i	$-0.642657\pi$
$571$	−20.7087			−0.866632			−0.433316	+	0.901242i	$0.642657\pi$
$572$		0			0
$573$	−5.41082	+	16.7546i	−0.226040	+	0.699932i
$574$		0			0
$575$	11.4741	+	13.6743i	0.478503	+	0.570258i
$576$		0			0
$577$	−8.69281	+	15.0564i	−0.361886	+	0.626805i	−0.988271	−	0.152708i	$-0.951200\pi$
$577$	−8.69281	+	15.0564i	−0.361886	+	0.626805i	0.626385	+	0.779514i	$0.284534\pi$
$578$		0			0
$579$	−21.4924	−	2.98142i	−0.893193	−	0.123904i
$580$		0			0
$581$	−21.1779	+	12.2271i	−0.878608	+	0.507265i
$582$		0			0
$583$	22.6593	+	3.99544i	0.938451	+	0.165474i
$584$		0			0
$585$	5.33441	−	52.5590i	0.220551	−	2.17305i
$586$		0			0
$587$	−10.0782	+	27.6896i	−0.415971	+	1.14287i	0.537992	+	0.842950i	$0.319183\pi$
$587$	−10.0782	+	27.6896i	−0.415971	+	1.14287i	−0.953964	+	0.299922i	$0.903039\pi$
$588$		0			0
$589$	−3.67683	−	23.7891i	−0.151501	−	0.980214i
$590$		0			0
$591$	−26.6896	−	29.5356i	−1.09786	−	1.21493i
$592$		0			0
$593$	8.16230	−	9.72745i	0.335185	−	0.399458i	−0.571956	−	0.820284i	$-0.693815\pi$
$593$	8.16230	−	9.72745i	0.335185	−	0.399458i	0.907141	+	0.420826i	$0.138260\pi$
$594$		0			0
$595$	−8.49279	+	48.1650i	−0.348170	+	1.97457i
$596$		0			0
$597$	43.8604	−	1.61008i	1.79509	−	0.0658963i
$598$		0			0
$599$	−16.8817	+	6.14443i	−0.689767	+	0.251055i	−0.663035	−	0.748588i	$-0.730732\pi$
$599$	−16.8817	+	6.14443i	−0.689767	+	0.251055i	−0.0267313	+	0.999643i	$0.508510\pi$
$600$		0			0
$601$	8.14038	+	4.69985i	0.332053	+	0.191711i	0.656752	−	0.754106i	$-0.271930\pi$
$601$	8.14038	+	4.69985i	0.332053	+	0.191711i	−0.324699	+	0.945817i	$0.605263\pi$
$602$		0			0
$603$	9.11174	−	32.2102i	0.371059	−	1.31170i
$604$		0			0
$605$	−12.5768	+	2.21764i	−0.511321	+	0.0901597i
$606$		0			0
$607$		−	9.88885i		−	0.401376i	−0.979655	−	0.200688i	$-0.935682\pi$
$607$		−	9.88885i		−	0.401376i	0.979655	−	0.200688i	$-0.0643177\pi$
$608$		0			0
$609$	10.3050	−	19.4648i	0.417582	−	0.788752i
$610$		0			0
$611$	−0.114667	−	0.650309i	−0.00463893	−	0.0263087i
$612$		0			0
$613$	−24.8777	+	20.8749i	−1.00480	+	0.843129i	−0.987642	−	0.156724i	$-0.949907\pi$
$613$	−24.8777	+	20.8749i	−1.00480	+	0.843129i	−0.0171592	+	0.999853i	$0.505462\pi$
$614$		0			0
$615$	8.39997	−	5.26977i	0.338720	−	0.212498i
$616$		0			0
$617$	−7.64721	−	21.0105i	−0.307865	−	0.845852i	−0.993072	−	0.117504i	$-0.962511\pi$
$617$	−7.64721	−	21.0105i	−0.307865	−	0.845852i	0.685207	−	0.728348i	$-0.259712\pi$
$618$		0			0
$619$	9.39662	+	16.2754i	0.377682	+	0.654164i	0.990725	−	0.135886i	$-0.0433880\pi$
$619$	9.39662	+	16.2754i	0.377682	+	0.654164i	−0.613043	+	0.790050i	$0.710055\pi$
$620$		0			0
$621$	13.6653	+	0.882017i	0.548372	+	0.0353941i
$622$		0			0
$623$	−3.11977	−	2.61780i	−0.124991	−	0.104880i
$624$		0			0
$625$	12.2044	+	4.44205i	0.488178	+	0.177682i
$626$		0			0
$627$	15.8038	+	12.8487i	0.631143	+	0.513128i
$628$		0			0
$629$	−20.5551	−	7.48143i	−0.819584	−	0.298304i
$630$		0			0
$631$	22.1517	+	18.5875i	0.881846	+	0.739956i	0.966558	−	0.256449i	$-0.0825526\pi$
$631$	22.1517	+	18.5875i	0.881846	+	0.739956i	−0.0847122	+	0.996405i	$0.526997\pi$
$632$		0			0
$633$	12.6690	−	16.2754i	0.503547	−	0.646889i
$634$		0			0
$635$	−9.48879	−	16.4351i	−0.376551	−	0.652206i
$636$		0			0
$637$	7.68350	+	21.1102i	0.304431	+	0.836418i
$638$		0			0
$639$	38.7104	−	2.84590i	1.53136	−	0.112582i
$640$		0			0
$641$	−18.2950	+	15.3513i	−0.722609	+	0.606341i	−0.928106	−	0.372317i	$-0.878563\pi$
$641$	−18.2950	+	15.3513i	−0.722609	+	0.606341i	0.205497	+	0.978658i	$0.434119\pi$
$642$		0			0
$643$	−6.83453	−	38.7606i	−0.269528	−	1.52857i	−0.755825	−	0.654774i	$-0.772764\pi$
$643$	−6.83453	−	38.7606i	−0.269528	−	1.52857i	0.486297	−	0.873793i	$-0.338347\pi$
$644$		0			0
$645$	−12.7398	−	6.74473i	−0.501631	−	0.265574i
$646$		0			0
$647$		−	24.3840i		−	0.958633i	−0.877642	−	0.479317i	$-0.840885\pi$
$647$		−	24.3840i		−	0.958633i	0.877642	−	0.479317i	$-0.159115\pi$
$648$		0			0
$649$	10.9605	−	1.93263i	0.430237	−	0.0758624i
$650$		0			0
$651$	31.5462	−	6.76427i	1.23639	−	0.265113i
$652$		0			0
$653$	−20.0643	−	11.5841i	−0.785178	−	0.453323i	0.0530845	−	0.998590i	$-0.483095\pi$
$653$	−20.0643	−	11.5841i	−0.785178	−	0.453323i	−0.838262	+	0.545268i	$0.816428\pi$
$654$		0			0
$655$	47.5322	−	17.3003i	1.85724	−	0.675979i
$656$		0			0
$657$	3.11735	−	6.44989i	0.121619	−	0.251634i
$658$		0			0
$659$	3.15401	−	17.8873i	0.122863	−	0.696790i	−0.859691	−	0.510814i	$-0.829344\pi$
$659$	3.15401	−	17.8873i	0.122863	−	0.696790i	0.982554	−	0.185976i	$-0.0595448\pi$
$660$		0			0
$661$	22.4662	−	26.7742i	0.873835	−	1.04140i	−0.124952	−	0.992163i	$-0.539878\pi$
$661$	22.4662	−	26.7742i	0.873835	−	1.04140i	0.998787	−	0.0492336i	$-0.0156779\pi$
$662$		0			0
$663$	−27.8704	+	25.1849i	−1.08240	+	0.978099i
$664$		0			0
$665$	−37.9501	−	33.2391i	−1.47164	−	1.28896i
$666$		0			0
$667$	−3.39794	+	9.33576i	−0.131569	+	0.361482i
$668$		0			0
$669$	−8.25518	−	20.3277i	−0.319164	−	0.785913i
$670$		0			0
$671$	12.2556	+	2.16099i	0.473122	+	0.0834242i
$672$		0			0
$673$	−8.97335	+	5.18077i	−0.345897	+	0.199704i	−0.662877	−	0.748729i	$-0.730665\pi$
$673$	−8.97335	+	5.18077i	−0.345897	+	0.199704i	0.316980	+	0.948432i	$0.397331\pi$
$674$		0			0
$675$	−31.5507	+	15.5981i	−1.21439	+	0.600372i
$676$		0			0
$677$	−2.66151	+	4.60988i	−0.102290	+	0.177172i	−0.912628	−	0.408791i	$-0.865950\pi$
$677$	−2.66151	+	4.60988i	−0.102290	+	0.177172i	0.810338	+	0.585963i	$0.199284\pi$
$678$		0			0
$679$	19.8590	+	23.6670i	0.762117	+	0.908255i
$680$		0			0
$681$	−6.22955	−	2.01181i	−0.238717	−	0.0770927i
$682$		0			0
$683$	29.5958			1.13245			0.566226	−	0.824250i	$-0.308403\pi$
$683$	29.5958			1.13245			0.566226	+	0.824250i	$0.308403\pi$
$684$		0			0
$685$	−68.4183			−2.61413
$686$		0			0
$687$	25.2545	+	8.15584i	0.963519	+	0.311165i
$688$		0			0
$689$	−28.1354	−	33.5305i	−1.07187	−	1.27741i
$690$		0			0
$691$	−9.35680	+	16.2065i	−0.355950	+	0.616523i	−0.987280	−	0.158991i	$-0.949176\pi$
$691$	−9.35680	+	16.2065i	−0.355950	+	0.616523i	0.631330	+	0.775514i	$0.282509\pi$
$692$		0			0
$693$	−15.9670	+	22.1427i	−0.606538	+	0.841130i
$694$		0			0
$695$	4.80833	−	2.77609i	0.182390	−	0.105303i
$696$		0			0
$697$	−6.94369	−	1.22436i	−0.263011	−	0.0463760i
$698$		0			0
$699$	−15.8428	−	39.0115i	−0.599229	−	1.47555i
$700$		0			0
$701$	9.40339	−	25.8356i	0.355161	−	0.975798i	−0.625524	−	0.780205i	$-0.715115\pi$
$701$	9.40339	−	25.8356i	0.355161	−	0.975798i	0.980685	−	0.195593i	$-0.0626630\pi$
$702$		0			0
$703$	17.5878	−	14.1339i	0.663337	−	0.533071i
$704$		0			0
$705$	−0.567355	+	0.512687i	−0.0213678	+	0.0193089i
$706$		0			0
$707$	12.2610	−	14.6120i	0.461121	−	0.549543i
$708$		0			0
$709$	7.22305	−	40.9640i	0.271267	−	1.53843i	−0.479307	−	0.877647i	$-0.659112\pi$
$709$	7.22305	−	40.9640i	0.271267	−	1.53843i	0.750574	−	0.660786i	$-0.229777\pi$
$710$		0			0
$711$	−6.09561	−	2.94612i	−0.228603	−	0.110488i
$712$		0			0
$713$	−13.6759	+	4.97762i	−0.512166	+	0.186413i
$714$		0			0
$715$	−41.1425	−	23.7536i	−1.53864	−	0.888335i
$716$		0			0
$717$	−22.6236	+	4.85105i	−0.844895	+	0.181166i
$718$		0			0
$719$	26.6001	−	4.69031i	0.992015	−	0.174919i	0.345992	−	0.938237i	$-0.387542\pi$
$719$	26.6001	−	4.69031i	0.992015	−	0.174919i	0.646022	+	0.763318i	$0.276431\pi$
$720$		0			0
$721$		−	13.0742i		−	0.486908i
$722$		0			0
$723$	−33.6292	−	17.8040i	−1.25068	−	0.662137i
$724$		0			0
$725$	−4.43406	−	25.1468i	−0.164677	−	0.933930i
$726$		0			0
$727$	−23.4708	+	19.6943i	−0.870483	+	0.730422i	−0.964200	−	0.265177i	$-0.914570\pi$
$727$	−23.4708	+	19.6943i	−0.870483	+	0.730422i	0.0937165	+	0.995599i	$0.470125\pi$
$728$		0			0
$729$	−8.06779	+	25.7665i	−0.298807	+	0.954314i
$730$		0			0
$731$	3.50562	+	9.63162i	0.129660	+	0.356238i
$732$		0			0
$733$	−24.9658	−	43.2420i	−0.922132	−	1.59718i	−0.796110	−	0.605152i	$-0.793112\pi$
$733$	−24.9658	−	43.2420i	−0.922132	−	1.59718i	−0.126023	−	0.992027i	$-0.540221\pi$
$734$		0			0
$735$	15.9797	−	20.5285i	0.589418	−	0.757205i
$736$		0			0
$737$	−23.0596	−	19.3493i	−0.849410	−	0.712740i
$738$		0			0
$739$	−32.2619	−	11.7424i	−1.18677	−	0.431950i	−0.328183	−	0.944614i	$-0.606436\pi$
$739$	−32.2619	−	11.7424i	−1.18677	−	0.431950i	−0.858589	+	0.512664i	$0.828659\pi$
$740$		0			0
$741$	−7.31916	−	38.0494i	−0.268876	−	1.39778i
$742$		0			0
$743$	−27.6540	−	10.0652i	−1.01453	−	0.369257i	−0.219357	−	0.975645i	$-0.570396\pi$
$743$	−27.6540	−	10.0652i	−1.01453	−	0.369257i	−0.795169	+	0.606387i	$0.792618\pi$
$744$		0			0
$745$	63.3446	+	53.1525i	2.32077	+	1.94736i
$746$		0			0
$747$	8.91734	+	19.8377i	0.326269	+	0.725822i
$748$		0			0
$749$	−11.7698	−	20.3860i	−0.430061	−	0.744887i
$750$		0			0
$751$	−0.559448	−	1.53707i	−0.0204145	−	0.0560885i	0.929067	−	0.369912i	$-0.120612\pi$
$751$	−0.559448	−	1.53707i	−0.0204145	−	0.0560885i	−0.949481	+	0.313824i	$0.898390\pi$
$752$		0			0
$753$	−9.94920	+	6.24169i	−0.362569	+	0.227460i
$754$		0			0
$755$	−38.6526	+	32.4334i	−1.40671	+	1.18037i
$756$		0			0
$757$	4.17165	+	23.6586i	0.151621	+	0.859887i	0.961810	+	0.273718i	$0.0882534\pi$
$757$	4.17165	+	23.6586i	0.151621	+	0.859887i	−0.810189	+	0.586169i	$0.800635\pi$
$758$		0			0
$759$	5.76179	−	10.8832i	0.209140	−	0.395035i
$760$		0			0
$761$		−	12.8974i		−	0.467530i	−0.972293	−	0.233765i	$-0.924895\pi$
$761$		−	12.8974i		−	0.467530i	0.972293	−	0.233765i	$-0.0751047\pi$
$762$		0			0
$763$	−19.0410	+	3.35745i	−0.689332	+	0.121548i
$764$		0			0
$765$	41.8567	+	11.8406i	1.51333	+	0.428096i
$766$		0			0
$767$	−18.3359	−	10.5862i	−0.662069	−	0.382246i
$768$		0			0
$769$	21.8210	−	7.94220i	0.786886	−	0.286403i	0.0828452	−	0.996562i	$-0.473599\pi$
$769$	21.8210	−	7.94220i	0.786886	−	0.286403i	0.704041	+	0.710159i	$0.251377\pi$
$770$		0			0
$771$	−30.8071	+	1.13090i	−1.10949	+	0.0407285i
$772$		0			0
$773$	−6.98308	+	39.6030i	−0.251164	+	1.42442i	0.554566	+	0.832140i	$0.312884\pi$
$773$	−6.98308	+	39.6030i	−0.251164	+	1.42442i	−0.805730	+	0.592283i	$0.798227\pi$
$774$		0			0
$775$	24.0439	−	28.6544i	0.863683	−	1.02930i
$776$		0			0
$777$	20.2757	+	22.4377i	0.727387	+	0.804949i
$778$		0			0
$779$	4.79191	−	5.47107i	0.171688	−	0.196021i
$780$		0			0
$781$	11.9381	−	32.7998i	0.427181	−	1.17367i
$782$		0			0
$783$	−16.2982	−	10.8666i	−0.582449	−	0.388342i
$784$		0			0
$785$	51.8465	+	9.14194i	1.85048	+	0.326290i
$786$		0			0
$787$	40.4947	−	23.3796i	1.44348	−	0.833393i	0.445400	−	0.895332i	$-0.353062\pi$
$787$	40.4947	−	23.3796i	1.44348	−	0.833393i	0.998080	+	0.0619383i	$0.0197282\pi$
$788$		0			0
$789$	6.58580	+	0.913581i	0.234461	+	0.0325244i
$790$		0			0
$791$	−28.4865	+	49.3400i	−1.01286	+	1.75433i
$792$		0			0
$793$	−15.2175	−	18.1355i	−0.540388	−	0.644009i
$794$		0			0
$795$	−15.5771	+	48.2343i	−0.552463	+	1.71070i
$796$		0			0
$797$	6.73284			0.238489			0.119245	−	0.992865i	$-0.461953\pi$
$797$	6.73284			0.238489			0.119245	+	0.992865i	$0.461953\pi$
$798$		0			0
$799$	0.543722			0.0192355
$800$		0			0
$801$	−2.59657	+	2.52547i	−0.0917454	+	0.0892331i
$802$		0			0
$803$	−4.14089	−	4.93492i	−0.146129	−	0.174149i
$804$		0			0
$805$	−15.2505	+	26.4146i	−0.537508	+	0.930992i
$806$		0			0
$807$	0.627685	−	4.52484i	0.0220955	−	0.159282i
$808$		0			0
$809$	7.36554	−	4.25250i	0.258959	−	0.149510i	−0.364901	−	0.931046i	$-0.618897\pi$
$809$	7.36554	−	4.25250i	0.258959	−	0.149510i	0.623859	+	0.781537i	$0.285564\pi$
$810$		0			0
$811$	−28.9589	−	5.10623i	−1.01688	−	0.179304i	−0.359727	−	0.933058i	$-0.617130\pi$
$811$	−28.9589	−	5.10623i	−1.01688	−	0.179304i	−0.657157	+	0.753753i	$0.728241\pi$
$812$		0			0
$813$	−22.4617	+	9.12184i	−0.787768	+	0.319917i
$814$		0			0
$815$	13.9943	−	38.4490i	0.490198	−	1.34681i
$816$		0			0
$817$	−10.3708	−	2.05609i	−0.362827	−	0.0719333i
$818$		0			0
$819$	50.3449	−	12.7436i	1.75919	−	0.445297i
$820$		0			0
$821$	6.42410	−	7.65594i	0.224203	−	0.267194i	−0.642204	−	0.766534i	$-0.721980\pi$
$821$	6.42410	−	7.65594i	0.224203	−	0.267194i	0.866406	+	0.499340i	$0.166424\pi$
$822$		0			0
$823$	8.07641	−	45.8036i	0.281526	−	1.59661i	−0.435911	−	0.899990i	$-0.643574\pi$
$823$	8.07641	−	45.8036i	0.281526	−	1.59661i	0.717437	−	0.696623i	$-0.245315\pi$
$824$		0			0
$825$	1.16108	+	31.6290i	0.0404235	+	1.10118i
$826$		0			0
$827$	46.9782	−	17.0987i	1.63359	−	0.594579i	0.647690	−	0.761904i	$-0.275735\pi$
$827$	46.9782	−	17.0987i	1.63359	−	0.594579i	0.985902	+	0.167325i	$0.0535131\pi$
$828$		0			0
$829$	16.9994	+	9.81460i	0.590413	+	0.340875i	0.765261	−	0.643720i	$-0.222610\pi$
$829$	16.9994	+	9.81460i	0.590413	+	0.340875i	−0.174848	+	0.984595i	$0.555943\pi$
$830$		0			0
$831$	−0.121019	−	0.564389i	−0.00419809	−	0.0195785i
$832$		0			0
$833$	−18.2166	+	3.21208i	−0.631168	+	0.111292i
$834$		0			0
$835$		−	6.17046i		−	0.213538i
$836$		0			0
$837$	−3.15235	−	28.5216i	−0.108961	−	0.985850i
$838$		0			0
$839$	2.71691	+	15.4084i	0.0937982	+	0.531956i	0.995109	+	0.0987829i	$0.0314949\pi$
$839$	2.71691	+	15.4084i	0.0937982	+	0.531956i	−0.901311	+	0.433173i	$0.857394\pi$
$840$		0			0
$841$	−11.3285	+	9.50576i	−0.390639	+	0.327785i
$842$		0			0
$843$	−2.31002	−	3.68215i	−0.0795613	−	0.126820i
$844$		0			0
$845$	15.6541	+	43.0092i	0.538516	+	1.47956i
$846$		0			0
$847$	−6.27709	−	10.8722i	−0.215683	−	0.373574i
$848$		0			0
$849$	36.0101	+	28.0307i	1.23586	+	0.962012i
$850$		0			0
$851$	−10.4501	−	8.76867i	−0.358225	−	0.300586i
$852$		0			0
$853$	6.82954	+	2.48575i	0.233839	+	0.0851104i	0.456282	−	0.889835i	$-0.349181\pi$
$853$	6.82954	+	2.48575i	0.233839	+	0.0851104i	−0.222443	+	0.974946i	$0.571403\pi$
$854$		0			0
$855$	−32.8203	+	30.5955i	−1.12243	+	1.04634i
$856$		0			0
$857$	−10.7658	−	3.91845i	−0.367754	−	0.133852i	0.151531	−	0.988452i	$-0.451580\pi$
$857$	−10.7658	−	3.91845i	−0.367754	−	0.133852i	−0.519285	+	0.854601i	$0.673802\pi$
$858$		0			0
$859$	38.6125	+	32.3998i	1.31744	+	1.10547i	0.986841	+	0.161695i	$0.0516962\pi$
$859$	38.6125	+	32.3998i	1.31744	+	1.10547i	0.330602	+	0.943770i	$0.392748\pi$
$860$		0			0
$861$	7.69216	+	5.98768i	0.262148	+	0.204060i
$862$		0			0
$863$	−13.4511	−	23.2980i	−0.457882	−	0.793075i	0.540967	−	0.841044i	$-0.318058\pi$
$863$	−13.4511	−	23.2980i	−0.457882	−	0.793075i	−0.998849	+	0.0479693i	$0.984725\pi$
$864$		0			0
$865$	−7.95239	−	21.8490i	−0.270389	−	0.742889i
$866$		0			0
$867$	−0.789156	−	1.25791i	−0.0268011	−	0.0427208i
$868$		0			0
$869$	−4.66385	+	3.91344i	−0.158210	+	0.132754i
$870$		0			0
$871$	9.94396	+	56.3950i	0.336938	+	1.91087i
$872$		0			0
$873$	22.7255	−	15.4470i	0.769143	−	0.522801i
$874$		0			0
$875$		−	20.5252i		−	0.693880i
$876$		0			0
$877$	3.93346	−	0.693575i	0.132823	−	0.0234204i	−0.106841	−	0.994276i	$-0.534074\pi$
$877$	3.93346	−	0.693575i	0.132823	−	0.0234204i	0.239665	+	0.970856i	$0.422963\pi$
$878$		0			0
$879$	4.74499	+	22.1290i	0.160044	+	0.746392i
$880$		0			0
$881$	27.5291	+	15.8939i	0.927479	+	0.535480i	0.886013	−	0.463660i	$-0.153464\pi$
$881$	27.5291	+	15.8939i	0.927479	+	0.535480i	0.0414655	+	0.999140i	$0.486797\pi$
$882$		0			0
$883$	−14.7726	+	5.37678i	−0.497136	+	0.180943i	−0.578406	−	0.815749i	$-0.696325\pi$
$883$	−14.7726	+	5.37678i	−0.497136	+	0.180943i	0.0812691	+	0.996692i	$0.474103\pi$
$884$		0			0
$885$	0.899427	+	24.5014i	0.0302339	+	0.823605i
$886$		0			0
$887$	−7.99628	+	45.3492i	−0.268489	+	1.52268i	0.490424	+	0.871484i	$0.336842\pi$
$887$	−7.99628	+	45.3492i	−0.268489	+	1.52268i	−0.758913	+	0.651192i	$0.774269\pi$
$888$		0			0
$889$	11.9916	−	14.2910i	0.402185	−	0.479305i
$890$		0			0
$891$	18.1593	+	16.1172i	0.608358	+	0.539948i
$892$		0			0
$893$	−0.290651	+	0.479659i	−0.00972628	+	0.0160512i
$894$		0			0
$895$	16.8494	−	46.2934i	0.563214	−	1.54742i
$896$		0			0
$897$	−21.7047	+	8.81439i	−0.724699	+	0.294304i
$898$		0			0
$899$	20.5023	+	3.61510i	0.683789	+	0.120570i
$900$		0			0
$901$	31.2123	−	18.0204i	1.03983	−	0.600347i
$902$		0			0
$903$	1.94709	−	14.0361i	0.0647950	−	0.467093i
$904$		0			0
$905$	20.5230	−	35.5469i	0.682208	−	1.18162i
$906$		0			0
$907$	0.695285	+	0.828609i	0.0230866	+	0.0275135i	0.777464	−	0.628927i	$-0.216506\pi$
$907$	0.695285	+	0.828609i	0.0230866	+	0.0275135i	−0.754378	+	0.656441i	$0.772061\pi$
$908$		0			0
$909$	−11.8285	−	12.1616i	−0.392327	−	0.403373i
$910$		0			0
$911$	−45.4512			−1.50587			−0.752933	−	0.658098i	$-0.771361\pi$
$911$	−45.4512			−1.50587			−0.752933	+	0.658098i	$0.771361\pi$
$912$		0			0
$913$	19.5587			0.647300
$914$		0			0
$915$	−8.42510	+	26.0882i	−0.278525	+	0.862451i
$916$		0			0
$917$	31.9623	+	38.0912i	1.05549	+	1.25788i
$918$		0			0
$919$	10.4915	−	18.1717i	0.346081	−	0.599430i	−0.639468	−	0.768817i	$-0.720845\pi$
$919$	10.4915	−	18.1717i	0.346081	−	0.599430i	0.985550	+	0.169387i	$0.0541788\pi$
$920$		0			0
$921$	−12.3075	−	1.70729i	−0.405545	−	0.0562571i
$922$		0			0
$923$	−57.5053	+	33.2007i	−1.89281	+	1.09281i
$924$		0			0
$925$	34.5291	+	6.08841i	1.13531	+	0.200186i
$926$		0			0
$927$	−11.5688	−	1.17417i	−0.379971	−	0.0385647i
$928$		0			0
$929$	−10.4843	+	28.8055i	−0.343980	+	0.945077i	0.640247	+	0.768169i	$0.278832\pi$
$929$	−10.4843	+	28.8055i	−0.343980	+	0.945077i	−0.984227	+	0.176908i	$0.943390\pi$
$930$		0			0
$931$	6.90422	−	17.7873i	0.226277	−	0.582956i
$932$		0			0
$933$	−13.3594	−	14.7839i	−0.437368	−	0.484005i
$934$		0			0
$935$	25.1441	−	29.9655i	0.822299	−	0.979978i
$936$		0			0
$937$	−0.894500	+	5.07296i	−0.0292221	+	0.165726i	−0.995926	−	0.0901691i	$-0.971259\pi$
$937$	−0.894500	+	5.07296i	−0.0292221	+	0.165726i	0.966704	+	0.255896i	$0.0823703\pi$
$938$		0			0
$939$	30.6952	−	1.12680i	1.00170	−	0.0367717i
$940$		0			0
$941$	−23.0587	+	8.39267i	−0.751691	+	0.273593i	−0.689317	−	0.724460i	$-0.742089\pi$
$941$	−23.0587	+	8.39267i	−0.751691	+	0.273593i	−0.0623740	+	0.998053i	$0.519867\pi$
$942$		0			0
$943$	−3.80805	−	2.19858i	−0.124007	−	0.0715956i
$944$		0			0
$945$	−43.4833	−	41.5434i	−1.41451	−	1.35141i
$946$		0			0
$947$	−23.9834	+	4.22892i	−0.779357	+	0.137422i	−0.549154	−	0.835721i	$-0.685050\pi$
$947$	−23.9834	+	4.22892i	−0.779357	+	0.137422i	−0.230203	+	0.973143i	$0.573939\pi$
$948$		0			0
$949$			12.2551i			0.397818i
$950$		0			0
$951$	27.6191	−	52.1686i	0.895612	−	1.69168i
$952$		0			0
$953$	−0.495016	−	2.80737i	−0.0160351	−	0.0909398i	0.975740	−	0.218933i	$-0.0702576\pi$
$953$	−0.495016	−	2.80737i	−0.0160351	−	0.0909398i	−0.991775	+	0.127993i	$0.959146\pi$
$954$		0			0
$955$	−26.7190	+	22.4199i	−0.864607	+	0.725492i
$956$		0			0
$957$	−14.9220	+	9.36138i	−0.482358	+	0.302610i
$958$		0			0
$959$	−23.0034	−	63.2014i	−0.742819	−	2.04088i
$960$		0			0
$961$	−0.251521	−	0.435647i	−0.00811358	−	0.0140531i
$962$		0			0
$963$	−19.0958	+	8.58387i	−0.615354	+	0.276611i
$964$		0			0
$965$	−32.9282	−	27.6301i	−1.06000	−	0.889444i
$966$		0			0
$967$	24.1580	+	8.79281i	0.776870	+	0.282758i	0.699867	−	0.714273i	$-0.253243\pi$
$967$	24.1580	+	8.79281i	0.776870	+	0.282758i	0.0770033	+	0.997031i	$0.475465\pi$
$968$		0			0
$969$	31.9002	−	0.494669i	1.02478	−	0.0158911i
$970$		0			0
$971$	8.94724	+	3.25653i	0.287131	+	0.104507i	0.481570	−	0.876407i	$-0.340067\pi$
$971$	8.94724	+	3.25653i	0.287131	+	0.104507i	−0.194440	+	0.980914i	$0.562289\pi$
$972$		0			0
$973$	4.18105	+	3.50832i	0.134038	+	0.112472i
$974$		0			0
$975$	36.9843	−	47.5124i	1.18444	−	1.52161i
$976$		0			0
$977$	−11.2275	−	19.4466i	−0.359199	−	0.622151i	0.628628	−	0.777706i	$-0.283617\pi$
$977$	−11.2275	−	19.4466i	−0.359199	−	0.622151i	−0.987827	+	0.155555i	$0.950283\pi$
$978$		0			0
$979$	1.11406	+	3.06085i	0.0356055	+	0.0978253i
$980$		0			0
$981$	1.26084	+	17.1502i	0.0402556	+	0.547565i
$982$		0			0
$983$	15.1924	−	12.7479i	0.484561	−	0.406595i	−0.367511	−	0.930019i	$-0.619790\pi$
$983$	15.1924	−	12.7479i	0.484561	−	0.406595i	0.852072	+	0.523424i	$0.175346\pi$
$984$		0			0
$985$	−13.6941	−	77.6630i	−0.436330	−	2.47455i
$986$		0			0
$987$	−0.664348	−	0.351719i	−0.0211464	−	0.0111954i
$988$		0			0
$989$			6.39215i			0.203258i
$990$		0			0
$991$	−11.0355	+	1.94586i	−0.350556	+	0.0618124i	−0.346154	−	0.938178i	$-0.612512\pi$
$991$	−11.0355	+	1.94586i	−0.350556	+	0.0618124i	−0.00440221	+	0.999990i	$0.501401\pi$
$992$		0			0
$993$	−35.3878	+	7.58801i	−1.12300	+	0.240798i
$994$		0			0
$995$	75.2987	+	43.4737i	2.38713	+	1.37821i
$996$		0			0
$997$	−6.92900	+	2.52195i	−0.219444	+	0.0798710i	−0.449402	−	0.893329i	$-0.648363\pi$
$997$	−6.92900	+	2.52195i	−0.219444	+	0.0798710i	0.229959	+	0.973200i	$0.426141\pi$
$998$		0			0
$999$	21.6752	−	15.9261i	0.685774	−	0.503880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.d.737.3		18
3.2	odd	2		912.2.cc.c.737.3		18
4.3	odd	2		114.2.l.a.53.1	✓	18
12.11	even	2		114.2.l.b.53.1	yes	18
19.14	odd	18		912.2.cc.c.641.3		18
57.14	even	18	inner	912.2.cc.d.641.3		18
76.71	even	18		114.2.l.b.71.1	yes	18
228.71	odd	18		114.2.l.a.71.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.1	✓	18	4.3	odd	2
114.2.l.a.71.1	yes	18	228.71	odd	18
114.2.l.b.53.1	yes	18	12.11	even	2
114.2.l.b.71.1	yes	18	76.71	even	18
912.2.cc.c.641.3		18	19.14	odd	18
912.2.cc.c.737.3		18	3.2	odd	2
912.2.cc.d.641.3		18	57.14	even	18	inner
912.2.cc.d.737.3		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.64823 + 0.532290i) q^{3} +(2.20556 + 2.62849i) q^{5} +(-1.68651 + 2.92113i) q^{7} +(2.43333 + 1.75467i) q^{9} +O(q^{10})\)	\(q+(1.64823 + 0.532290i) q^{3} +(2.20556 + 2.62849i) q^{5} +(-1.68651 + 2.92113i) q^{7} +(2.43333 + 1.75467i) q^{9} +(2.33635 - 1.34889i) q^{11} +(-5.05419 - 0.891189i) q^{13} +(2.23616 + 5.50635i) q^{15} +(1.44531 - 3.97095i) q^{17} +(2.73048 + 3.39772i) q^{19} +(-4.33465 + 3.91698i) q^{21} +(1.69398 - 2.01881i) q^{23} +(-1.17620 + 6.67054i) q^{25} +(3.07670 + 4.18735i) q^{27} +(-3.54249 + 1.28936i) q^{29} +(-4.78254 - 2.76120i) q^{31} +(4.56886 - 0.979673i) q^{33} +(-11.3979 + 2.00975i) q^{35} -5.17636i q^{37} +(-7.85610 - 4.15918i) q^{39} +(-0.289735 - 1.64317i) q^{41} +(-1.85806 + 1.55910i) q^{43} +(0.754733 + 10.2660i) q^{45} +(0.0440069 + 0.120908i) q^{47} +(-2.18866 - 3.79087i) q^{49} +(4.49590 - 5.77572i) q^{51} +(6.53342 + 5.48219i) q^{53} +(8.69853 + 3.16600i) q^{55} +(2.69188 + 7.05363i) q^{57} +(3.87665 + 1.41099i) q^{59} +(3.53369 + 2.96512i) q^{61} +(-9.22948 + 4.14880i) q^{63} +(-8.80484 - 15.2504i) q^{65} +(-3.81629 - 10.4852i) q^{67} +(3.86667 - 2.42578i) q^{69} +(9.91131 - 8.31658i) q^{71} +(-0.414656 - 2.35163i) q^{73} +(-5.48930 + 10.3685i) q^{75} +9.09972i q^{77} +(-2.22246 + 0.391880i) q^{79} +(2.84224 + 8.53942i) q^{81} +(6.27861 + 3.62496i) q^{83} +(13.6253 - 4.95920i) q^{85} +(-6.52515 + 0.239533i) q^{87} +(-0.209662 + 1.18905i) q^{89} +(11.1272 - 13.2609i) q^{91} +(-6.41298 - 7.09680i) q^{93} +(-2.90863 + 14.6709i) q^{95} +(3.13271 - 8.60706i) q^{97} +(8.05200 + 0.817228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) \) 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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