LMFDB - Embedded newform 912.2.cc.c.641.3

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			641.3
Root			$-0.363139 + 1.69356i$ of defining polynomial
Character	$\chi$	$=$	912.641
Dual form			912.2.cc.c.737.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36678 + 1.06392i) q^{3} +(-2.20556 + 2.62849i) q^{5} +(-1.68651 - 2.92113i) q^{7} +(0.736160 + 2.90828i) q^{9} +O(q^{10})$	\(q+(1.36678 + 1.06392i) q^{3} +(-2.20556 + 2.62849i) q^{5} +(-1.68651 - 2.92113i) q^{7} +(0.736160 + 2.90828i) q^{9} +(-2.33635 - 1.34889i) q^{11} +(-5.05419 + 0.891189i) q^{13} +(-5.81100 + 1.24602i) q^{15} +(-1.44531 - 3.97095i) q^{17} +(2.73048 - 3.39772i) q^{19} +(0.802750 - 5.78684i) q^{21} +(-1.69398 - 2.01881i) q^{23} +(-1.17620 - 6.67054i) q^{25} +(-2.08800 + 4.75818i) q^{27} +(3.54249 + 1.28936i) q^{29} +(-4.78254 + 2.76120i) q^{31} +(-1.75816 - 4.32933i) q^{33} +(11.3979 + 2.00975i) q^{35} +5.17636i q^{37} +(-7.85610 - 4.15918i) q^{39} +(0.289735 - 1.64317i) q^{41} +(-1.85806 - 1.55910i) q^{43} +(-9.26801 - 4.47940i) q^{45} +(-0.0440069 + 0.120908i) q^{47} +(-2.18866 + 3.79087i) q^{49} +(2.24935 - 6.96509i) q^{51} +(-6.53342 + 5.48219i) q^{53} +(8.69853 - 3.16600i) q^{55} +(7.34685 - 1.73892i) q^{57} +(-3.87665 + 1.41099i) q^{59} +(3.53369 - 2.96512i) q^{61} +(7.25390 - 7.05526i) q^{63} +(8.80484 - 15.2504i) q^{65} +(-3.81629 + 10.4852i) q^{67} +(-0.167450 - 4.56152i) q^{69} +(-9.91131 - 8.31658i) q^{71} +(-0.414656 + 2.35163i) q^{73} +(5.48930 - 10.3685i) q^{75} +9.09972i q^{77} +(-2.22246 - 0.391880i) q^{79} +(-7.91614 + 4.28191i) q^{81} +(-6.27861 + 3.62496i) q^{83} +(13.6253 + 4.95920i) q^{85} +(3.47002 + 5.53118i) q^{87} +(0.209662 + 1.18905i) q^{89} +(11.1272 + 13.2609i) q^{91} +(-9.47436 - 1.31428i) q^{93} +(2.90863 + 14.6709i) q^{95} +(3.13271 + 8.60706i) q^{97} +(2.20303 - 7.78777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 - 3 * q^9	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$	$-1$	$1$

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
$3$	1.36678	+	1.06392i	0.789109	+	0.614253i
$3$	1.36678	+	1.06392i	0.789109	+	0.614253i
$4$		0			0
$5$	−2.20556	+	2.62849i	−0.986357	+	1.17549i	−0.00187711	+	0.999998i	$0.500598\pi$
$5$	−2.20556	+	2.62849i	−0.986357	+	1.17549i	−0.984480	+	0.175496i	$0.943847\pi$
$6$		0			0
$7$	−1.68651	−	2.92113i	−0.637442	−	1.10408i	−0.985992	−	0.166792i	$-0.946659\pi$
$7$	−1.68651	−	2.92113i	−0.637442	−	1.10408i	0.348550	−	0.937290i	$-0.386674\pi$
$8$		0			0
$9$	0.736160	+	2.90828i	0.245387	+	0.969425i
$10$		0			0
$11$	−2.33635	−	1.34889i	−0.704437	−	0.406707i	0.104561	−	0.994519i	$-0.466656\pi$
$11$	−2.33635	−	1.34889i	−0.704437	−	0.406707i	−0.808998	+	0.587811i	$0.799990\pi$
$12$		0			0
$13$	−5.05419	+	0.891189i	−1.40178	+	0.247171i	−0.822874	−	0.568224i	$-0.807631\pi$
$13$	−5.05419	+	0.891189i	−1.40178	+	0.247171i	−0.578905	+	0.815395i	$0.696520\pi$
$14$		0			0
$15$	−5.81100	+	1.24602i	−1.50039	+	0.321721i
$16$		0			0
$17$	−1.44531	−	3.97095i	−0.350538	−	0.963096i	−0.982198	−	0.187850i	$-0.939848\pi$
$17$	−1.44531	−	3.97095i	−0.350538	−	0.963096i	0.631659	−	0.775246i	$-0.282374\pi$
$18$		0			0
$19$	2.73048	−	3.39772i	0.626414	−	0.779490i
$19$	2.73048	−	3.39772i	0.626414	−	0.779490i
$20$		0			0
$21$	0.802750	−	5.78684i	0.175174	−	1.26279i
$22$		0			0
$23$	−1.69398	−	2.01881i	−0.353220	−	0.420951i	0.559952	−	0.828525i	$-0.310819\pi$
$23$	−1.69398	−	2.01881i	−0.353220	−	0.420951i	−0.913172	+	0.407574i	$0.866375\pi$
$24$		0			0
$25$	−1.17620	−	6.67054i	−0.235239	−	1.33411i
$26$		0			0
$27$	−2.08800	+	4.75818i	−0.401836	+	0.915712i
$28$		0			0
$29$	3.54249	+	1.28936i	0.657823	+	0.239428i	0.649296	−	0.760536i	$-0.275064\pi$
$29$	3.54249	+	1.28936i	0.657823	+	0.239428i	0.00852691	+	0.999964i	$0.497286\pi$
$30$		0			0
$31$	−4.78254	+	2.76120i	−0.858970	+	0.495927i	−0.863667	−	0.504062i	$-0.831838\pi$
$31$	−4.78254	+	2.76120i	−0.858970	+	0.495927i	0.00469717	+	0.999989i	$0.498505\pi$
$32$		0			0
$33$	−1.75816	−	4.32933i	−0.306057	−	0.753639i
$34$		0			0
$35$	11.3979	+	2.00975i	1.92659	+	0.339710i
$36$		0			0
$37$			5.17636i			0.850989i	0.904961	+	0.425494i	$0.139900\pi$
$37$			5.17636i			0.850989i	−0.904961	+	0.425494i	$0.860100\pi$
$38$		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	$-0.902854\pi$
$41$	0.289735	−	1.64317i	0.0452490	−	0.256620i	0.999038	+	0.0438581i	$0.0139649\pi$
$42$		0			0
$43$	−1.85806	−	1.55910i	−0.283351	−	0.237760i	0.490023	−	0.871709i	$-0.336988\pi$
$43$	−1.85806	−	1.55910i	−0.283351	−	0.237760i	−0.773374	+	0.633950i	$0.781433\pi$
$44$		0			0
$45$	−9.26801	−	4.47940i	−1.38159	−	0.667749i
$46$		0			0
$47$	−0.0440069	+	0.120908i	−0.00641906	+	0.0176362i	−0.942861	−	0.333187i	$-0.891876\pi$
$47$	−0.0440069	+	0.120908i	−0.00641906	+	0.0176362i	0.936442	+	0.350823i	$0.114098\pi$
$48$		0			0
$49$	−2.18866	+	3.79087i	−0.312665	+	0.541552i
$50$		0			0
$51$	2.24935	−	6.96509i	0.314972	−	0.975307i
$52$		0			0
$53$	−6.53342	+	5.48219i	−0.897434	+	0.753036i	−0.969687	−	0.244350i	$-0.921425\pi$
$53$	−6.53342	+	5.48219i	−0.897434	+	0.753036i	0.0722533	+	0.997386i	$0.476981\pi$
$54$		0			0
$55$	8.69853	−	3.16600i	1.17291	−	0.426904i
$56$		0			0
$57$	7.34685	−	1.73892i	0.973113	−	0.230326i
$58$		0			0
$59$	−3.87665	+	1.41099i	−0.504697	+	0.183695i	−0.581805	−	0.813328i	$-0.697653\pi$
$59$	−3.87665	+	1.41099i	−0.504697	+	0.183695i	0.0771085	+	0.997023i	$0.475431\pi$
$60$		0			0
$61$	3.53369	−	2.96512i	0.452443	−	0.379645i	−0.387898	−	0.921702i	$-0.626799\pi$
$61$	3.53369	−	2.96512i	0.452443	−	0.379645i	0.840342	+	0.542057i	$0.182354\pi$
$62$		0			0
$63$	7.25390	−	7.05526i	0.913906	−	0.888880i
$64$		0			0
$65$	8.80484	−	15.2504i	1.09211	−	1.89158i
$66$		0			0
$67$	−3.81629	+	10.4852i	−0.466234	+	1.28097i	0.454490	+	0.890752i	$0.349821\pi$
$67$	−3.81629	+	10.4852i	−0.466234	+	1.28097i	−0.920724	+	0.390215i	$0.872401\pi$
$68$		0			0
$69$	−0.167450	−	4.56152i	−0.0201586	−	0.549143i
$70$		0			0
$71$	−9.91131	−	8.31658i	−1.17626	−	0.986996i	−0.999996	−	0.00265261i	$-0.999156\pi$
$71$	−9.91131	−	8.31658i	−1.17626	−	0.986996i	−0.176260	−	0.984344i	$-0.556400\pi$
$72$		0			0
$73$	−0.414656	+	2.35163i	−0.0485318	+	0.275238i	−0.999411	−	0.0343255i	$-0.989072\pi$
$73$	−0.414656	+	2.35163i	−0.0485318	+	0.275238i	0.950879	+	0.309563i	$0.100183\pi$
$74$		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	0.0472200	−	0.998885i	$-0.484964\pi$
$79$	−2.22246	−	0.391880i	−0.250046	−	0.0440899i	−0.297266	+	0.954795i	$0.596075\pi$
$80$		0			0
$81$	−7.91614	+	4.28191i	−0.879571	+	0.475768i
$82$		0			0
$83$	−6.27861	+	3.62496i	−0.689167	+	0.397891i	−0.803300	−	0.595575i	$-0.796924\pi$
$83$	−6.27861	+	3.62496i	−0.689167	+	0.397891i	0.114133	+	0.993465i	$0.463591\pi$
$84$		0			0
$85$	13.6253	+	4.95920i	1.47787	+	0.537901i
$86$		0			0
$87$	3.47002	+	5.53118i	0.372025	+	0.593005i
$88$		0			0
$89$	0.209662	+	1.18905i	0.0222241	+	0.126039i	0.993901	−	0.110273i	$-0.0351724\pi$
$89$	0.209662	+	1.18905i	0.0222241	+	0.126039i	−0.971677	+	0.236312i	$0.924061\pi$
$90$		0			0
$91$	11.1272	+	13.2609i	1.16645	+	1.39012i
$92$		0			0
$93$	−9.47436	−	1.31428i	−0.982446	−	0.136285i
$94$		0			0
$95$	2.90863	+	14.6709i	0.298419	+	1.50520i
$96$		0			0
$97$	3.13271	+	8.60706i	0.318079	+	0.873914i	0.990959	+	0.134163i	$0.0428346\pi$
$97$	3.13271	+	8.60706i	0.318079	+	0.873914i	−0.672880	+	0.739751i	$0.734943\pi$
$98$		0			0
$99$	2.20303	−	7.78777i	0.221413	−	0.782700i
$100$		0			0
$101$	5.56915	−	0.981991i	0.554151	−	0.0977117i	0.110442	−	0.993883i	$-0.464773\pi$
$101$	5.56915	−	0.981991i	0.554151	−	0.0977117i	0.443709	+	0.896171i	$0.353662\pi$
$102$		0			0
$103$	−3.35680	−	1.93805i	−0.330755	−	0.190961i	0.325421	−	0.945569i	$-0.394494\pi$
$103$	−3.35680	−	1.93805i	−0.330755	−	0.190961i	−0.656176	+	0.754608i	$0.727827\pi$
$104$		0			0
$105$	13.4401	+	14.8733i	1.31162	+	1.45148i
$106$		0			0
$107$	3.48940	+	6.04382i	0.337333	+	0.584278i	0.983930	−	0.178554i	$-0.0571419\pi$
$107$	3.48940	+	6.04382i	0.337333	+	0.584278i	−0.646597	+	0.762832i	$0.723809\pi$
$108$		0			0
$109$	3.68457	−	4.39110i	0.352918	−	0.420591i	−0.560155	−	0.828388i	$-0.689258\pi$
$109$	3.68457	−	4.39110i	0.352918	−	0.420591i	0.913073	+	0.407797i	$0.133703\pi$
$110$		0			0
$111$	−5.50722	+	7.07493i	−0.522722	+	0.671523i
$112$		0			0
$113$	−16.8907			−1.58895			−0.794474	−	0.607298i	$-0.792253\pi$
$113$	−16.8907			−1.58895			−0.794474	+	0.607298i	$0.792253\pi$
$114$		0			0
$115$	9.04260			0.843227
$116$		0			0
$117$	−6.31251	−	14.0429i	−0.583592	−	1.29827i
$118$		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
$123$	2.14420	−	1.93759i	0.193336	−	0.174707i
$124$		0			0
$125$	5.26986	+	3.04256i	0.471351	+	0.272134i
$126$		0			0
$127$	−5.44679	+	0.960416i	−0.483324	+	0.0852231i	−0.410001	−	0.912085i	$-0.634472\pi$
$127$	−5.44679	+	0.960416i	−0.483324	+	0.0852231i	−0.0733234	+	0.997308i	$0.523361\pi$
$128$		0			0
$129$	−0.880802	−	4.10776i	−0.0775503	−	0.361668i
$130$		0			0
$131$	−5.04199	−	13.8528i	−0.440521	−	1.21032i	−0.939150	−	0.343506i	$-0.888385\pi$
$131$	−5.04199	−	13.8528i	−0.440521	−	1.21032i	0.498629	−	0.866815i	$-0.333837\pi$
$132$		0			0
$133$	−14.5302	−	2.24577i	−1.25992	−	0.194733i
$134$		0			0
$135$	−7.90159	−	15.9827i	−0.680061	−	1.37557i
$136$		0			0
$137$	12.8171	+	15.2748i	1.09503	+	1.30501i	0.948840	+	0.315756i	$0.102258\pi$
$137$	12.8171	+	15.2748i	1.09503	+	1.30501i	0.146195	+	0.989256i	$0.453297\pi$
$138$		0			0
$139$	0.280984	+	1.59354i	0.0238328	+	0.135162i	0.994403	−	0.105658i	$-0.0336948\pi$
$139$	0.280984	+	1.59354i	0.0238328	+	0.135162i	−0.970570	+	0.240820i	$0.922584\pi$
$140$		0			0
$141$	−0.188784	+	0.118434i	−0.0158984	+	0.00997398i
$142$		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
$147$	−7.02457	+	2.85272i	−0.579377	+	0.235288i
$148$		0			0
$149$	−23.7332	−	4.18480i	−1.94430	−	0.342832i	−0.999902	−	0.0140170i	$-0.995538\pi$
$149$	−23.7332	−	4.18480i	−1.94430	−	0.342832i	−0.944394	−	0.328815i	$-0.893351\pi$
$150$		0			0
$151$		−	14.7053i		−	1.19670i	−0.801235	−	0.598349i	$-0.795824\pi$
$151$		−	14.7053i		−	1.19670i	0.801235	−	0.598349i	$-0.204176\pi$
$152$		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	0.977243	−	0.212124i	$-0.0680380\pi$
$157$	11.7536	+	9.86243i	0.938038	+	0.787108i	−0.0392046	+	0.999231i	$0.512482\pi$
$158$		0			0
$159$	−14.7623	+	0.541913i	−1.17073	+	0.0429765i
$160$		0			0
$161$	−3.04028	+	8.35309i	−0.239607	+	0.658316i
$162$		0			0
$163$	−5.96235	+	10.3271i	−0.467007	+	0.808880i	−0.999290	−	0.0376868i	$-0.988001\pi$
$163$	−5.96235	+	10.3271i	−0.467007	+	0.808880i	0.532283	+	0.846567i	$0.321334\pi$
$164$		0			0
$165$	15.2573	+	4.92729i	1.18778	+	0.383589i
$166$		0			0
$167$	1.37759	−	1.15593i	0.106601	−	0.0894489i	−0.587929	−	0.808912i	$-0.700057\pi$
$167$	1.37759	−	1.15593i	0.106601	−	0.0894489i	0.694530	+	0.719463i	$0.255612\pi$
$168$		0			0
$169$	12.5346	−	4.56221i	0.964198	−	0.350939i
$170$		0			0
$171$	11.8916	+	5.43971i	0.909371	+	0.415985i
$172$		0			0
$173$	6.36766	−	2.31764i	0.484124	−	0.176207i	−0.0884156	−	0.996084i	$-0.528180\pi$
$173$	6.36766	−	2.31764i	0.484124	−	0.176207i	0.572540	+	0.819877i	$0.305958\pi$
$174$		0			0
$175$	−17.5018	+	14.6858i	−1.32301	+	1.11014i
$176$		0			0
$177$	−6.79969	−	2.19593i	−0.511096	−	0.165056i
$178$		0			0
$179$	7.17879	−	12.4340i	0.536568	−	0.929363i	−0.462518	−	0.886610i	$-0.653054\pi$
$179$	7.17879	−	12.4340i	0.536568	−	0.929363i	0.999086	−	0.0427531i	$-0.0136129\pi$
$180$		0			0
$181$	−4.09139	+	11.2410i	−0.304111	+	0.835537i	0.689664	+	0.724129i	$0.257758\pi$
$181$	−4.09139	+	11.2410i	−0.304111	+	0.835537i	−0.993775	+	0.111408i	$0.964464\pi$
$182$		0			0
$183$	7.98441	−	0.293102i	0.590225	−	0.0216667i
$184$		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	−0.289027	−	0.957321i	$-0.593332\pi$
$193$	−12.3371	−	2.17537i	−0.888046	−	0.156587i	−0.599019	+	0.800734i	$0.704443\pi$
$194$		0			0
$195$	28.2595	−	11.4763i	2.02370	−	0.821836i
$196$		0			0
$197$	19.9041	−	11.4916i	1.41811	−	0.818744i	0.421974	−	0.906608i	$-0.361338\pi$
$197$	19.9041	−	11.4916i	1.41811	−	0.818744i	0.996132	+	0.0878643i	$0.0280042\pi$
$198$		0			0
$199$	23.8117	+	8.66676i	1.68797	+	0.614370i	0.994367	−	0.105990i	$-0.0338011\pi$
$199$	23.8117	+	8.66676i	1.68797	+	0.614370i	0.693601	+	0.720360i	$0.256023\pi$
$200$		0			0
$201$	−16.3714	+	10.2707i	−1.15475	+	0.724437i
$202$		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
$207$	4.62422	−	6.41274i	0.321405	−	0.445716i
$208$		0			0
$209$	−10.9625	+	4.25515i	−0.758294	+	0.294335i
$210$		0			0
$211$	4.07273	+	11.1897i	0.280378	+	0.770333i	0.997317	+	0.0731972i	$0.0233202\pi$
$211$	4.07273	+	11.1897i	0.280378	+	0.770333i	−0.716939	+	0.697136i	$0.754458\pi$
$212$		0			0
$213$	−4.69840	−	21.9117i	−0.321929	−	1.50137i
$214$		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
$219$	−3.06868	+	2.77300i	−0.207362	+	0.187382i
$220$		0			0
$221$	10.8437	+	18.7819i	0.729427	+	1.26341i
$222$		0			0
$223$	−8.14222	+	9.70352i	−0.545243	+	0.649796i	−0.966355	−	0.257213i	$-0.917196\pi$
$223$	−8.14222	+	9.70352i	−0.545243	+	0.649796i	0.421111	+	0.907009i	$0.361640\pi$
$224$		0			0
$225$	18.5339	−	8.33128i	1.23559	−	0.555419i
$226$		0			0
$227$	3.77953			0.250857			0.125428	−	0.992103i	$-0.459970\pi$
$227$	3.77953			0.250857			0.125428	+	0.992103i	$0.459970\pi$
$228$		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
$231$	−9.68135	+	12.4373i	−0.636986	+	0.818313i
$232$		0			0
$233$	15.6260	−	18.6223i	1.02369	−	1.21999i	0.0484572	−	0.998825i	$-0.484570\pi$
$233$	15.6260	−	18.6223i	1.02369	−	1.21999i	0.975236	−	0.221165i	$-0.0709860\pi$
$234$		0			0
$235$	−0.220745	−	0.382341i	−0.0143998	−	0.0249412i
$236$		0			0
$237$	−2.62068	−	2.90013i	−0.170232	−	0.188384i
$238$		0			0
$239$	11.5689	+	6.67933i	0.748332	+	0.432050i	0.825091	−	0.565000i	$-0.191124\pi$
$239$	11.5689	+	6.67933i	0.748332	+	0.432050i	−0.0767587	+	0.997050i	$0.524457\pi$
$240$		0			0
$241$	−21.6352	+	3.81487i	−1.39365	+	0.245737i	−0.819530	−	0.573037i	$-0.805765\pi$
$241$	−21.6352	+	3.81487i	−1.39365	+	0.245737i	−0.574116	+	0.818774i	$0.694654\pi$
$242$		0			0
$243$	−15.3752	−	2.56970i	−0.986319	−	0.164846i
$244$		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
$249$	−12.4381	−	1.72541i	−0.788234	−	0.109344i
$250$		0			0
$251$	4.35873	+	5.19453i	0.275121	+	0.327876i	0.885857	−	0.463958i	$-0.153571\pi$
$251$	4.35873	+	5.19453i	0.275121	+	0.327876i	−0.610737	+	0.791834i	$0.709127\pi$
$252$		0			0
$253$	1.23458	+	7.00166i	0.0776175	+	0.440191i
$254$		0			0
$255$	13.3466	+	21.2743i	0.835794	+	1.33225i
$256$		0			0
$257$	16.7251	+	6.08743i	1.04328	+	0.379724i	0.806123	−	0.591747i	$-0.201562\pi$
$257$	16.7251	+	6.08743i	1.04328	+	0.379724i	0.237158	+	0.971471i	$0.423784\pi$
$258$		0			0
$259$	15.1208	−	8.73000i	0.939561	−	0.542456i
$260$		0			0
$261$	−1.14198	+	11.2517i	−0.0706866	+	0.696463i
$262$		0			0
$263$	−3.78041	−	0.666587i	−0.233110	−	0.0411035i	0.0558728	−	0.998438i	$-0.482206\pi$
$263$	−3.78041	−	0.666587i	−0.233110	−	0.0411035i	−0.288983	+	0.957334i	$0.593317\pi$
$264$		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	$-0.918824\pi$
$269$	0.457985	−	2.59736i	0.0279239	−	0.158364i	0.995581	+	0.0939040i	$0.0299347\pi$
$270$		0			0
$271$	−10.7222	−	8.99702i	−0.651329	−	0.546530i	0.256145	−	0.966638i	$-0.417548\pi$
$271$	−10.7222	−	8.99702i	−0.651329	−	0.546530i	−0.907474	+	0.420108i	$0.861992\pi$
$272$		0			0
$273$	1.09993	+	29.9632i	0.0665705	+	1.81345i
$274$		0			0
$275$	−6.24984	+	17.1713i	−0.376880	+	1.03547i
$276$		0			0
$277$	−0.166629	+	0.288609i	−0.0100117	+	0.0173408i	−0.870988	−	0.491305i	$-0.836520\pi$
$277$	−0.166629	+	0.288609i	−0.0100117	+	0.0173408i	0.860976	+	0.508645i	$0.169854\pi$
$278$		0			0
$279$	−11.5511	−	11.8763i	−0.691544	−	0.711014i
$280$		0			0
$281$	1.92247	−	1.61315i	0.114685	−	0.0962323i	−0.583642	−	0.812011i	$-0.698373\pi$
$281$	1.92247	−	1.61315i	0.114685	−	0.0962323i	0.698327	+	0.715779i	$0.253928\pi$
$282$		0			0
$283$	24.7578	−	9.01110i	1.47170	−	0.535655i	0.523138	−	0.852248i	$-0.324761\pi$
$283$	24.7578	−	9.01110i	1.47170	−	0.535655i	0.948561	+	0.316594i	$0.102539\pi$
$284$		0			0
$285$	−11.6332	+	23.1464i	−0.689090	+	1.37107i
$286$		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
$291$	−4.87548	+	15.0969i	−0.285806	+	0.884995i
$292$		0			0
$293$	−6.53329	+	11.3160i	−0.381679	+	0.661087i	−0.991302	−	0.131604i	$-0.957987\pi$
$293$	−6.53329	+	11.3160i	−0.381679	+	0.661087i	0.609624	+	0.792691i	$0.291321\pi$
$294$		0			0
$295$	4.84144	−	13.3017i	0.281879	−	0.774457i
$296$		0			0
$297$	11.2966	−	8.30030i	0.655495	−	0.481632i
$298$		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	−0.0316333	−	0.999500i	$-0.510071\pi$
$307$	−7.06477	−	1.24571i	−0.403208	−	0.0710964i	−0.371575	+	0.928403i	$0.621182\pi$
$308$		0			0
$309$	−2.52607	−	6.22023i	−0.143703	−	0.353857i
$310$		0			0
$311$	9.96292	−	5.75210i	0.564945	−	0.326171i	−0.190183	−	0.981749i	$-0.560908\pi$
$311$	9.96292	−	5.75210i	0.564945	−	0.326171i	0.755128	+	0.655577i	$0.227575\pi$
$312$		0			0
$313$	16.6644	+	6.06533i	0.941925	+	0.342833i	0.766926	−	0.641736i	$-0.221785\pi$
$313$	16.6644	+	6.06533i	0.941925	+	0.342833i	0.174999	+	0.984569i	$0.444008\pi$
$314$		0			0
$315$	2.54574	+	34.6276i	0.143436	+	1.95104i
$316$		0			0
$317$	−5.91797	−	33.5625i	−0.332386	−	1.88506i	−0.451653	−	0.892194i	$-0.649165\pi$
$317$	−5.91797	−	33.5625i	−0.332386	−	1.88506i	0.119267	−	0.992862i	$-0.461946\pi$
$318$		0			0
$319$	−6.53729	−	7.79084i	−0.366018	−	0.436203i
$320$		0			0
$321$	−1.66089	+	11.9730i	−0.0927019	+	0.668267i
$322$		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
$327$	9.70775	−	2.08158i	0.536840	−	0.115111i
$328$		0			0
$329$	0.427405	−	0.0753631i	0.0235636	−	0.00415490i
$330$		0			0
$331$	−18.0961	−	10.4478i	−0.994652	−	0.574263i	−0.0879907	−	0.996121i	$-0.528045\pi$
$331$	−18.0961	−	10.4478i	−0.994652	−	0.574263i	−0.906662	+	0.421858i	$0.861378\pi$
$332$		0			0
$333$	−15.0543	+	3.81063i	−0.824970	+	0.208821i
$334$		0			0
$335$	−19.1430	−	33.1567i	−1.04590	−	1.81155i
$336$		0			0
$337$	−19.1366	+	22.8061i	−1.04244	+	1.24233i	−0.0729092	+	0.997339i	$0.523228\pi$
$337$	−19.1366	+	22.8061i	−1.04244	+	1.24233i	−0.969526	+	0.244988i	$0.921216\pi$
$338$		0			0
$339$	−23.0859	−	17.9704i	−1.25385	−	0.976016i
$340$		0			0
$341$	14.8983			0.806788
$342$		0			0
$343$	−8.84639			−0.477660
$344$		0			0
$345$	12.3592	+	9.62058i	0.665398	+	0.517955i
$346$		0			0
$347$	−3.49226	+	4.16191i	−0.187474	+	0.223423i	−0.851592	−	0.524204i	$-0.824363\pi$
$347$	−3.49226	+	4.16191i	−0.187474	+	0.223423i	0.664118	+	0.747628i	$0.268807\pi$
$348$		0			0
$349$	−8.07643	−	13.9888i	−0.432322	−	0.748803i	0.564751	−	0.825261i	$-0.308972\pi$
$349$	−8.07643	−	13.9888i	−0.432322	−	0.748803i	−0.997073	+	0.0764582i	$0.975639\pi$
$350$		0			0
$351$	6.31270	−	25.9095i	0.336947	−	1.38295i
$352$		0			0
$353$	18.1153	+	10.4589i	0.964180	+	0.556670i	0.897457	−	0.441102i	$-0.145412\pi$
$353$	18.1153	+	10.4589i	0.964180	+	0.556670i	0.0667232	+	0.997772i	$0.478746\pi$
$354$		0			0
$355$	43.7200	−	7.70902i	2.32042	−	0.409152i
$356$		0			0
$357$	−24.1395	+	5.17608i	−1.27760	+	0.273947i
$358$		0			0
$359$	−8.05343	−	22.1266i	−0.425044	−	1.16780i	−0.948785	−	0.315921i	$-0.897686\pi$
$359$	−8.05343	−	22.1266i	−0.425044	−	1.16780i	0.523741	−	0.851877i	$-0.324536\pi$
$360$		0			0
$361$	−4.08900	−	18.5548i	−0.215211	−	0.976568i
$362$		0			0
$363$	0.885785	−	6.38543i	0.0464917	−	0.335148i
$364$		0			0
$365$	−5.26668	−	6.27659i	−0.275671	−	0.328532i
$366$		0			0
$367$	−3.11469	−	17.6643i	−0.162586	−	0.922069i	−0.951519	−	0.307590i	$-0.900477\pi$
$367$	−3.11469	−	17.6643i	−0.162586	−	0.922069i	0.788933	−	0.614479i	$-0.210634\pi$
$368$		0			0
$369$	4.99208	−	0.367005i	0.259877	−	0.0191055i
$370$		0			0
$371$	27.0329	+	9.83916i	1.40348	+	0.510824i
$372$		0			0
$373$	12.2615	−	7.07917i	0.634876	−	0.366546i	−0.147762	−	0.989023i	$-0.547207\pi$
$373$	12.2615	−	7.07917i	0.634876	−	0.366546i	0.782638	+	0.622477i	$0.213874\pi$
$374$		0			0
$375$	3.96570	+	9.76519i	0.204788	+	0.504272i
$376$		0			0
$377$	−19.0534	−	3.35964i	−0.981303	−	0.173030i
$378$		0			0
$379$			1.25595i			0.0645137i	0.999480	+	0.0322569i	$0.0102695\pi$
$379$			1.25595i			0.0645137i	−0.999480	+	0.0322569i	$0.989731\pi$
$380$		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	$-0.966253\pi$
$383$	−0.465296	+	2.63882i	−0.0237755	+	0.134838i	0.970610	+	0.240660i	$0.0773637\pi$
$384$		0			0
$385$	−23.9185	−	20.0700i	−1.21900	−	1.02286i
$386$		0			0
$387$	3.16645	−	6.55149i	0.160960	−	0.333031i
$388$		0			0
$389$	11.2472	−	30.9013i	0.570253	−	1.56676i	−0.233852	−	0.972272i	$-0.575133\pi$
$389$	11.2472	−	30.9013i	0.570253	−	1.56676i	0.804106	−	0.594486i	$-0.202645\pi$
$390$		0			0
$391$	−5.56827	+	9.64452i	−0.281599	+	0.487744i
$392$		0			0
$393$	7.84692	−	24.2979i	0.395825	−	1.22567i
$394$		0			0
$395$	5.93183	−	4.97739i	0.298463	−	0.250440i
$396$		0			0
$397$	−2.19998	+	0.800726i	−0.110414	+	0.0401873i	−0.396636	−	0.917976i	$-0.629823\pi$
$397$	−2.19998	+	0.800726i	−0.110414	+	0.0401873i	0.286223	+	0.958163i	$0.407600\pi$
$398$		0			0
$399$	−17.4702	−	18.5284i	−0.874603	−	0.927578i
$400$		0			0
$401$	12.8782	−	4.68726i	0.643104	−	0.234071i	0.000179351	−	1.00000i	$-0.499943\pi$
$401$	12.8782	−	4.68726i	0.643104	−	0.234071i	0.642925	+	0.765929i	$0.277721\pi$
$402$		0			0
$403$	21.7111	−	18.2178i	1.08151	−	0.907492i
$404$		0			0
$405$	6.20459	−	30.2515i	0.308308	−	1.50321i
$406$		0			0
$407$	6.98237	−	12.0938i	0.346103	−	0.599468i
$408$		0			0
$409$	7.27394	−	19.9850i	0.359673	−	0.988194i	−0.619470	−	0.785020i	$-0.712652\pi$
$409$	7.27394	−	19.9850i	0.359673	−	0.988194i	0.979143	−	0.203173i	$-0.0651254\pi$
$410$		0			0
$411$	1.26696	+	34.5135i	0.0624947	+	1.70243i
$412$		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	0.352378	−	0.935858i	$-0.385373\pi$
$421$	7.45681	+	1.31484i	0.363423	+	0.0640812i	0.0110448	+	0.999939i	$0.496484\pi$
$422$		0			0
$423$	−0.384029	−	0.0389766i	−0.0186722	−	0.00189511i
$424$		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
$429$	12.7443	+	20.3144i	0.615302	+	0.980787i
$430$		0			0
$431$	4.16028	+	23.5941i	0.200394	+	1.13649i	0.904526	+	0.426419i	$0.140225\pi$
$431$	4.16028	+	23.5941i	0.200394	+	1.13649i	−0.704132	+	0.710069i	$0.748664\pi$
$432$		0			0
$433$	−9.89407	−	11.7913i	−0.475479	−	0.566654i	0.473984	−	0.880534i	$-0.342816\pi$
$433$	−9.89407	−	11.7913i	−0.475479	−	0.566654i	−0.949463	+	0.313880i	$0.898371\pi$
$434$		0			0
$435$	−22.1920	−	3.07847i	−1.06402	−	0.147601i
$436$		0			0
$437$	−11.4847	+	0.243366i	−0.549389	+	0.0116418i
$438$		0			0
$439$	7.60564	+	20.8963i	0.362997	+	0.997327i	0.977964	+	0.208774i	$0.0669472\pi$
$439$	7.60564	+	20.8963i	0.362997	+	0.997327i	−0.614967	+	0.788553i	$0.710831\pi$
$440$		0			0
$441$	−12.6361	−	3.57454i	−0.601718	−	0.170216i
$442$		0			0
$443$	−30.8547	+	5.44051i	−1.46595	+	0.258486i	−0.848948	−	0.528476i	$-0.822764\pi$
$443$	−30.8547	+	5.44051i	−1.46595	+	0.258486i	−0.617001	+	0.786963i	$0.711652\pi$
$444$		0			0
$445$	−3.58782	−	2.07143i	−0.170079	−	0.0981952i
$446$		0			0
$447$	−27.9857	−	30.9698i	−1.32368	−	1.46482i
$448$		0			0
$449$	−6.15216	−	10.6559i	−0.290338	−	0.502881i	0.683551	−	0.729902i	$-0.260435\pi$
$449$	−6.15216	−	10.6559i	−0.290338	−	0.502881i	−0.973890	+	0.227022i	$0.927101\pi$
$450$		0			0
$451$	−2.89339	+	3.44820i	−0.136244	+	0.162370i
$452$		0			0
$453$	15.6452	−	20.0988i	0.735076	−	0.944326i
$454$		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
$459$	21.9123	+	1.41431i	1.02278	+	0.0660142i
$460$		0			0
$461$	−24.9818	+	29.7722i	−1.16352	+	1.38663i	−0.255970	+	0.966685i	$0.582395\pi$
$461$	−24.9818	+	29.7722i	−1.16352	+	1.38663i	−0.907550	+	0.419945i	$0.862050\pi$
$462$		0			0
$463$	−12.3259	−	21.3492i	−0.572835	−	0.992180i	−0.996273	−	0.0862548i	$-0.972510\pi$
$463$	−12.3259	−	21.3492i	−0.572835	−	0.992180i	0.423438	−	0.905925i	$-0.360823\pi$
$464$		0			0
$465$	24.3509	−	22.0045i	1.12924	−	1.02043i
$466$		0			0
$467$	−3.17931	−	1.83558i	−0.147121	−	0.0849404i	0.424632	−	0.905366i	$-0.360403\pi$
$467$	−3.17931	−	1.83558i	−0.147121	−	0.0849404i	−0.571754	+	0.820425i	$0.693737\pi$
$468$		0			0
$469$	37.0647	−	6.53551i	1.71149	−	0.301782i
$470$		0			0
$471$	5.57172	+	25.9846i	0.256731	+	1.19731i
$472$		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
$477$	−20.7534	−	14.9652i	−0.950231	−	0.685210i
$478$		0			0
$479$	16.6874	+	19.8872i	0.762465	+	0.908670i	0.998001	−	0.0631952i	$-0.0201291\pi$
$479$	16.6874	+	19.8872i	0.762465	+	0.908670i	−0.235536	+	0.971866i	$0.575685\pi$
$480$		0			0
$481$	−4.61312	−	26.1623i	−0.210340	−	1.19290i
$482$		0			0
$483$	−13.0424	+	8.18221i	−0.593449	+	0.372304i
$484$		0			0
$485$	−29.5329	−	10.7491i	−1.34102	−	0.488092i
$486$		0			0
$487$	−8.59327	+	4.96133i	−0.389398	+	0.224819i	−0.681899	−	0.731446i	$-0.738846\pi$
$487$	−8.59327	+	4.96133i	−0.389398	+	0.224819i	0.292501	+	0.956265i	$0.405512\pi$
$488$		0			0
$489$	−19.1364	+	7.77138i	−0.865376	+	0.351434i
$490$		0			0
$491$	−14.8971	−	2.62676i	−0.672296	−	0.118544i	−0.172929	−	0.984934i	$-0.555323\pi$
$491$	−14.8971	−	2.62676i	−0.672296	−	0.118544i	−0.499367	+	0.866391i	$0.666434\pi$
$492$		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	0.199917	−	0.979813i	$-0.435933\pi$
$499$	−16.3136	−	13.6887i	−0.730296	−	0.612791i	−0.930212	+	0.367022i	$0.880377\pi$
$500$		0			0
$501$	3.11268	−	0.114264i	0.139064	−	0.00510494i
$502$		0			0
$503$	1.99181	−	5.47245i	0.0888104	−	0.244004i	−0.887334	−	0.461128i	$-0.847445\pi$
$503$	1.99181	−	5.47245i	0.0888104	−	0.244004i	0.976144	+	0.217123i	$0.0696673\pi$
$504$		0			0
$505$	−9.70195	+	16.8043i	−0.431731	+	0.747780i
$506$		0			0
$507$	21.9858	+	7.10023i	0.976423	+	0.315332i
$508$		0			0
$509$	−10.9586	+	9.19535i	−0.485731	+	0.407577i	−0.852493	−	0.522738i	$-0.824911\pi$
$509$	−10.9586	+	9.19535i	−0.485731	+	0.407577i	0.366763	+	0.930315i	$0.380466\pi$
$510$		0			0
$511$	7.56874	−	2.75480i	0.334821	−	0.121865i
$512$		0			0
$513$	10.4657	+	20.0865i	0.462073	+	0.886842i
$514$		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
$519$	11.1690	+	3.60697i	0.490263	+	0.158328i
$520$		0			0
$521$	−5.93133	+	10.2734i	−0.259856	+	0.450084i	−0.966203	−	0.257781i	$-0.917009\pi$
$521$	−5.93133	+	10.2734i	−0.259856	+	0.450084i	0.706347	+	0.707866i	$0.250342\pi$
$522$		0			0
$523$	−10.6971	+	29.3899i	−0.467750	+	1.28513i	0.451787	+	0.892126i	$0.350787\pi$
$523$	−10.6971	+	29.3899i	−0.467750	+	1.28513i	−0.919536	+	0.393005i	$0.871435\pi$
$524$		0			0
$525$	−39.5455	+	1.45169i	−1.72591	+	0.0633568i
$526$		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
$537$	23.0406	−	9.35691i	0.994275	−	0.403780i
$538$		0			0
$539$	10.2270	−	5.90454i	0.440506	−	0.254326i
$540$		0			0
$541$	−26.2388	−	9.55016i	−1.12810	−	0.410593i	−0.290495	−	0.956876i	$-0.593820\pi$
$541$	−26.2388	−	9.55016i	−1.12810	−	0.410593i	−0.837601	+	0.546283i	$0.816042\pi$
$542$		0			0
$543$	−17.5515	+	11.0110i	−0.753207	+	0.472529i
$544$		0			0
$545$	3.41540	+	19.3697i	0.146300	+	0.829706i
$546$		0			0
$547$	−12.0859	−	14.4034i	−0.516757	−	0.615847i	0.443054	−	0.896495i	$-0.353895\pi$
$547$	−12.0859	−	14.4034i	−0.516757	−	0.615847i	−0.959811	+	0.280648i	$0.909451\pi$
$548$		0			0
$549$	11.2248	+	8.09415i	0.479061	+	0.345450i
$550$		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
$555$	−6.44985	−	30.0799i	−0.273781	−	1.27682i
$556$		0			0
$557$	−22.6372	+	3.99155i	−0.959170	+	0.169128i	−0.631251	−	0.775578i	$-0.717458\pi$
$557$	−22.6372	+	3.99155i	−0.959170	+	0.169128i	−0.327919	+	0.944706i	$0.606347\pi$
$558$		0			0
$559$	10.7804	+	6.22408i	0.455963	+	0.263250i
$560$		0			0
$561$	−14.6504	+	13.2388i	−0.618542	+	0.558942i
$562$		0			0
$563$	−6.45057	−	11.1727i	−0.271859	−	0.470874i	0.697479	−	0.716605i	$-0.254305\pi$
$563$	−6.45057	−	11.1727i	−0.271859	−	0.470874i	−0.969338	+	0.245732i	$0.920972\pi$
$564$		0			0
$565$	37.2536	−	44.3971i	1.56727	−	1.86780i
$566$		0			0
$567$	25.8587	+	15.9025i	1.08596	+	0.667844i
$568$		0			0
$569$	−37.8380			−1.58625			−0.793125	−	0.609059i	$-0.791547\pi$
$569$	−37.8380			−1.58625			−0.793125	+	0.609059i	$0.791547\pi$
$570$		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
$573$	−10.8149	+	13.8935i	−0.451799	+	0.580411i
$574$		0			0
$575$	−11.4741	+	13.6743i	−0.478503	+	0.570258i
$576$		0			0
$577$	−8.69281	−	15.0564i	−0.361886	−	0.626805i	0.626385	−	0.779514i	$-0.284534\pi$
$577$	−8.69281	−	15.0564i	−0.361886	−	0.626805i	−0.988271	+	0.152708i	$0.951200\pi$
$578$		0			0
$579$	−14.5477	−	16.0989i	−0.604582	−	0.669049i
$580$		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
$585$	50.8342	+	14.3802i	2.10174	+	0.594546i
$586$		0			0
$587$	10.0782	+	27.6896i	0.415971	+	1.14287i	0.953964	+	0.299922i	$0.0969607\pi$
$587$	10.0782	+	27.6896i	0.415971	+	1.14287i	−0.537992	+	0.842950i	$0.680817\pi$
$588$		0			0
$589$	−3.67683	+	23.7891i	−0.151501	+	0.980214i
$590$		0			0
$591$	39.4306	+	5.46980i	1.62196	+	0.224998i
$592$		0			0
$593$	−8.16230	−	9.72745i	−0.335185	−	0.399458i	0.571956	−	0.820284i	$-0.306185\pi$
$593$	−8.16230	−	9.72745i	−0.335185	−	0.399458i	−0.907141	+	0.420826i	$0.861740\pi$
$594$		0			0
$595$	−8.49279	−	48.1650i	−0.348170	−	1.97457i
$596$		0			0
$597$	23.3246	+	37.1792i	0.954612	+	1.52164i
$598$		0			0
$599$	16.8817	+	6.14443i	0.689767	+	0.251055i	0.663035	−	0.748588i	$-0.269268\pi$
$599$	16.8817	+	6.14443i	0.689767	+	0.251055i	0.0267313	+	0.999643i	$0.491490\pi$
$600$		0			0
$601$	8.14038	−	4.69985i	0.332053	−	0.191711i	−0.324699	−	0.945817i	$-0.605263\pi$
$601$	8.14038	−	4.69985i	0.332053	−	0.191711i	0.656752	+	0.754106i	$0.271930\pi$
$602$		0			0
$603$	−33.3031	−	3.38006i	−1.35621	−	0.137647i
$604$		0			0
$605$	12.5768	+	2.21764i	0.511321	+	0.0901597i
$606$		0			0
$607$			9.88885i			0.401376i	0.979655	+	0.200688i	$0.0643177\pi$
$607$			9.88885i			0.401376i	−0.979655	+	0.200688i	$0.935682\pi$
$608$		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	−0.0171592	−	0.999853i	$-0.505462\pi$
$613$	−24.8777	−	20.8749i	−1.00480	−	0.843129i	−0.987642	+	0.156724i	$0.949907\pi$
$614$		0			0
$615$	0.363769	+	9.90947i	0.0146686	+	0.399589i
$616$		0			0
$617$	7.64721	−	21.0105i	0.307865	−	0.845852i	−0.685207	−	0.728348i	$-0.740288\pi$
$617$	7.64721	−	21.0105i	0.307865	−	0.845852i	0.993072	−	0.117504i	$-0.0374893\pi$
$618$		0			0
$619$	9.39662	−	16.2754i	0.377682	−	0.654164i	−0.613043	−	0.790050i	$-0.710055\pi$
$619$	9.39662	−	16.2754i	0.377682	−	0.654164i	0.990725	+	0.135886i	$0.0433880\pi$
$620$		0			0
$621$	13.1429	−	3.84500i	0.527406	−	0.154295i
$622$		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
$627$	−19.5105	−	5.84738i	−0.779173	−	0.233522i
$628$		0			0
$629$	20.5551	−	7.48143i	0.819584	−	0.298304i
$630$		0			0
$631$	22.1517	−	18.5875i	0.881846	−	0.739956i	−0.0847122	−	0.996405i	$-0.526997\pi$
$631$	22.1517	−	18.5875i	0.881846	−	0.739956i	0.966558	+	0.256449i	$0.0825526\pi$
$632$		0			0
$633$	−6.33844	+	19.6269i	−0.251930	+	0.780100i
$634$		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
$639$	16.8906	−	34.9472i	0.668182	−	1.38249i
$640$		0			0
$641$	18.2950	+	15.3513i	0.722609	+	0.606341i	0.928106	−	0.372317i	$-0.121437\pi$
$641$	18.2950	+	15.3513i	0.722609	+	0.606341i	−0.205497	+	0.978658i	$0.565881\pi$
$642$		0			0
$643$	−6.83453	+	38.7606i	−0.269528	+	1.52857i	0.486297	+	0.873793i	$0.338347\pi$
$643$	−6.83453	+	38.7606i	−0.269528	+	1.52857i	−0.755825	+	0.654774i	$0.772764\pi$
$644$		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
$651$	12.1395	+	29.8924i	0.475783	+	1.17157i
$652$		0			0
$653$	20.0643	−	11.5841i	0.785178	−	0.453323i	−0.0530845	−	0.998590i	$-0.516905\pi$
$653$	20.0643	−	11.5841i	0.785178	−	0.453323i	0.838262	+	0.545268i	$0.183572\pi$
$654$		0			0
$655$	47.5322	+	17.3003i	1.85724	+	0.675979i
$656$		0			0
$657$	−7.14445	+	0.525242i	−0.278731	+	0.0204916i
$658$		0			0
$659$	−3.15401	−	17.8873i	−0.122863	−	0.696790i	−0.982554	−	0.185976i	$-0.940455\pi$
$659$	−3.15401	−	17.8873i	−0.122863	−	0.696790i	0.859691	−	0.510814i	$-0.170656\pi$
$660$		0			0
$661$	22.4662	+	26.7742i	0.873835	+	1.04140i	0.998787	+	0.0492336i	$0.0156779\pi$
$661$	22.4662	+	26.7742i	0.873835	+	1.04140i	−0.124952	+	0.992163i	$0.539878\pi$
$662$		0			0
$663$	−5.16141	+	37.2074i	−0.200453	+	1.44502i
$664$		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
$669$	−21.4523	+	4.59990i	−0.829395	+	0.177842i
$670$		0			0
$671$	−12.2556	+	2.16099i	−0.473122	+	0.0834242i
$672$		0			0
$673$	−8.97335	−	5.18077i	−0.345897	−	0.199704i	0.316980	−	0.948432i	$-0.397331\pi$
$673$	−8.97335	−	5.18077i	−0.345897	−	0.199704i	−0.662877	+	0.748729i	$0.730665\pi$
$674$		0			0
$675$	34.1955	+	8.33153i	1.31619	+	0.320681i
$676$		0			0
$677$	2.66151	+	4.60988i	0.102290	+	0.177172i	0.912628	−	0.408791i	$-0.134050\pi$
$677$	2.66151	+	4.60988i	0.102290	+	0.177172i	−0.810338	+	0.585963i	$0.800716\pi$
$678$		0			0
$679$	19.8590	−	23.6670i	0.762117	−	0.908255i
$680$		0			0
$681$	5.16578	+	4.02111i	0.197953	+	0.154089i
$682$		0			0
$683$	−29.5958			−1.13245			−0.566226	−	0.824250i	$-0.691597\pi$
$683$	−29.5958			−1.13245			−0.566226	+	0.824250i	$0.691597\pi$
$684$		0			0
$685$	−68.4183			−2.61413
$686$		0			0
$687$	20.9420	+	16.3015i	0.798987	+	0.621942i
$688$		0			0
$689$	28.1354	−	33.5305i	1.07187	−	1.27741i
$690$		0			0
$691$	−9.35680	−	16.2065i	−0.355950	−	0.616523i	0.631330	−	0.775514i	$-0.282509\pi$
$691$	−9.35680	−	16.2065i	−0.355950	−	0.616523i	−0.987280	+	0.158991i	$0.949176\pi$
$692$		0			0
$693$	−26.4645	+	6.69885i	−1.00530	+	0.254468i
$694$		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
$699$	41.1699	−	8.82782i	1.55719	−	0.333899i
$700$		0			0
$701$	−9.40339	−	25.8356i	−0.355161	−	0.975798i	−0.980685	−	0.195593i	$-0.937337\pi$
$701$	−9.40339	−	25.8356i	−0.355161	−	0.975798i	0.625524	−	0.780205i	$-0.284885\pi$
$702$		0			0
$703$	17.5878	+	14.1339i	0.663337	+	0.533071i
$704$		0			0
$705$	0.105070	−	0.757429i	0.00395718	−	0.0285264i
$706$		0			0
$707$	−12.2610	−	14.6120i	−0.461121	−	0.549543i
$708$		0			0
$709$	7.22305	+	40.9640i	0.271267	+	1.53843i	0.750574	+	0.660786i	$0.229777\pi$
$709$	7.22305	+	40.9640i	0.271267	+	1.53843i	−0.479307	+	0.877647i	$0.659112\pi$
$710$		0			0
$711$	−0.496392	−	6.75202i	−0.0186161	−	0.253220i
$712$		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
$717$	8.70590	+	21.4375i	0.325128	+	0.800600i
$718$		0			0
$719$	−26.6001	−	4.69031i	−0.992015	−	0.174919i	−0.345992	−	0.938237i	$-0.612458\pi$
$719$	−26.6001	−	4.69031i	−0.992015	−	0.174919i	−0.646022	+	0.763318i	$0.723569\pi$
$720$		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	0.0937165	−	0.995599i	$-0.470125\pi$
$727$	−23.4708	−	19.6943i	−0.870483	−	0.730422i	−0.964200	+	0.265177i	$0.914570\pi$
$728$		0			0
$729$	−18.2805	−	19.8701i	−0.677056	−	0.735931i
$730$		0			0
$731$	−3.50562	+	9.63162i	−0.129660	+	0.356238i
$732$		0			0
$733$	−24.9658	+	43.2420i	−0.922132	+	1.59718i	−0.126023	+	0.992027i	$0.540221\pi$
$733$	−24.9658	+	43.2420i	−0.922132	+	1.59718i	−0.796110	+	0.605152i	$0.793112\pi$
$734$		0			0
$735$	7.99480	−	24.7558i	0.294893	−	0.913133i
$736$		0			0
$737$	23.0596	−	19.3493i	0.849410	−	0.712740i
$738$		0			0
$739$	−32.2619	+	11.7424i	−1.18677	+	0.431950i	−0.858589	−	0.512664i	$-0.828659\pi$
$739$	−32.2619	+	11.7424i	−1.18677	+	0.431950i	−0.328183	+	0.944614i	$0.606436\pi$
$740$		0			0
$741$	−35.5826	+	15.3363i	−1.30716	+	0.563392i
$742$		0			0
$743$	27.6540	−	10.0652i	1.01453	−	0.369257i	0.219357	−	0.975645i	$-0.429604\pi$
$743$	27.6540	−	10.0652i	1.01453	−	0.369257i	0.795169	+	0.606387i	$0.207382\pi$
$744$		0			0
$745$	63.3446	−	53.1525i	2.32077	−	1.94736i
$746$		0			0
$747$	−15.1644	−	15.5914i	−0.554838	−	0.570459i
$748$		0			0
$749$	11.7698	−	20.3860i	0.430061	−	0.744887i
$750$		0			0
$751$	−0.559448	+	1.53707i	−0.0204145	+	0.0560885i	−0.949481	−	0.313824i	$-0.898390\pi$
$751$	−0.559448	+	1.53707i	−0.0204145	+	0.0560885i	0.929067	+	0.369912i	$0.120612\pi$
$752$		0			0
$753$	0.430860	+	11.7371i	0.0157014	+	0.427724i
$754$		0			0
$755$	38.6526	+	32.4334i	1.40671	+	1.18037i
$756$		0			0
$757$	4.17165	−	23.6586i	0.151621	−	0.859887i	−0.810189	−	0.586169i	$-0.800635\pi$
$757$	4.17165	−	23.6586i	0.151621	−	0.859887i	0.961810	−	0.273718i	$-0.0882534\pi$
$758$		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
$765$	−4.39233	+	43.2769i	−0.158805	+	1.56468i
$766$		0			0
$767$	18.3359	−	10.5862i	0.662069	−	0.382246i
$768$		0			0
$769$	21.8210	+	7.94220i	0.786886	+	0.286403i	0.704041	−	0.710159i	$-0.251377\pi$
$769$	21.8210	+	7.94220i	0.786886	+	0.286403i	0.0828452	+	0.996562i	$0.473599\pi$
$770$		0			0
$771$	16.3829	+	26.1143i	0.590017	+	0.940482i
$772$		0			0
$773$	6.98308	+	39.6030i	0.251164	+	1.42442i	0.805730	+	0.592283i	$0.201773\pi$
$773$	6.98308	+	39.6030i	0.251164	+	1.42442i	−0.554566	+	0.832140i	$0.687116\pi$
$774$		0			0
$775$	24.0439	+	28.6544i	0.863683	+	1.02930i
$776$		0			0
$777$	29.9548	+	4.15532i	1.07462	+	0.149071i
$778$		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
$783$	−13.5317	+	14.1636i	−0.483584	+	0.506166i
$784$		0			0
$785$	−51.8465	+	9.14194i	−1.85048	+	0.326290i
$786$		0			0
$787$	40.4947	+	23.3796i	1.44348	+	0.833393i	0.998080	−	0.0619383i	$-0.0197282\pi$
$787$	40.4947	+	23.3796i	1.44348	+	0.833393i	0.445400	+	0.895332i	$0.353062\pi$
$788$		0			0
$789$	−4.45778	−	4.93312i	−0.158701	−	0.175624i
$790$		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
$795$	31.1348	−	39.9978i	1.10424	−	1.41857i
$796$		0			0
$797$	−6.73284			−0.238489			−0.119245	−	0.992865i	$-0.538047\pi$
$797$	−6.73284			−0.238489			−0.119245	+	0.992865i	$0.538047\pi$
$798$		0			0
$799$	0.543722			0.0192355
$800$		0			0
$801$	−3.30374	+	1.48508i	−0.116732	+	0.0524729i
$802$		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
$807$	3.38934	−	3.06276i	0.119311	−	0.107814i
$808$		0			0
$809$	−7.36554	−	4.25250i	−0.258959	−	0.149510i	0.364901	−	0.931046i	$-0.381103\pi$
$809$	−7.36554	−	4.25250i	−0.258959	−	0.149510i	−0.623859	+	0.781537i	$0.714436\pi$
$810$		0			0
$811$	−28.9589	+	5.10623i	−1.01688	+	0.179304i	−0.657157	−	0.753753i	$-0.728241\pi$
$811$	−28.9589	+	5.10623i	−1.01688	+	0.179304i	−0.359727	+	0.933058i	$0.617130\pi$
$812$		0			0
$813$	−5.08282	−	23.7045i	−0.178262	−	0.831353i
$814$		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
$819$	−30.3750	+	42.1232i	−1.06139	+	1.47190i
$820$		0			0
$821$	−6.42410	−	7.65594i	−0.224203	−	0.267194i	0.642204	−	0.766534i	$-0.278020\pi$
$821$	−6.42410	−	7.65594i	−0.224203	−	0.267194i	−0.866406	+	0.499340i	$0.833576\pi$
$822$		0			0
$823$	8.07641	+	45.8036i	0.281526	+	1.59661i	0.717437	+	0.696623i	$0.245315\pi$
$823$	8.07641	+	45.8036i	0.281526	+	1.59661i	−0.435911	+	0.899990i	$0.643574\pi$
$824$		0			0
$825$	−26.8110	+	16.8200i	−0.933439	+	0.585598i
$826$		0			0
$827$	−46.9782	−	17.0987i	−1.63359	−	0.594579i	−0.647690	−	0.761904i	$-0.724265\pi$
$827$	−46.9782	−	17.0987i	−1.63359	−	0.594579i	−0.985902	+	0.167325i	$0.946487\pi$
$828$		0			0
$829$	16.9994	−	9.81460i	0.590413	−	0.340875i	−0.174848	−	0.984595i	$-0.555943\pi$
$829$	16.9994	−	9.81460i	0.590413	−	0.340875i	0.765261	+	0.643720i	$0.222610\pi$
$830$		0			0
$831$	−0.534800	+	0.217185i	−0.0185520	+	0.00753408i
$832$		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	0.901311	+	0.433173i	$0.142606\pi$
$839$	−2.71691	+	15.4084i	−0.0937982	+	0.531956i	−0.995109	+	0.0987829i	$0.968505\pi$
$840$		0			0
$841$	−11.3285	−	9.50576i	−0.390639	−	0.327785i
$842$		0			0
$843$	4.34385	−	0.159459i	0.149610	−	0.00549207i
$844$		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
$849$	43.4255	+	14.0241i	1.49036	+	0.481305i
$850$		0			0
$851$	10.4501	−	8.76867i	0.358225	−	0.300586i
$852$		0			0
$853$	6.82954	−	2.48575i	0.233839	−	0.0851104i	−0.222443	−	0.974946i	$-0.571403\pi$
$853$	6.82954	−	2.48575i	0.233839	−	0.0851104i	0.456282	+	0.889835i	$0.349181\pi$
$854$		0			0
$855$	−40.5258	+	19.2592i	−1.38595	+	0.658651i
$856$		0			0
$857$	10.7658	−	3.91845i	0.367754	−	0.133852i	−0.151531	−	0.988452i	$-0.548420\pi$
$857$	10.7658	−	3.91845i	0.367754	−	0.133852i	0.519285	+	0.854601i	$0.326198\pi$
$858$		0			0
$859$	38.6125	−	32.3998i	1.31744	−	1.10547i	0.330602	−	0.943770i	$-0.392748\pi$
$859$	38.6125	−	32.3998i	1.31744	−	1.10547i	0.986841	−	0.161695i	$-0.0516962\pi$
$860$		0			0
$861$	−9.27617	−	2.99570i	−0.316131	−	0.102093i
$862$		0			0
$863$	13.4511	−	23.2980i	0.457882	−	0.793075i	−0.540967	−	0.841044i	$-0.681942\pi$
$863$	13.4511	−	23.2980i	0.457882	−	0.793075i	0.998849	+	0.0479693i	$0.0152749\pi$
$864$		0			0
$865$	−7.95239	+	21.8490i	−0.270389	+	0.742889i
$866$		0			0
$867$	−1.48396	+	0.0544750i	−0.0503979	+	0.00185007i
$868$		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	0.239665	−	0.970856i	$-0.422963\pi$
$877$	3.93346	+	0.693575i	0.132823	+	0.0234204i	−0.106841	+	0.994276i	$0.534074\pi$
$878$		0			0
$879$	−20.9688	+	8.51555i	−0.707261	+	0.287223i
$880$		0			0
$881$	−27.5291	+	15.8939i	−0.927479	+	0.535480i	−0.886013	−	0.463660i	$-0.846536\pi$
$881$	−27.5291	+	15.8939i	−0.927479	+	0.535480i	−0.0414655	+	0.999140i	$0.513203\pi$
$882$		0			0
$883$	−14.7726	−	5.37678i	−0.497136	−	0.180943i	0.0812691	−	0.996692i	$-0.474103\pi$
$883$	−14.7726	−	5.37678i	−0.497136	−	0.180943i	−0.578406	+	0.815749i	$0.696325\pi$
$884$		0			0
$885$	20.7691	−	13.0296i	0.698146	−	0.437986i
$886$		0			0
$887$	7.99628	+	45.3492i	0.268489	+	1.52268i	0.758913	+	0.651192i	$0.225731\pi$
$887$	7.99628	+	45.3492i	0.268489	+	1.52268i	−0.490424	+	0.871484i	$0.663158\pi$
$888$		0			0
$889$	11.9916	+	14.2910i	0.402185	+	0.479305i
$890$		0			0
$891$	24.2708	+	0.673976i	0.813101	+	0.0225790i
$892$		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
$897$	4.91150	+	22.9056i	0.163990	+	0.764794i
$898$		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
$903$	−10.5138	+	9.50072i	−0.349877	+	0.316164i
$904$		0			0
$905$	−20.5230	−	35.5469i	−0.682208	−	1.18162i
$906$		0			0
$907$	0.695285	−	0.828609i	0.0230866	−	0.0275135i	−0.754378	−	0.656441i	$-0.772061\pi$
$907$	0.695285	−	0.828609i	0.0230866	−	0.0275135i	0.777464	+	0.628927i	$0.216506\pi$
$908$		0			0
$909$	6.95568	+	15.4737i	0.230705	+	0.513231i
$910$		0			0
$911$	45.4512			1.50587			0.752933	−	0.658098i	$-0.228639\pi$
$911$	45.4512			1.50587			0.752933	+	0.658098i	$0.228639\pi$
$912$		0			0
$913$	19.5587			0.647300
$914$		0			0
$915$	−16.8397	+	21.6334i	−0.556704	+	0.715177i
$916$		0			0
$917$	−31.9623	+	38.0912i	−1.05549	+	1.25788i
$918$		0			0
$919$	10.4915	+	18.1717i	0.346081	+	0.599430i	0.985550	−	0.169387i	$-0.0541788\pi$
$919$	10.4915	+	18.1717i	0.346081	+	0.599430i	−0.639468	+	0.768817i	$0.720845\pi$
$920$		0			0
$921$	−8.33064	−	9.21894i	−0.274504	−	0.303774i
$922$		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
$927$	3.16524	−	11.1892i	0.103960	−	0.367502i
$928$		0			0
$929$	10.4843	+	28.8055i	0.343980	+	0.945077i	0.984227	+	0.176908i	$0.0566096\pi$
$929$	10.4843	+	28.8055i	0.343980	+	0.945077i	−0.640247	+	0.768169i	$0.721168\pi$
$930$		0			0
$931$	6.90422	+	17.7873i	0.226277	+	0.582956i
$932$		0			0
$933$	19.7368	+	2.73789i	0.646155	+	0.0896346i
$934$		0			0
$935$	−25.1441	−	29.9655i	−0.822299	−	0.979978i
$936$		0			0
$937$	−0.894500	−	5.07296i	−0.0292221	−	0.165726i	0.966704	−	0.255896i	$-0.0823703\pi$
$937$	−0.894500	−	5.07296i	−0.0292221	−	0.165726i	−0.995926	+	0.0901691i	$0.971259\pi$
$938$		0			0
$939$	16.3235	+	26.0195i	0.532696	+	0.849113i
$940$		0			0
$941$	23.0587	+	8.39267i	0.751691	+	0.273593i	0.689317	−	0.724460i	$-0.257911\pi$
$941$	23.0587	+	8.39267i	0.751691	+	0.273593i	0.0623740	+	0.998053i	$0.480133\pi$
$942$		0			0
$943$	−3.80805	+	2.19858i	−0.124007	+	0.0715956i
$944$		0			0
$945$	−33.3614	+	50.0367i	−1.08525	+	1.62769i
$946$		0			0
$947$	23.9834	+	4.22892i	0.779357	+	0.137422i	0.549154	−	0.835721i	$-0.314950\pi$
$947$	23.9834	+	4.22892i	0.779357	+	0.137422i	0.230203	+	0.973143i	$0.426061\pi$
$948$		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	$-0.929742\pi$
$953$	0.495016	−	2.80737i	0.0160351	−	0.0909398i	0.991775	+	0.127993i	$0.0408535\pi$
$954$		0			0
$955$	−26.7190	−	22.4199i	−0.864607	−	0.725492i
$956$		0			0
$957$	−0.646210	−	17.6035i	−0.0208890	−	0.569040i
$958$		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
$963$	−15.0083	+	14.5973i	−0.483637	+	0.470393i
$964$		0			0
$965$	32.9282	−	27.6301i	1.06000	−	0.889444i
$966$		0			0
$967$	24.1580	−	8.79281i	0.776870	−	0.282758i	0.0770033	−	0.997031i	$-0.475465\pi$
$967$	24.1580	−	8.79281i	0.776870	−	0.282758i	0.699867	+	0.714273i	$0.253243\pi$
$968$		0			0
$969$	−17.5236	−	26.6607i	−0.562940	−	0.856464i
$970$		0			0
$971$	−8.94724	+	3.25653i	−0.287131	+	0.104507i	−0.481570	−	0.876407i	$-0.659933\pi$
$971$	−8.94724	+	3.25653i	−0.287131	+	0.104507i	0.194440	+	0.980914i	$0.437711\pi$
$972$		0			0
$973$	4.18105	−	3.50832i	0.134038	−	0.112472i
$974$		0			0
$975$	−18.5037	+	57.2964i	−0.592591	+	1.83495i
$976$		0			0
$977$	11.2275	−	19.4466i	0.359199	−	0.622151i	−0.628628	−	0.777706i	$-0.716383\pi$
$977$	11.2275	−	19.4466i	0.359199	−	0.622151i	0.987827	+	0.155555i	$0.0497166\pi$
$978$		0			0
$979$	1.11406	−	3.06085i	0.0356055	−	0.0978253i
$980$		0			0
$981$	15.4830	+	7.48319i	0.494333	+	0.238920i
$982$		0			0
$983$	−15.1924	−	12.7479i	−0.484561	−	0.406595i	0.367511	−	0.930019i	$-0.380210\pi$
$983$	−15.1924	−	12.7479i	−0.484561	−	0.406595i	−0.852072	+	0.523424i	$0.824654\pi$
$984$		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	−0.00440221	−	0.999990i	$-0.501401\pi$
$991$	−11.0355	−	1.94586i	−0.350556	−	0.0618124i	−0.346154	+	0.938178i	$0.612512\pi$
$992$		0			0
$993$	−13.6178	−	33.5326i	−0.432147	−	1.06412i
$994$		0			0
$995$	−75.2987	+	43.4737i	−2.38713	+	1.37821i
$996$		0			0
$997$	−6.92900	−	2.52195i	−0.219444	−	0.0798710i	0.229959	−	0.973200i	$-0.426141\pi$
$997$	−6.92900	−	2.52195i	−0.219444	−	0.0798710i	−0.449402	+	0.893329i	$0.648363\pi$
$998$		0			0
$999$	−24.6300	−	10.8082i	−0.779260	−	0.341957i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.1	✓	18	76.15	even	18
114.2.l.a.71.1	yes	18	12.11	even	2
114.2.l.b.53.1	yes	18	228.167	odd	18
114.2.l.b.71.1	yes	18	4.3	odd	2
912.2.cc.c.641.3		18	1.1	even	1	trivial
912.2.cc.c.737.3		18	57.53	even	18	inner
912.2.cc.d.641.3		18	3.2	odd	2
912.2.cc.d.737.3		18	19.15	odd	18

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)

\(f(q)\)	\(=\)	\(q+(1.36678 + 1.06392i) q^{3} +(-2.20556 + 2.62849i) q^{5} +(-1.68651 - 2.92113i) q^{7} +(0.736160 + 2.90828i) q^{9} +O(q^{10})\)	\(q+(1.36678 + 1.06392i) q^{3} +(-2.20556 + 2.62849i) q^{5} +(-1.68651 - 2.92113i) q^{7} +(0.736160 + 2.90828i) q^{9} +(-2.33635 - 1.34889i) q^{11} +(-5.05419 + 0.891189i) q^{13} +(-5.81100 + 1.24602i) q^{15} +(-1.44531 - 3.97095i) q^{17} +(2.73048 - 3.39772i) q^{19} +(0.802750 - 5.78684i) q^{21} +(-1.69398 - 2.01881i) q^{23} +(-1.17620 - 6.67054i) q^{25} +(-2.08800 + 4.75818i) q^{27} +(3.54249 + 1.28936i) q^{29} +(-4.78254 + 2.76120i) q^{31} +(-1.75816 - 4.32933i) q^{33} +(11.3979 + 2.00975i) q^{35} +5.17636i q^{37} +(-7.85610 - 4.15918i) q^{39} +(0.289735 - 1.64317i) q^{41} +(-1.85806 - 1.55910i) q^{43} +(-9.26801 - 4.47940i) q^{45} +(-0.0440069 + 0.120908i) q^{47} +(-2.18866 + 3.79087i) q^{49} +(2.24935 - 6.96509i) q^{51} +(-6.53342 + 5.48219i) q^{53} +(8.69853 - 3.16600i) q^{55} +(7.34685 - 1.73892i) q^{57} +(-3.87665 + 1.41099i) q^{59} +(3.53369 - 2.96512i) q^{61} +(7.25390 - 7.05526i) q^{63} +(8.80484 - 15.2504i) q^{65} +(-3.81629 + 10.4852i) q^{67} +(-0.167450 - 4.56152i) q^{69} +(-9.91131 - 8.31658i) q^{71} +(-0.414656 + 2.35163i) q^{73} +(5.48930 - 10.3685i) q^{75} +9.09972i q^{77} +(-2.22246 - 0.391880i) q^{79} +(-7.91614 + 4.28191i) q^{81} +(-6.27861 + 3.62496i) q^{83} +(13.6253 + 4.95920i) q^{85} +(3.47002 + 5.53118i) q^{87} +(0.209662 + 1.18905i) q^{89} +(11.1272 + 13.2609i) q^{91} +(-9.47436 - 1.31428i) q^{93} +(2.90863 + 14.6709i) q^{95} +(3.13271 + 8.60706i) q^{97} +(2.20303 - 7.78777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 - 3 * q^9	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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