LMFDB - Embedded newform 1848.2.bg.f.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1848,2,Mod(529,1848)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1848, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1848.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1848.bg (of order $3$, degree $2$, 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:	$14.7563542935$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 9x^{6} + 56x^{4} - 8x^{3} + 112x^{2} + 48x + 144 $ x^8 - x^7 + 9x^6 + 56x^4 - 8x^3 + 112x^2 + 48*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$-1.13622 - 1.96799i$ of defining polynomial
Character	$\chi$	$=$	1848.529
Dual form			1848.2.bg.f.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-1.71822 - 2.97604i) q^{5} +(1.76833 + 1.96799i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.71822 - 2.97604i) q^{5} +(1.76833 + 1.96799i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -4.27244 q^{13} +3.43644 q^{15} +(1.40216 - 2.42862i) q^{17} +(0.898054 + 1.55548i) q^{19} +(-2.58850 + 0.547425i) q^{21} +(3.98655 + 6.90491i) q^{23} +(-3.40455 + 5.89686i) q^{25} +1.00000 q^{27} -4.63211 q^{29} +(2.13622 - 3.70004i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(2.81845 - 8.64408i) q^{35} +(2.05422 + 3.55802i) q^{37} +(2.13622 - 3.70004i) q^{39} +9.65333 q^{41} -0.159213 q^{43} +(-1.71822 + 2.97604i) q^{45} +(-0.800217 - 1.38602i) q^{47} +(-0.745994 + 6.96014i) q^{49} +(1.40216 + 2.42862i) q^{51} +(5.99066 - 10.3761i) q^{53} +3.43644 q^{55} -1.79611 q^{57} +(2.72233 - 4.71521i) q^{59} +(5.25489 + 9.10173i) q^{61} +(0.820165 - 2.51542i) q^{63} +(7.34099 + 12.7150i) q^{65} +(-7.73666 + 13.4003i) q^{67} -7.97311 q^{69} +3.40954 q^{71} +(4.46421 - 7.73224i) q^{73} +(-3.40455 - 5.89686i) q^{75} +(-2.58850 + 0.547425i) q^{77} +(7.57266 + 13.1162i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.5545 q^{83} -9.63690 q^{85} +(2.31606 - 4.01153i) q^{87} +(3.70888 + 6.42397i) q^{89} +(-7.55510 - 8.40814i) q^{91} +(2.13622 + 3.70004i) q^{93} +(3.08611 - 5.34529i) q^{95} +2.74399 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + q^7 - 4 * q^9	$ 8 q - 4 q^{3} + q^{7} - 4 q^{9} - 4 q^{11} - 14 q^{13} - q^{17} + 2 q^{19} + q^{21} + 5 q^{23} - 4 q^{25} + 8 q^{27} - 34 q^{29} + 7 q^{31} - 4 q^{33} + 10 q^{35} + 10 q^{37} + 7 q^{39} + 24 q^{41} - 16 q^{43} + 11 q^{47} + 5 q^{49} - q^{51} + 14 q^{53} - 4 q^{57} + q^{59} + 2 q^{61} - 2 q^{63} + 8 q^{65} - 17 q^{67} - 10 q^{69} - 54 q^{71} + 11 q^{73} - 4 q^{75} + q^{77} + 23 q^{79} - 4 q^{81} + 16 q^{83} - 52 q^{85} + 17 q^{87} - 18 q^{89} - 3 q^{91} + 7 q^{93} + 14 q^{95} + 14 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + q^7 - 4 * q^9 - 4 * q^11 - 14 * q^13 - q^17 + 2 * q^19 + q^21 + 5 * q^23 - 4 * q^25 + 8 * q^27 - 34 * q^29 + 7 * q^31 - 4 * q^33 + 10 * q^35 + 10 * q^37 + 7 * q^39 + 24 * q^41 - 16 * q^43 + 11 * q^47 + 5 * q^49 - q^51 + 14 * q^53 - 4 * q^57 + q^59 + 2 * q^61 - 2 * q^63 + 8 * q^65 - 17 * q^67 - 10 * q^69 - 54 * q^71 + 11 * q^73 - 4 * q^75 + q^77 + 23 * q^79 - 4 * q^81 + 16 * q^83 - 52 * q^85 + 17 * q^87 - 18 * q^89 - 3 * q^91 + 7 * q^93 + 14 * q^95 + 14 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1848\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$673$	$925$	$1585$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−1.71822	−	2.97604i	−0.768411	−	1.33093i	−0.938424	−	0.345485i	$-0.887714\pi$
$5$	−1.71822	−	2.97604i	−0.768411	−	1.33093i	0.170013	−	0.985442i	$-0.445619\pi$
$6$		0			0
$7$	1.76833	+	1.96799i	0.668367	+	0.743831i
$7$	1.76833	+	1.96799i	0.668367	+	0.743831i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−4.27244			−1.18496			−0.592481	−	0.805584i	$-0.701852\pi$
$13$	−4.27244			−1.18496			−0.592481	+	0.805584i	$0.701852\pi$
$14$		0			0
$15$	3.43644			0.887285
$16$		0			0
$17$	1.40216	−	2.42862i	0.340075	−	0.589026i	−0.644372	−	0.764712i	$-0.722881\pi$
$17$	1.40216	−	2.42862i	0.340075	−	0.589026i	0.984446	+	0.175686i	$0.0562144\pi$
$18$		0			0
$19$	0.898054	+	1.55548i	0.206028	+	0.356850i	0.950460	−	0.310848i	$-0.100613\pi$
$19$	0.898054	+	1.55548i	0.206028	+	0.356850i	−0.744432	+	0.667698i	$0.767280\pi$
$20$		0			0
$21$	−2.58850	+	0.547425i	−0.564857	+	0.119458i
$22$		0			0
$23$	3.98655	+	6.90491i	0.831254	+	1.43977i	0.897045	+	0.441940i	$0.145710\pi$
$23$	3.98655	+	6.90491i	0.831254	+	1.43977i	−0.0657908	+	0.997833i	$0.520957\pi$
$24$		0			0
$25$	−3.40455	+	5.89686i	−0.680911	+	1.17937i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−4.63211			−0.860162			−0.430081	−	0.902790i	$-0.641515\pi$
$29$	−4.63211			−0.860162			−0.430081	+	0.902790i	$0.641515\pi$
$30$		0			0
$31$	2.13622	−	3.70004i	0.383677	−	0.664548i	−0.607908	−	0.794007i	$-0.707991\pi$
$31$	2.13622	−	3.70004i	0.383677	−	0.664548i	0.991585	+	0.129460i	$0.0413244\pi$
$32$		0			0
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$		0			0
$35$	2.81845	−	8.64408i	0.476405	−	1.46112i
$36$		0			0
$37$	2.05422	+	3.55802i	0.337712	+	0.584935i	0.984002	−	0.178157i	$-0.0570136\pi$
$37$	2.05422	+	3.55802i	0.337712	+	0.584935i	−0.646290	+	0.763092i	$0.723680\pi$
$38$		0			0
$39$	2.13622	−	3.70004i	0.342069	−	0.592481i
$40$		0			0
$41$	9.65333			1.50760			0.753799	−	0.657106i	$-0.228219\pi$
$41$	9.65333			1.50760			0.753799	+	0.657106i	$0.228219\pi$
$42$		0			0
$43$	−0.159213			−0.0242797			−0.0121399	−	0.999926i	$-0.503864\pi$
$43$	−0.159213			−0.0242797			−0.0121399	+	0.999926i	$0.503864\pi$
$44$		0			0
$45$	−1.71822	+	2.97604i	−0.256137	+	0.443642i
$46$		0			0
$47$	−0.800217	−	1.38602i	−0.116724	−	0.202171i	0.801744	−	0.597668i	$-0.203906\pi$
$47$	−0.800217	−	1.38602i	−0.116724	−	0.202171i	−0.918467	+	0.395497i	$0.870573\pi$
$48$		0			0
$49$	−0.745994	+	6.96014i	−0.106571	+	0.994305i
$50$		0			0
$51$	1.40216	+	2.42862i	0.196342	+	0.340075i
$52$		0			0
$53$	5.99066	−	10.3761i	0.822881	−	1.42527i	−0.0806476	−	0.996743i	$-0.525699\pi$
$53$	5.99066	−	10.3761i	0.822881	−	1.42527i	0.903528	−	0.428529i	$-0.140968\pi$
$54$		0			0
$55$	3.43644			0.463369
$56$		0			0
$57$	−1.79611			−0.237900
$58$		0			0
$59$	2.72233	−	4.71521i	0.354417	−	0.613868i	−0.632601	−	0.774478i	$-0.718013\pi$
$59$	2.72233	−	4.71521i	0.354417	−	0.613868i	0.987018	+	0.160610i	$0.0513460\pi$
$60$		0			0
$61$	5.25489	+	9.10173i	0.672819	+	1.16536i	0.977101	+	0.212775i	$0.0682502\pi$
$61$	5.25489	+	9.10173i	0.672819	+	1.16536i	−0.304282	+	0.952582i	$0.598417\pi$
$62$		0			0
$63$	0.820165	−	2.51542i	0.103331	−	0.316913i
$64$		0			0
$65$	7.34099	+	12.7150i	0.910538	+	1.57710i
$66$		0			0
$67$	−7.73666	+	13.4003i	−0.945183	+	1.63710i	−0.189798	+	0.981823i	$0.560783\pi$
$67$	−7.73666	+	13.4003i	−0.945183	+	1.63710i	−0.755385	+	0.655282i	$0.772550\pi$
$68$		0			0
$69$	−7.97311			−0.959849
$70$		0			0
$71$	3.40954			0.404638			0.202319	−	0.979320i	$-0.435152\pi$
$71$	3.40954			0.404638			0.202319	+	0.979320i	$0.435152\pi$
$72$		0			0
$73$	4.46421	−	7.73224i	0.522497	−	0.904991i	−0.477161	−	0.878816i	$-0.658334\pi$
$73$	4.46421	−	7.73224i	0.522497	−	0.904991i	0.999657	−	0.0261747i	$-0.00833260\pi$
$74$		0			0
$75$	−3.40455	−	5.89686i	−0.393124	−	0.680911i
$76$		0			0
$77$	−2.58850	+	0.547425i	−0.294987	+	0.0623849i
$78$		0			0
$79$	7.57266	+	13.1162i	0.851991	+	1.47569i	0.879409	+	0.476067i	$0.157938\pi$
$79$	7.57266	+	13.1162i	0.851991	+	1.47569i	−0.0274181	+	0.999624i	$0.508729\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.5545			1.37803			0.689015	−	0.724747i	$-0.258043\pi$
$83$	12.5545			1.37803			0.689015	+	0.724747i	$0.258043\pi$
$84$		0			0
$85$	−9.63690			−1.04527
$86$		0			0
$87$	2.31606	−	4.01153i	0.248307	−	0.430081i
$88$		0			0
$89$	3.70888	+	6.42397i	0.393141	+	0.680940i	0.992862	−	0.119269i	$-0.0380552\pi$
$89$	3.70888	+	6.42397i	0.393141	+	0.680940i	−0.599721	+	0.800209i	$0.704722\pi$
$90$		0			0
$91$	−7.55510	−	8.40814i	−0.791990	−	0.881412i
$92$		0			0
$93$	2.13622	+	3.70004i	0.221516	+	0.383677i
$94$		0			0
$95$	3.08611	−	5.34529i	0.316628	−	0.548416i
$96$		0			0
$97$	2.74399			0.278610			0.139305	−	0.990249i	$-0.455513\pi$
$97$	2.74399			0.278610			0.139305	+	0.990249i	$0.455513\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$		0			0
$101$	−0.480052	+	0.831474i	−0.0477669	+	0.0827348i	−0.888920	−	0.458062i	$-0.848544\pi$
$101$	−0.480052	+	0.831474i	−0.0477669	+	0.0827348i	0.841153	+	0.540797i	$0.181877\pi$
$102$		0			0
$103$	2.15856	+	3.73874i	0.212689	+	0.368389i	0.952555	−	0.304366i	$-0.0984444\pi$
$103$	2.15856	+	3.73874i	0.212689	+	0.368389i	−0.739866	+	0.672754i	$0.765111\pi$
$104$		0			0
$105$	6.07677	+	6.76289i	0.593032	+	0.659990i
$106$		0			0
$107$	−5.29478	−	9.17083i	−0.511866	−	0.886578i	−0.999905	−	0.0137562i	$-0.995621\pi$
$107$	−5.29478	−	9.17083i	−0.511866	−	0.886578i	0.488039	−	0.872822i	$-0.337712\pi$
$108$		0			0
$109$	−2.24467	+	3.88788i	−0.215000	+	0.372391i	−0.953273	−	0.302111i	$-0.902309\pi$
$109$	−2.24467	+	3.88788i	−0.215000	+	0.372391i	0.738272	+	0.674503i	$0.235642\pi$
$110$		0			0
$111$	−4.10845			−0.389957
$112$		0			0
$113$	14.6633			1.37941			0.689704	−	0.724091i	$-0.257741\pi$
$113$	14.6633			1.37941			0.689704	+	0.724091i	$0.257741\pi$
$114$		0			0
$115$	13.6995	−	23.7283i	1.27749	−	2.21268i
$116$		0			0
$117$	2.13622	+	3.70004i	0.197494	+	0.342069i
$118$		0			0
$119$	7.25900	−	1.53516i	0.665431	−	0.140728i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−4.82667	+	8.36003i	−0.435206	+	0.753799i
$124$		0			0
$125$	6.21689			0.556056
$126$		0			0
$127$	−6.73234			−0.597399			−0.298699	−	0.954347i	$-0.596553\pi$
$127$	−6.73234			−0.597399			−0.298699	+	0.954347i	$0.596553\pi$
$128$		0			0
$129$	0.0796063	−	0.137882i	0.00700895	−	0.0121399i
$130$		0			0
$131$	6.98244	+	12.0939i	0.610059	+	1.05665i	0.991230	+	0.132148i	$0.0421876\pi$
$131$	6.98244	+	12.0939i	0.610059	+	1.05665i	−0.381171	+	0.924505i	$0.624479\pi$
$132$		0			0
$133$	−1.47311	+	4.51796i	−0.127734	+	0.391757i
$134$		0			0
$135$	−1.71822	−	2.97604i	−0.147881	−	0.256137i
$136$		0			0
$137$	3.00822	−	5.21039i	0.257009	−	0.445153i	−0.708430	−	0.705781i	$-0.750596\pi$
$137$	3.00822	−	5.21039i	0.257009	−	0.445153i	0.965439	+	0.260628i	$0.0839295\pi$
$138$		0			0
$139$	13.4494			1.14077			0.570383	−	0.821379i	$-0.306795\pi$
$139$	13.4494			1.14077			0.570383	+	0.821379i	$0.306795\pi$
$140$		0			0
$141$	1.60043			0.134781
$142$		0			0
$143$	2.13622	−	3.70004i	0.178640	−	0.309413i
$144$		0			0
$145$	7.95898	+	13.7854i	0.660958	+	1.14481i
$146$		0			0
$147$	−5.65466	−	4.12612i	−0.466388	−	0.340316i
$148$		0			0
$149$	10.3115	+	17.8600i	0.844751	+	1.46315i	0.885837	+	0.463996i	$0.153585\pi$
$149$	10.3115	+	17.8600i	0.844751	+	1.46315i	−0.0410861	+	0.999156i	$0.513082\pi$
$150$		0			0
$151$	−1.92583	+	3.33563i	−0.156722	+	0.271450i	−0.933685	−	0.358096i	$-0.883426\pi$
$151$	−1.92583	+	3.33563i	−0.156722	+	0.271450i	0.776963	+	0.629546i	$0.216759\pi$
$152$		0			0
$153$	−2.80433			−0.226716
$154$		0			0
$155$	−14.6820			−1.17929
$156$		0			0
$157$	−3.93100	+	6.80870i	−0.313728	+	0.543393i	−0.979166	−	0.203060i	$-0.934911\pi$
$157$	−3.93100	+	6.80870i	−0.313728	+	0.543393i	0.665438	+	0.746453i	$0.268245\pi$
$158$		0			0
$159$	5.99066	+	10.3761i	0.475090	+	0.822881i
$160$		0			0
$161$	−6.53926	+	20.0557i	−0.515366	+	1.58061i
$162$		0			0
$163$	0.818448	+	1.41759i	0.0641058	+	0.111034i	0.896297	−	0.443454i	$-0.146247\pi$
$163$	0.818448	+	1.41759i	0.0641058	+	0.111034i	−0.832191	+	0.554489i	$0.812914\pi$
$164$		0			0
$165$	−1.71822	+	2.97604i	−0.133763	+	0.231685i
$166$		0			0
$167$	−24.5075			−1.89645			−0.948225	−	0.317600i	$-0.897123\pi$
$167$	−24.5075			−1.89645			−0.948225	+	0.317600i	$0.897123\pi$
$168$		0			0
$169$	5.25377			0.404136
$170$		0			0
$171$	0.898054	−	1.55548i	0.0686759	−	0.118950i
$172$		0			0
$173$	11.6596	+	20.1951i	0.886467	+	1.53541i	0.844024	+	0.536306i	$0.180181\pi$
$173$	11.6596	+	20.1951i	0.886467	+	1.53541i	0.0424430	+	0.999099i	$0.486486\pi$
$174$		0			0
$175$	−17.6254	+	3.72748i	−1.33235	+	0.281771i
$176$		0			0
$177$	2.72233	+	4.71521i	0.204623	+	0.354417i
$178$		0			0
$179$	0.736450	−	1.27557i	0.0550448	−	0.0953405i	−0.837190	−	0.546912i	$-0.815803\pi$
$179$	0.736450	−	1.27557i	0.0550448	−	0.0953405i	0.892235	+	0.451572i	$0.149136\pi$
$180$		0			0
$181$	−13.7253			−1.02019			−0.510097	−	0.860117i	$-0.670391\pi$
$181$	−13.7253			−1.02019			−0.510097	+	0.860117i	$0.670391\pi$
$182$		0			0
$183$	−10.5098			−0.776905
$184$		0			0
$185$	7.05921	−	12.2269i	0.519004	−	0.898941i
$186$		0			0
$187$	1.40216	+	2.42862i	0.102536	+	0.177598i
$188$		0			0
$189$	1.76833	+	1.96799i	0.128627	+	0.143150i
$190$		0			0
$191$	−1.57178	−	2.72240i	−0.113730	−	0.196986i	0.803541	−	0.595249i	$-0.202947\pi$
$191$	−1.57178	−	2.72240i	−0.113730	−	0.196986i	−0.917271	+	0.398263i	$0.869613\pi$
$192$		0			0
$193$	1.25401	−	2.17200i	0.0902653	−	0.156344i	−0.817357	−	0.576131i	$-0.804562\pi$
$193$	1.25401	−	2.17200i	0.0902653	−	0.156344i	0.907623	+	0.419787i	$0.137895\pi$
$194$		0			0
$195$	−14.6820			−1.05140
$196$		0			0
$197$	−7.54010			−0.537210			−0.268605	−	0.963250i	$-0.586563\pi$
$197$	−7.54010			−0.537210			−0.268605	+	0.963250i	$0.586563\pi$
$198$		0			0
$199$	5.62733	−	9.74682i	0.398911	−	0.690934i	−0.594681	−	0.803962i	$-0.702722\pi$
$199$	5.62733	−	9.74682i	0.398911	−	0.690934i	0.993592	+	0.113028i	$0.0360550\pi$
$200$		0			0
$201$	−7.73666	−	13.4003i	−0.545702	−	0.945183i
$202$		0			0
$203$	−8.19112	−	9.11596i	−0.574904	−	0.639815i
$204$		0			0
$205$	−16.5865	−	28.7287i	−1.15845	−	2.00650i
$206$		0			0
$207$	3.98655	−	6.90491i	0.277085	−	0.479925i
$208$		0			0
$209$	−1.79611			−0.124239
$210$		0			0
$211$	5.01222			0.345055			0.172528	−	0.985005i	$-0.444807\pi$
$211$	5.01222			0.345055			0.172528	+	0.985005i	$0.444807\pi$
$212$		0			0
$213$	−1.70477	+	2.95275i	−0.116809	+	0.202319i
$214$		0			0
$215$	0.273562	+	0.473824i	0.0186568	+	0.0323145i
$216$		0			0
$217$	11.0592	−	2.33884i	0.750748	−	0.158771i
$218$		0			0
$219$	4.46421	+	7.73224i	0.301664	+	0.522497i
$220$		0			0
$221$	−5.99066	+	10.3761i	−0.402976	+	0.697974i
$222$		0			0
$223$	14.8446			0.994070			0.497035	−	0.867730i	$-0.334422\pi$
$223$	14.8446			0.994070			0.497035	+	0.867730i	$0.334422\pi$
$224$		0			0
$225$	6.80911			0.453941
$226$		0			0
$227$	2.73234	−	4.73255i	0.181352	−	0.314111i	−0.760989	−	0.648764i	$-0.775286\pi$
$227$	2.73234	−	4.73255i	0.181352	−	0.314111i	0.942341	+	0.334654i	$0.108619\pi$
$228$		0			0
$229$	−14.3642	−	24.8795i	−0.949214	−	1.64409i	−0.747086	−	0.664728i	$-0.768548\pi$
$229$	−14.3642	−	24.8795i	−0.949214	−	1.64409i	−0.202128	−	0.979359i	$-0.564786\pi$
$230$		0			0
$231$	0.820165	−	2.51542i	0.0539629	−	0.165502i
$232$		0			0
$233$	5.68873	+	9.85316i	0.372681	+	0.645502i	0.989977	−	0.141229i	$-0.0451053\pi$
$233$	5.68873	+	9.85316i	0.372681	+	0.645502i	−0.617296	+	0.786731i	$0.711772\pi$
$234$		0			0
$235$	−2.74990	+	4.76296i	−0.179384	+	0.310701i
$236$		0			0
$237$	−15.1453			−0.983794
$238$		0			0
$239$	−4.49064			−0.290475			−0.145238	−	0.989397i	$-0.546395\pi$
$239$	−4.49064			−0.290475			−0.145238	+	0.989397i	$0.546395\pi$
$240$		0			0
$241$	−5.39654	+	9.34709i	−0.347622	+	0.602099i	−0.985826	−	0.167768i	$-0.946344\pi$
$241$	−5.39654	+	9.34709i	−0.347622	+	0.602099i	0.638205	+	0.769867i	$0.279677\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	21.9954	−	9.73893i	1.40524	−	0.622197i
$246$		0			0
$247$	−3.83688	−	6.64568i	−0.244135	−	0.422854i
$248$		0			0
$249$	−6.27723	+	10.8725i	−0.397803	+	0.689015i
$250$		0			0
$251$	−4.94445			−0.312091			−0.156045	−	0.987750i	$-0.549875\pi$
$251$	−4.94445			−0.312091			−0.156045	+	0.987750i	$0.549875\pi$
$252$		0			0
$253$	−7.97311			−0.501265
$254$		0			0
$255$	4.81845	−	8.34580i	0.301743	−	0.522634i
$256$		0			0
$257$	−5.06377	−	8.77070i	−0.315869	−	0.547101i	0.663753	−	0.747952i	$-0.268963\pi$
$257$	−5.06377	−	8.77070i	−0.315869	−	0.547101i	−0.979622	+	0.200851i	$0.935629\pi$
$258$		0			0
$259$	−3.36961	+	10.3345i	−0.209377	+	0.642152i
$260$		0			0
$261$	2.31606	+	4.01153i	0.143360	+	0.248307i
$262$		0			0
$263$	5.27723	−	9.14042i	0.325408	−	0.563623i	−0.656187	−	0.754598i	$-0.727832\pi$
$263$	5.27723	−	9.14042i	0.325408	−	0.563623i	0.981595	+	0.190976i	$0.0611651\pi$
$264$		0			0
$265$	−41.1731			−2.52924
$266$		0			0
$267$	−7.41776			−0.453960
$268$		0			0
$269$	−2.87400	+	4.97791i	−0.175231	+	0.303508i	−0.940241	−	0.340509i	$-0.889400\pi$
$269$	−2.87400	+	4.97791i	−0.175231	+	0.303508i	0.765010	+	0.644018i	$0.222734\pi$
$270$		0			0
$271$	−12.5321	−	21.7063i	−0.761272	−	1.31856i	−0.942195	−	0.335064i	$-0.891242\pi$
$271$	−12.5321	−	21.7063i	−0.761272	−	1.31856i	0.180924	−	0.983497i	$-0.442091\pi$
$272$		0			0
$273$	11.0592	−	2.33884i	0.669334	−	0.141553i
$274$		0			0
$275$	−3.40455	−	5.89686i	−0.205302	−	0.355594i
$276$		0			0
$277$	−3.49477	+	6.05312i	−0.209980	+	0.363697i	−0.951708	−	0.307004i	$-0.900673\pi$
$277$	−3.49477	+	6.05312i	−0.209980	+	0.363697i	0.741728	+	0.670701i	$0.234007\pi$
$278$		0			0
$279$	−4.27244			−0.255784
$280$		0			0
$281$	14.0759			0.839696			0.419848	−	0.907594i	$-0.362083\pi$
$281$	14.0759			0.839696			0.419848	+	0.907594i	$0.362083\pi$
$282$		0			0
$283$	11.1093	−	19.2419i	0.660381	−	1.14381i	−0.320135	−	0.947372i	$-0.603728\pi$
$283$	11.1093	−	19.2419i	0.660381	−	1.14381i	0.980516	−	0.196441i	$-0.0629385\pi$
$284$		0			0
$285$	3.08611	+	5.34529i	0.182805	+	0.316628i
$286$		0			0
$287$	17.0703	+	18.9977i	1.00763	+	1.12140i
$288$		0			0
$289$	4.56788	+	7.91179i	0.268699	+	0.465400i
$290$		0			0
$291$	−1.37200	+	2.37637i	−0.0804279	+	0.139305i
$292$		0			0
$293$	−23.6845			−1.38367			−0.691833	−	0.722058i	$-0.743196\pi$
$293$	−23.6845			−1.38367			−0.691833	+	0.722058i	$0.743196\pi$
$294$		0			0
$295$	−18.7102			−1.08935
$296$		0			0
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$		0			0
$299$	−17.0323	−	29.5008i	−0.985004	−	1.70608i
$300$		0			0
$301$	−0.281541	−	0.313329i	−0.0162278	−	0.0180600i
$302$		0			0
$303$	−0.480052	−	0.831474i	−0.0275783	−	0.0477669i
$304$		0			0
$305$	18.0581	−	31.2775i	1.03400	−	1.79095i
$306$		0			0
$307$	33.0915			1.88863			0.944317	−	0.329038i	$-0.106724\pi$
$307$	33.0915			1.88863			0.944317	+	0.329038i	$0.106724\pi$
$308$		0			0
$309$	−4.31712			−0.245592
$310$		0			0
$311$	−12.1401	+	21.0273i	−0.688401	+	1.19235i	0.283953	+	0.958838i	$0.408354\pi$
$311$	−12.1401	+	21.0273i	−0.688401	+	1.19235i	−0.972355	+	0.233508i	$0.924979\pi$
$312$		0			0
$313$	−0.281987	−	0.488415i	−0.0159388	−	0.0276069i	0.857946	−	0.513740i	$-0.171740\pi$
$313$	−0.281987	−	0.488415i	−0.0159388	−	0.0276069i	−0.873885	+	0.486133i	$0.838407\pi$
$314$		0			0
$315$	−8.89522	+	1.88119i	−0.501189	+	0.105993i
$316$		0			0
$317$	−1.95857	−	3.39235i	−0.110004	−	0.190533i	0.805767	−	0.592232i	$-0.201753\pi$
$317$	−1.95857	−	3.39235i	−0.110004	−	0.190533i	−0.915772	+	0.401699i	$0.868420\pi$
$318$		0			0
$319$	2.31606	−	4.01153i	0.129674	−	0.224602i
$320$		0			0
$321$	10.5896			0.591052
$322$		0			0
$323$	5.03687			0.280259
$324$		0			0
$325$	14.5458	−	25.1940i	0.806854	−	1.39751i
$326$		0			0
$327$	−2.24467	−	3.88788i	−0.124130	−	0.215000i
$328$		0			0
$329$	1.31262	−	4.02576i	0.0723671	−	0.221947i
$330$		0			0
$331$	2.36245	+	4.09189i	0.129852	+	0.224911i	0.923619	−	0.383311i	$-0.125216\pi$
$331$	2.36245	+	4.09189i	0.129852	+	0.224911i	−0.793767	+	0.608222i	$0.791883\pi$
$332$		0			0
$333$	2.05422	−	3.55802i	0.112571	−	0.194978i
$334$		0			0
$335$	53.1731			2.90516
$336$		0			0
$337$	−31.0155			−1.68952			−0.844762	−	0.535142i	$-0.820258\pi$
$337$	−31.0155			−1.68952			−0.844762	+	0.535142i	$0.820258\pi$
$338$		0			0
$339$	−7.33166	+	12.6988i	−0.398201	+	0.689704i
$340$		0			0
$341$	2.13622	+	3.70004i	0.115683	+	0.200369i
$342$		0			0
$343$	−15.0167	+	10.8397i	−0.810824	+	0.585290i
$344$		0			0
$345$	13.6995	+	23.7283i	0.737559	+	1.27749i
$346$		0			0
$347$	−9.12298	+	15.8015i	−0.489747	+	0.848267i	−0.999930	−	0.0117987i	$-0.996244\pi$
$347$	−9.12298	+	15.8015i	−0.489747	+	0.848267i	0.510183	+	0.860066i	$0.329578\pi$
$348$		0			0
$349$	11.0287			0.590350			0.295175	−	0.955443i	$-0.404622\pi$
$349$	11.0287			0.590350			0.295175	+	0.955443i	$0.404622\pi$
$350$		0			0
$351$	−4.27244			−0.228046
$352$		0			0
$353$	5.67832	−	9.83514i	0.302227	−	0.523472i	−0.674413	−	0.738354i	$-0.735603\pi$
$353$	5.67832	−	9.83514i	0.302227	−	0.523472i	0.976640	+	0.214882i	$0.0689367\pi$
$354$		0			0
$355$	−5.85834	−	10.1469i	−0.310929	−	0.538544i
$356$		0			0
$357$	−2.30001	+	7.05405i	−0.121730	+	0.373340i
$358$		0			0
$359$	6.67089	+	11.5543i	0.352076	+	0.609814i	0.986613	−	0.163079i	$-0.0521425\pi$
$359$	6.67089	+	11.5543i	0.352076	+	0.609814i	−0.634537	+	0.772893i	$0.718809\pi$
$360$		0			0
$361$	7.88700	−	13.6607i	0.415105	−	0.718983i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	−30.6820			−1.60597
$366$		0			0
$367$	−4.28154	+	7.41585i	−0.223495	+	0.387104i	−0.955867	−	0.293801i	$-0.905080\pi$
$367$	−4.28154	+	7.41585i	−0.223495	+	0.387104i	0.732372	+	0.680905i	$0.238413\pi$
$368$		0			0
$369$	−4.82667	−	8.36003i	−0.251266	−	0.435206i
$370$		0			0
$371$	31.0136	−	6.55888i	1.61015	−	0.340520i
$372$		0			0
$373$	−17.6829	−	30.6276i	−0.915584	−	1.58584i	−0.806044	−	0.591856i	$-0.798395\pi$
$373$	−17.6829	−	30.6276i	−0.915584	−	1.58584i	−0.109540	−	0.993982i	$-0.534938\pi$
$374$		0			0
$375$	−3.10845	+	5.38399i	−0.160520	+	0.278028i
$376$		0			0
$377$	19.7904			1.01926
$378$		0			0
$379$	20.7002			1.06330			0.531648	−	0.846965i	$-0.321573\pi$
$379$	20.7002			1.06330			0.531648	+	0.846965i	$0.321573\pi$
$380$		0			0
$381$	3.36617	−	5.83038i	0.172454	−	0.298699i
$382$		0			0
$383$	−13.8676	−	24.0195i	−0.708604	−	1.22734i	−0.965375	−	0.260865i	$-0.915992\pi$
$383$	−13.8676	−	24.0195i	−0.708604	−	1.22734i	0.256771	−	0.966472i	$-0.417341\pi$
$384$		0			0
$385$	6.07677	+	6.76289i	0.309701	+	0.344669i
$386$		0			0
$387$	0.0796063	+	0.137882i	0.00404662	+	0.00700895i
$388$		0			0
$389$	17.6104	−	30.5021i	0.892883	−	1.54652i	0.0564808	−	0.998404i	$-0.482012\pi$
$389$	17.6104	−	30.5021i	0.892883	−	1.54652i	0.836403	−	0.548116i	$-0.184655\pi$
$390$		0			0
$391$	22.3592			1.13075
$392$		0			0
$393$	−13.9649			−0.704435
$394$		0			0
$395$	26.0230	−	45.0731i	1.30936	−	2.26787i
$396$		0			0
$397$	3.22165	+	5.58007i	0.161690	+	0.280056i	0.935475	−	0.353393i	$-0.114972\pi$
$397$	3.22165	+	5.58007i	0.161690	+	0.280056i	−0.773785	+	0.633449i	$0.781639\pi$
$398$		0			0
$399$	−3.17612	−	3.53473i	−0.159005	−	0.176958i
$400$		0			0
$401$	−18.2526	−	31.6145i	−0.911494	−	1.57875i	−0.811955	−	0.583720i	$-0.801597\pi$
$401$	−18.2526	−	31.6145i	−0.911494	−	1.57875i	−0.0995384	−	0.995034i	$-0.531737\pi$
$402$		0			0
$403$	−9.12688	+	15.8082i	−0.454642	+	0.787464i
$404$		0			0
$405$	3.43644			0.170758
$406$		0			0
$407$	−4.10845			−0.203648
$408$		0			0
$409$	9.87678	−	17.1071i	0.488375	−	0.845891i	−0.511535	−	0.859262i	$-0.670923\pi$
$409$	9.87678	−	17.1071i	0.488375	−	0.845891i	0.999911	+	0.0133714i	$0.00425637\pi$
$410$		0			0
$411$	3.00822	+	5.21039i	0.148384	+	0.257009i
$412$		0			0
$413$	14.0935	−	2.98054i	0.693495	−	0.146663i
$414$		0			0
$415$	−21.5713	−	37.3626i	−1.05889	−	1.83406i
$416$		0			0
$417$	−6.72472	+	11.6476i	−0.329311	+	0.570383i
$418$		0			0
$419$	−15.0278			−0.734154			−0.367077	−	0.930191i	$-0.619641\pi$
$419$	−15.0278			−0.734154			−0.367077	+	0.930191i	$0.619641\pi$
$420$		0			0
$421$	−7.93623			−0.386788			−0.193394	−	0.981121i	$-0.561950\pi$
$421$	−7.93623			−0.386788			−0.193394	+	0.981121i	$0.561950\pi$
$422$		0			0
$423$	−0.800217	+	1.38602i	−0.0389079	+	0.0673904i
$424$		0			0
$425$	9.54748	+	16.5367i	0.463121	+	0.802149i
$426$		0			0
$427$	−8.61975	+	26.4365i	−0.417139	+	1.27935i
$428$		0			0
$429$	2.13622	+	3.70004i	0.103138	+	0.178640i
$430$		0			0
$431$	4.62277	−	8.00688i	0.222671	−	0.385678i	−0.732947	−	0.680286i	$-0.761856\pi$
$431$	4.62277	−	8.00688i	0.222671	−	0.385678i	0.955618	+	0.294608i	$0.0951890\pi$
$432$		0			0
$433$	8.35665			0.401595			0.200797	−	0.979633i	$-0.435647\pi$
$433$	8.35665			0.401595			0.200797	+	0.979633i	$0.435647\pi$
$434$		0			0
$435$	−15.9180			−0.763208
$436$		0			0
$437$	−7.16028	+	12.4020i	−0.342523	+	0.593267i
$438$		0			0
$439$	13.2928	+	23.0238i	0.634432	+	1.09887i	0.986635	+	0.162945i	$0.0520992\pi$
$439$	13.2928	+	23.0238i	0.634432	+	1.09887i	−0.352203	+	0.935924i	$0.614567\pi$
$440$		0			0
$441$	6.40065	−	2.83402i	0.304793	−	0.134953i
$442$		0			0
$443$	−8.78744	−	15.2203i	−0.417504	−	0.723138i	0.578184	−	0.815907i	$-0.303762\pi$
$443$	−8.78744	−	15.2203i	−0.417504	−	0.723138i	−0.995688	+	0.0927684i	$0.970428\pi$
$444$		0			0
$445$	12.7453	−	22.0756i	0.604187	−	1.04648i
$446$		0			0
$447$	−20.6230			−0.975435
$448$		0			0
$449$	−37.7084			−1.77957			−0.889785	−	0.456380i	$-0.849146\pi$
$449$	−37.7084			−1.77957			−0.889785	+	0.456380i	$0.849146\pi$
$450$		0			0
$451$	−4.82667	+	8.36003i	−0.227279	+	0.393658i
$452$		0			0
$453$	−1.92583	−	3.33563i	−0.0904833	−	0.156722i
$454$		0			0
$455$	−12.0417	+	36.9313i	−0.564522	+	1.73137i
$456$		0			0
$457$	10.8287	+	18.7558i	0.506544	+	0.877359i	0.999971	+	0.00757246i	$0.00241041\pi$
$457$	10.8287	+	18.7558i	0.506544	+	0.877359i	−0.493428	+	0.869787i	$0.664256\pi$
$458$		0			0
$459$	1.40216	−	2.42862i	0.0654474	−	0.113358i
$460$		0			0
$461$	−1.42900			−0.0665554			−0.0332777	−	0.999446i	$-0.510595\pi$
$461$	−1.42900			−0.0665554			−0.0332777	+	0.999446i	$0.510595\pi$
$462$		0			0
$463$	−26.8300			−1.24689			−0.623447	−	0.781866i	$-0.714268\pi$
$463$	−26.8300			−1.24689			−0.623447	+	0.781866i	$0.714268\pi$
$464$		0			0
$465$	7.34099	−	12.7150i	0.340430	−	0.589643i
$466$		0			0
$467$	−14.0633	−	24.3584i	−0.650773	−	1.12717i	−0.982936	−	0.183950i	$-0.941112\pi$
$467$	−14.0633	−	24.3584i	−0.650773	−	1.12717i	0.332163	−	0.943222i	$-0.392222\pi$
$468$		0			0
$469$	−40.0526	+	8.47048i	−1.84946	+	0.391130i
$470$		0			0
$471$	−3.93100	−	6.80870i	−0.181131	−	0.313728i
$472$		0			0
$473$	0.0796063	−	0.137882i	0.00366030	−	0.00633983i
$474$		0			0
$475$	−12.2299			−0.561146
$476$		0			0
$477$	−11.9813			−0.548587
$478$		0			0
$479$	12.6980	−	21.9936i	0.580187	−	1.00491i	−0.415270	−	0.909698i	$-0.636313\pi$
$479$	12.6980	−	21.9936i	0.580187	−	1.00491i	0.995457	−	0.0952150i	$-0.0303539\pi$
$480$		0			0
$481$	−8.77655	−	15.2014i	−0.400176	−	0.693126i
$482$		0			0
$483$	−14.0991	−	15.6910i	−0.641532	−	0.713966i
$484$		0			0
$485$	−4.71478	−	8.16625i	−0.214087	−	0.370810i
$486$		0			0
$487$	−21.1388	+	36.6134i	−0.957889	+	1.65911i	−0.230275	+	0.973126i	$0.573962\pi$
$487$	−21.1388	+	36.6134i	−0.957889	+	1.65911i	−0.727614	+	0.685987i	$0.759371\pi$
$488$		0			0
$489$	−1.63690			−0.0740230
$490$		0			0
$491$	29.1188			1.31411			0.657057	−	0.753841i	$-0.271801\pi$
$491$	29.1188			1.31411			0.657057	+	0.753841i	$0.271801\pi$
$492$		0			0
$493$	−6.49498	+	11.2496i	−0.292519	+	0.506658i
$494$		0			0
$495$	−1.71822	−	2.97604i	−0.0772282	−	0.133763i
$496$		0			0
$497$	6.02921	+	6.70996i	0.270447	+	0.300983i
$498$		0			0
$499$	22.0824	+	38.2479i	0.988545	+	1.71221i	0.624976	+	0.780644i	$0.285109\pi$
$499$	22.0824	+	38.2479i	0.988545	+	1.71221i	0.363569	+	0.931567i	$0.381558\pi$
$500$		0			0
$501$	12.2538	−	21.2241i	0.547458	−	0.948225i
$502$		0			0
$503$	35.8000			1.59624			0.798122	−	0.602496i	$-0.205827\pi$
$503$	35.8000			1.59624			0.798122	+	0.602496i	$0.205827\pi$
$504$		0			0
$505$	3.29934			0.146819
$506$		0			0
$507$	−2.62688	+	4.54990i	−0.116664	+	0.202068i
$508$		0			0
$509$	−14.5214	−	25.1518i	−0.643651	−	1.11484i	−0.984611	−	0.174758i	$-0.944086\pi$
$509$	−14.5214	−	25.1518i	−0.643651	−	1.11484i	0.340960	−	0.940078i	$-0.389248\pi$
$510$		0			0
$511$	23.1112	−	4.88764i	1.02238	−	0.216217i
$512$		0			0
$513$	0.898054	+	1.55548i	0.0396501	+	0.0686759i
$514$		0			0
$515$	7.41776	−	12.8479i	0.326866	−	0.566148i
$516$		0			0
$517$	1.60043			0.0703870
$518$		0			0
$519$	−23.3193			−1.02360
$520$		0			0
$521$	−22.0703	+	38.2269i	−0.966918	+	1.67475i	−0.262546	+	0.964919i	$0.584562\pi$
$521$	−22.0703	+	38.2269i	−0.966918	+	1.67475i	−0.704372	+	0.709831i	$0.748771\pi$
$522$		0			0
$523$	0.995685	+	1.72458i	0.0435383	+	0.0754105i	0.886973	−	0.461821i	$-0.152804\pi$
$523$	0.995685	+	1.72458i	0.0435383	+	0.0754105i	−0.843435	+	0.537231i	$0.819470\pi$
$524$		0			0
$525$	5.58460	−	17.1278i	0.243732	−	0.747517i
$526$		0			0
$527$	−5.99066	−	10.3761i	−0.260957	−	0.451991i
$528$		0			0
$529$	−20.2852	+	35.1350i	−0.881965	+	1.52761i
$530$		0			0
$531$	−5.44466			−0.236278
$532$		0			0
$533$	−41.2433			−1.78645
$534$		0			0
$535$	−18.1952	+	31.5150i	−0.786647	+	1.36251i
$536$		0			0
$537$	0.736450	+	1.27557i	0.0317802	+	0.0550448i
$538$		0			0
$539$	−5.65466	−	4.12612i	−0.243563	−	0.177724i
$540$		0			0
$541$	5.26334	+	9.11638i	0.226289	+	0.391944i	0.956705	−	0.291058i	$-0.0940073\pi$
$541$	5.26334	+	9.11638i	0.226289	+	0.391944i	−0.730416	+	0.683002i	$0.760674\pi$
$542$		0			0
$543$	6.86266	−	11.8865i	0.294505	−	0.510097i
$544$		0			0
$545$	15.4273			0.660834
$546$		0			0
$547$	−14.5054			−0.620206			−0.310103	−	0.950703i	$-0.600364\pi$
$547$	−14.5054			−0.620206			−0.310103	+	0.950703i	$0.600364\pi$
$548$		0			0
$549$	5.25489	−	9.10173i	0.224273	−	0.388452i
$550$		0			0
$551$	−4.15989	−	7.20513i	−0.177217	−	0.306949i
$552$		0			0
$553$	−12.4217	+	38.0968i	−0.528223	+	1.62004i
$554$		0			0
$555$	7.05921	+	12.2269i	0.299647	+	0.519004i
$556$		0			0
$557$	9.91761	−	17.1778i	0.420223	−	0.727847i	−0.575738	−	0.817634i	$-0.695285\pi$
$557$	9.91761	−	17.1778i	0.420223	−	0.727847i	0.995961	+	0.0897871i	$0.0286186\pi$
$558$		0			0
$559$	0.680227			0.0287705
$560$		0			0
$561$	−2.80433			−0.118399
$562$		0			0
$563$	3.64186	−	6.30789i	0.153486	−	0.265846i	−0.779021	−	0.626998i	$-0.784283\pi$
$563$	3.64186	−	6.30789i	0.153486	−	0.265846i	0.932507	+	0.361152i	$0.117617\pi$
$564$		0			0
$565$	−25.1948	−	43.6386i	−1.05995	−	1.83589i
$566$		0			0
$567$	−2.58850	+	0.547425i	−0.108707	+	0.0229897i
$568$		0			0
$569$	21.0047	+	36.3813i	0.880564	+	1.52518i	0.850715	+	0.525627i	$0.176169\pi$
$569$	21.0047	+	36.3813i	0.880564	+	1.52518i	0.0298491	+	0.999554i	$0.490497\pi$
$570$		0			0
$571$	0.845940	−	1.46521i	0.0354015	−	0.0613172i	−0.847782	−	0.530345i	$-0.822062\pi$
$571$	0.845940	−	1.46521i	0.0354015	−	0.0613172i	0.883183	+	0.469028i	$0.155396\pi$
$572$		0			0
$573$	3.14356			0.131324
$574$		0			0
$575$	−54.2897			−2.26404
$576$		0			0
$577$	−23.3889	+	40.5107i	−0.973691	+	1.68648i	−0.289504	+	0.957177i	$0.593490\pi$
$577$	−23.3889	+	40.5107i	−0.973691	+	1.68648i	−0.684188	+	0.729306i	$0.739843\pi$
$578$		0			0
$579$	1.25401	+	2.17200i	0.0521147	+	0.0902653i
$580$		0			0
$581$	22.2005	+	24.7071i	0.921030	+	1.02502i
$582$		0			0
$583$	5.99066	+	10.3761i	0.248108	+	0.429735i
$584$		0			0
$585$	7.34099	−	12.7150i	0.303513	−	0.525699i
$586$		0			0
$587$	−20.8287			−0.859691			−0.429845	−	0.902903i	$-0.641432\pi$
$587$	−20.8287			−0.859691			−0.429845	+	0.902903i	$0.641432\pi$
$588$		0			0
$589$	7.67377			0.316192
$590$		0			0
$591$	3.77005	−	6.52992i	0.155079	−	0.268605i
$592$		0			0
$593$	−2.80061	−	4.85080i	−0.115007	−	0.199198i	0.802775	−	0.596282i	$-0.203356\pi$
$593$	−2.80061	−	4.85080i	−0.115007	−	0.199198i	−0.917783	+	0.397083i	$0.870022\pi$
$594$		0			0
$595$	−17.0412	−	18.9653i	−0.698623	−	0.777503i
$596$		0			0
$597$	5.62733	+	9.74682i	0.230311	+	0.398911i
$598$		0			0
$599$	−20.1232	+	34.8544i	−0.822212	+	1.42411i	0.0818195	+	0.996647i	$0.473927\pi$
$599$	−20.1232	+	34.8544i	−0.822212	+	1.42411i	−0.904032	+	0.427466i	$0.859406\pi$
$600$		0			0
$601$	5.70201			0.232590			0.116295	−	0.993215i	$-0.462898\pi$
$601$	5.70201			0.232590			0.116295	+	0.993215i	$0.462898\pi$
$602$		0			0
$603$	15.4733			0.630122
$604$		0			0
$605$	−1.71822	+	2.97604i	−0.0698555	+	0.120993i
$606$		0			0
$607$	−4.23645	−	7.33775i	−0.171952	−	0.297830i	0.767150	−	0.641468i	$-0.221674\pi$
$607$	−4.23645	−	7.33775i	−0.171952	−	0.297830i	−0.939102	+	0.343638i	$0.888341\pi$
$608$		0			0
$609$	11.9902	−	2.53573i	0.485868	−	0.102753i
$610$		0			0
$611$	3.41888	+	5.92168i	0.138313	+	0.239565i
$612$		0			0
$613$	−4.44466	+	7.69837i	−0.179518	+	0.310934i	−0.941716	−	0.336410i	$-0.890787\pi$
$613$	−4.44466	+	7.69837i	−0.179518	+	0.310934i	0.762198	+	0.647344i	$0.224120\pi$
$614$		0			0
$615$	33.1731			1.33767
$616$		0			0
$617$	−26.8100			−1.07933			−0.539665	−	0.841880i	$-0.681449\pi$
$617$	−26.8100			−1.07933			−0.539665	+	0.841880i	$0.681449\pi$
$618$		0			0
$619$	−0.101108	+	0.175125i	−0.00406388	+	0.00703885i	−0.868050	−	0.496476i	$-0.834627\pi$
$619$	−0.101108	+	0.175125i	−0.00406388	+	0.00703885i	0.863986	+	0.503515i	$0.167960\pi$
$620$		0			0
$621$	3.98655	+	6.90491i	0.159975	+	0.277085i
$622$		0			0
$623$	−6.08379	+	18.6588i	−0.243742	+	0.747548i
$624$		0			0
$625$	6.34079	+	10.9826i	0.253631	+	0.439303i
$626$		0			0
$627$	0.898054	−	1.55548i	0.0358648	−	0.0621197i
$628$		0			0
$629$	11.5214			0.459389
$630$		0			0
$631$	4.37267			0.174073			0.0870366	−	0.996205i	$-0.472260\pi$
$631$	4.37267			0.174073			0.0870366	+	0.996205i	$0.472260\pi$
$632$		0			0
$633$	−2.50611	+	4.34071i	−0.0996089	+	0.172528i
$634$		0			0
$635$	11.5676	+	20.0357i	0.459048	+	0.795094i
$636$		0			0
$637$	3.18722	−	29.7368i	0.126282	−	1.17821i
$638$		0			0
$639$	−1.70477	−	2.95275i	−0.0674397	−	0.116809i
$640$		0			0
$641$	−5.05099	+	8.74858i	−0.199502	+	0.345548i	−0.948367	−	0.317175i	$-0.897266\pi$
$641$	−5.05099	+	8.74858i	−0.199502	+	0.345548i	0.748865	+	0.662723i	$0.230599\pi$
$642$		0			0
$643$	37.4329			1.47621			0.738105	−	0.674686i	$-0.235721\pi$
$643$	37.4329			1.47621			0.738105	+	0.674686i	$0.235721\pi$
$644$		0			0
$645$	−0.547124			−0.0215430
$646$		0			0
$647$	−13.1266	+	22.7360i	−0.516062	+	0.893845i	0.483765	+	0.875198i	$0.339269\pi$
$647$	−13.1266	+	22.7360i	−0.516062	+	0.893845i	−0.999826	+	0.0186467i	$0.994064\pi$
$648$		0			0
$649$	2.72233	+	4.71521i	0.106861	+	0.185088i
$650$		0			0
$651$	−3.50411	+	10.7470i	−0.137337	+	0.421207i
$652$		0			0
$653$	−8.82211	−	15.2803i	−0.345236	−	0.597966i	0.640161	−	0.768241i	$-0.278868\pi$
$653$	−8.82211	−	15.2803i	−0.345236	−	0.597966i	−0.985397	+	0.170275i	$0.945534\pi$
$654$		0			0
$655$	23.9947	−	41.5601i	0.937552	−	1.62389i
$656$		0			0
$657$	−8.92843			−0.348331
$658$		0			0
$659$	−17.5662			−0.684282			−0.342141	−	0.939649i	$-0.611152\pi$
$659$	−17.5662			−0.684282			−0.342141	+	0.939649i	$0.611152\pi$
$660$		0			0
$661$	11.3564	−	19.6699i	0.441714	−	0.765072i	−0.556103	−	0.831114i	$-0.687704\pi$
$661$	11.3564	−	19.6699i	0.441714	−	0.765072i	0.997817	+	0.0660421i	$0.0210372\pi$
$662$		0			0
$663$	−5.99066	−	10.3761i	−0.232658	−	0.402976i
$664$		0			0
$665$	15.9768	−	3.37883i	0.619553	−	0.131025i
$666$		0			0
$667$	−18.4662	−	31.9843i	−0.715013	−	1.23844i
$668$		0			0
$669$	−7.42232	+	12.8558i	−0.286963	+	0.497035i
$670$		0			0
$671$	−10.5098			−0.405725
$672$		0			0
$673$	10.0182			0.386173			0.193087	−	0.981182i	$-0.438150\pi$
$673$	10.0182			0.386173			0.193087	+	0.981182i	$0.438150\pi$
$674$		0			0
$675$	−3.40455	+	5.89686i	−0.131041	+	0.226970i
$676$		0			0
$677$	−9.66639	−	16.7427i	−0.371509	−	0.643473i	0.618289	−	0.785951i	$-0.287826\pi$
$677$	−9.66639	−	16.7427i	−0.371509	−	0.643473i	−0.989798	+	0.142478i	$0.954493\pi$
$678$		0			0
$679$	4.85230	+	5.40016i	0.186214	+	0.207239i
$680$		0			0
$681$	2.73234	+	4.73255i	0.104704	+	0.181352i
$682$		0			0
$683$	−10.6305	+	18.4126i	−0.406767	+	0.704540i	−0.994525	−	0.104496i	$-0.966677\pi$
$683$	−10.6305	+	18.4126i	−0.406767	+	0.704540i	0.587759	+	0.809036i	$0.300010\pi$
$684$		0			0
$685$	−20.6751			−0.789956
$686$		0			0
$687$	28.7284			1.09606
$688$		0			0
$689$	−25.5948	+	44.3314i	−0.975083	+	1.68889i
$690$		0			0
$691$	22.0827	+	38.2483i	0.840064	+	1.45503i	0.889840	+	0.456273i	$0.150816\pi$
$691$	22.0827	+	38.2483i	0.840064	+	1.45503i	−0.0497758	+	0.998760i	$0.515851\pi$
$692$		0			0
$693$	1.76833	+	1.96799i	0.0671734	+	0.0747579i
$694$		0			0
$695$	−23.1091	−	40.0261i	−0.876578	−	1.51828i
$696$		0			0
$697$	13.5355	−	23.4443i	0.512695	−	0.888015i
$698$		0			0
$699$	−11.3775			−0.430335
$700$		0			0
$701$	−20.3236			−0.767613			−0.383806	−	0.923414i	$-0.625387\pi$
$701$	−20.3236			−0.767613			−0.383806	+	0.923414i	$0.625387\pi$
$702$		0			0
$703$	−3.68961	+	6.39059i	−0.139156	+	0.241026i
$704$		0			0
$705$	−2.74990	−	4.76296i	−0.103567	−	0.179384i
$706$		0			0
$707$	−2.48523	+	0.525585i	−0.0934666	+	0.0197667i
$708$		0			0
$709$	5.19156	+	8.99205i	0.194973	+	0.337704i	0.946892	−	0.321552i	$-0.104205\pi$
$709$	5.19156	+	8.99205i	0.194973	+	0.337704i	−0.751918	+	0.659256i	$0.770871\pi$
$710$		0			0
$711$	7.57266	−	13.1162i	0.283997	−	0.491897i
$712$		0			0
$713$	34.0646			1.27573
$714$		0			0
$715$	−14.6820			−0.549075
$716$		0			0
$717$	2.24532	−	3.88901i	0.0838530	−	0.145238i
$718$		0			0
$719$	−1.09612	−	1.89853i	−0.0408783	−	0.0708034i	0.844862	−	0.534984i	$-0.179682\pi$
$719$	−1.09612	−	1.89853i	−0.0408783	−	0.0708034i	−0.885741	+	0.464180i	$0.846349\pi$
$720$		0			0
$721$	−3.54075	+	10.8594i	−0.131865	+	0.404424i
$722$		0			0
$723$	−5.39654	−	9.34709i	−0.200700	−	0.347622i
$724$		0			0
$725$	15.7703	−	27.3149i	0.585693	−	1.01445i
$726$		0			0
$727$	−6.24690			−0.231685			−0.115842	−	0.993268i	$-0.536957\pi$
$727$	−6.24690			−0.231685			−0.115842	+	0.993268i	$0.536957\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.223242	+	0.386667i	−0.00825691	+	0.0143014i
$732$		0			0
$733$	6.08635	+	10.5419i	0.224804	+	0.389373i	0.956261	−	0.292516i	$-0.0944924\pi$
$733$	6.08635	+	10.5419i	0.224804	+	0.389373i	−0.731456	+	0.681888i	$0.761159\pi$
$734$		0			0
$735$	−2.56356	+	23.9181i	−0.0945584	+	0.882232i
$736$		0			0
$737$	−7.73666	−	13.4003i	−0.284983	−	0.493606i
$738$		0			0
$739$	1.24945	−	2.16411i	0.0459618	−	0.0796082i	−0.842129	−	0.539276i	$-0.818698\pi$
$739$	1.24945	−	2.16411i	0.0459618	−	0.0796082i	0.888091	+	0.459668i	$0.152031\pi$
$740$		0			0
$741$	7.67377			0.281903
$742$		0			0
$743$	43.9922			1.61392			0.806958	−	0.590609i	$-0.201112\pi$
$743$	43.9922			1.61392			0.806958	+	0.590609i	$0.201112\pi$
$744$		0			0
$745$	35.4348	−	61.3749i	1.29823	−	2.24860i
$746$		0			0
$747$	−6.27723	−	10.8725i	−0.229672	−	0.397803i
$748$		0			0
$749$	8.68519	−	26.6372i	0.317350	−	0.973302i
$750$		0			0
$751$	17.9759	+	31.1352i	0.655950	+	1.13614i	0.981655	+	0.190667i	$0.0610649\pi$
$751$	17.9759	+	31.1352i	0.655950	+	1.13614i	−0.325705	+	0.945471i	$0.605602\pi$
$752$		0			0
$753$	2.47223	−	4.28202i	0.0900929	−	0.156045i
$754$		0			0
$755$	13.2360			0.481707
$756$		0			0
$757$	37.0873			1.34796			0.673981	−	0.738749i	$-0.264583\pi$
$757$	37.0873			1.34796			0.673981	+	0.738749i	$0.264583\pi$
$758$		0			0
$759$	3.98655	−	6.90491i	0.144703	−	0.250632i
$760$		0			0
$761$	−4.20023	−	7.27501i	−0.152258	−	0.263719i	0.779799	−	0.626030i	$-0.215321\pi$
$761$	−4.20023	−	7.27501i	−0.152258	−	0.263719i	−0.932057	+	0.362311i	$0.881988\pi$
$762$		0			0
$763$	−11.6206	+	2.45758i	−0.420695	+	0.0889702i
$764$		0			0
$765$	4.81845	+	8.34580i	0.174211	+	0.301743i
$766$		0			0
$767$	−11.6310	+	20.1455i	−0.419971	+	0.727411i
$768$		0			0
$769$	−10.2842			−0.370859			−0.185430	−	0.982658i	$-0.559368\pi$
$769$	−10.2842			−0.370859			−0.185430	+	0.982658i	$0.559368\pi$
$770$		0			0
$771$	10.1275			0.364734
$772$		0			0
$773$	−11.2997	+	19.5717i	−0.406424	+	0.703947i	−0.994486	−	0.104869i	$-0.966558\pi$
$773$	−11.2997	+	19.5717i	−0.406424	+	0.703947i	0.588062	+	0.808816i	$0.299891\pi$
$774$		0			0
$775$	14.5458	+	25.1940i	0.522499	+	0.904995i
$776$		0			0
$777$	−7.26510	−	8.08540i	−0.260634	−	0.290062i
$778$		0			0
$779$	8.66921	+	15.0155i	0.310607	+	0.537987i
$780$		0			0
$781$	−1.70477	+	2.95275i	−0.0610015	+	0.105658i
$782$		0			0
$783$	−4.63211			−0.165538
$784$		0			0
$785$	27.0173			0.964289
$786$		0			0
$787$	14.7831	−	25.6050i	0.526959	−	0.912720i	−0.472548	−	0.881305i	$-0.656665\pi$
$787$	14.7831	−	25.6050i	0.526959	−	0.912720i	0.999506	−	0.0314144i	$-0.0100012\pi$
$788$		0			0
$789$	5.27723	+	9.14042i	0.187874	+	0.325408i
$790$		0			0
$791$	25.9296	+	28.8573i	0.921951	+	1.02605i
$792$		0			0
$793$	−22.4512	−	38.8866i	−0.797265	−	1.38090i
$794$		0			0
$795$	20.5865	−	35.6569i	0.730129	−	1.26462i
$796$		0			0
$797$	17.6087			0.623730			0.311865	−	0.950126i	$-0.399046\pi$
$797$	17.6087			0.623730			0.311865	+	0.950126i	$0.399046\pi$
$798$		0			0
$799$	−4.48814			−0.158779
$800$		0			0
$801$	3.70888	−	6.42397i	0.131047	−	0.226980i
$802$		0			0
$803$	4.46421	+	7.73224i	0.157539	+	0.272865i
$804$		0			0
$805$	70.9225	−	14.9989i	2.49969	−	0.528643i
$806$		0			0
$807$	−2.87400	−	4.97791i	−0.101169	−	0.175231i
$808$		0			0
$809$	13.9907	−	24.2325i	0.491885	−	0.851971i	−0.508071	−	0.861315i	$-0.669641\pi$
$809$	13.9907	−	24.2325i	0.491885	−	0.851971i	0.999956	+	0.00934463i	$0.00297453\pi$
$810$		0			0
$811$	19.9745			0.701398			0.350699	−	0.936488i	$-0.385944\pi$
$811$	19.9745			0.701398			0.350699	+	0.936488i	$0.385944\pi$
$812$		0			0
$813$	25.0642			0.879041
$814$		0			0
$815$	2.81254	−	4.87147i	0.0985192	−	0.170640i
$816$		0			0
$817$	−0.142982	−	0.247651i	−0.00500229	−	0.00866422i
$818$		0			0
$819$	−3.50411	+	10.7470i	−0.122443	+	0.375530i
$820$		0			0
$821$	27.0726	+	46.8912i	0.944841	+	1.63651i	0.756069	+	0.654492i	$0.227117\pi$
$821$	27.0726	+	46.8912i	0.944841	+	1.63651i	0.188772	+	0.982021i	$0.439549\pi$
$822$		0			0
$823$	−16.7647	+	29.0372i	−0.584379	+	1.01217i	0.410573	+	0.911828i	$0.365329\pi$
$823$	−16.7647	+	29.0372i	−0.584379	+	1.01217i	−0.994953	+	0.100347i	$0.968005\pi$
$824$		0			0
$825$	6.80911			0.237063
$826$		0			0
$827$	16.8537			0.586062			0.293031	−	0.956103i	$-0.405336\pi$
$827$	16.8537			0.586062			0.293031	+	0.956103i	$0.405336\pi$
$828$		0			0
$829$	7.85168	−	13.5995i	0.272700	−	0.472330i	−0.696852	−	0.717215i	$-0.745417\pi$
$829$	7.85168	−	13.5995i	0.272700	−	0.472330i	0.969552	+	0.244884i	$0.0787500\pi$
$830$		0			0
$831$	−3.49477	−	6.05312i	−0.121232	−	0.209980i
$832$		0			0
$833$	15.8575	+	11.5710i	0.549430	+	0.400911i
$834$		0			0
$835$	42.1093	+	72.9355i	1.45725	+	2.52404i
$836$		0			0
$837$	2.13622	−	3.70004i	0.0738386	−	0.127892i
$838$		0			0
$839$	−9.40641			−0.324745			−0.162373	−	0.986729i	$-0.551915\pi$
$839$	−9.40641			−0.324745			−0.162373	+	0.986729i	$0.551915\pi$
$840$		0			0
$841$	−7.54354			−0.260122
$842$		0			0
$843$	−7.03794	+	12.1901i	−0.242399	+	0.419848i
$844$		0			0
$845$	−9.02712	−	15.6354i	−0.310542	−	0.537875i
$846$		0			0
$847$	0.820165	−	2.51542i	0.0281812	−	0.0864308i
$848$		0			0
$849$	11.1093	+	19.2419i	0.381271	+	0.660381i
$850$		0			0
$851$	−16.3785	+	28.3685i	−0.561449	+	0.972458i
$852$		0			0
$853$	−5.19178			−0.177763			−0.0888816	−	0.996042i	$-0.528329\pi$
$853$	−5.19178			−0.177763			−0.0888816	+	0.996042i	$0.528329\pi$
$854$		0			0
$855$	−6.17221			−0.211085
$856$		0			0
$857$	1.60150	−	2.77388i	0.0547062	−	0.0947539i	−0.837375	−	0.546628i	$-0.815911\pi$
$857$	1.60150	−	2.77388i	0.0547062	−	0.0947539i	0.892082	+	0.451874i	$0.149244\pi$
$858$		0			0
$859$	17.2433	+	29.8663i	0.588334	+	1.01902i	0.994451	+	0.105203i	$0.0335493\pi$
$859$	17.2433	+	29.8663i	0.588334	+	1.01902i	−0.406117	+	0.913821i	$0.633117\pi$
$860$		0			0
$861$	−24.9876	+	5.28448i	−0.851576	+	0.180094i
$862$		0			0
$863$	5.30588	+	9.19005i	0.180614	+	0.312833i	0.942090	−	0.335360i	$-0.108858\pi$
$863$	5.30588	+	9.19005i	0.180614	+	0.312833i	−0.761476	+	0.648194i	$0.775525\pi$
$864$		0			0
$865$	40.0677	−	69.3992i	1.36234	−	2.35964i
$866$		0			0
$867$	−9.13575			−0.310266
$868$		0			0
$869$	−15.1453			−0.513770
$870$		0			0
$871$	33.0544	−	57.2519i	1.12001	−	1.93991i
$872$		0			0
$873$	−1.37200	−	2.37637i	−0.0464351	−	0.0804279i
$874$		0			0
$875$	10.9935	+	12.2348i	0.371650	+	0.413612i
$876$		0			0
$877$	−1.34290	−	2.32597i	−0.0453464	−	0.0785423i	0.842461	−	0.538757i	$-0.181106\pi$
$877$	−1.34290	−	2.32597i	−0.0453464	−	0.0785423i	−0.887808	+	0.460215i	$0.847772\pi$
$878$		0			0
$879$	11.8423	−	20.5114i	0.399430	−	0.691833i
$880$		0			0
$881$	28.0737			0.945829			0.472914	−	0.881108i	$-0.343202\pi$
$881$	28.0737			0.945829			0.472914	+	0.881108i	$0.343202\pi$
$882$		0			0
$883$	−4.81270			−0.161960			−0.0809801	−	0.996716i	$-0.525805\pi$
$883$	−4.81270			−0.161960			−0.0809801	+	0.996716i	$0.525805\pi$
$884$		0			0
$885$	9.35511	−	16.2035i	0.314469	−	0.544676i
$886$		0			0
$887$	−18.7755	−	32.5202i	−0.630421	−	1.09192i	−0.987466	−	0.157833i	$-0.949549\pi$
$887$	−18.7755	−	32.5202i	−0.630421	−	1.09192i	0.357045	−	0.934087i	$-0.383784\pi$
$888$		0			0
$889$	−11.9050	−	13.2492i	−0.399282	−	0.444364i
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$		0			0
$893$	1.43728	−	2.48944i	0.0480966	−	0.0833058i
$894$		0			0
$895$	−5.06153			−0.169188
$896$		0			0
$897$	34.0646			1.13739
$898$		0			0
$899$	−9.89522	+	17.1390i	−0.330024	+	0.571618i
$900$		0			0
$901$	−16.7998	−	29.0981i	−0.559682	−	0.969397i
$902$		0			0
$903$	0.412122	−	0.0871570i	0.0137146	−	0.00290040i
$904$		0			0
$905$	23.5831	+	40.8471i	0.783929	+	1.35780i
$906$		0			0
$907$	0.225992	−	0.391430i	0.00750395	−	0.0129972i	−0.862249	−	0.506485i	$-0.830945\pi$
$907$	0.225992	−	0.391430i	0.00750395	−	0.0129972i	0.869753	+	0.493487i	$0.164278\pi$
$908$		0			0
$909$	0.960104			0.0318446
$910$		0			0
$911$	52.4082			1.73636			0.868180	−	0.496249i	$-0.165290\pi$
$911$	52.4082			1.73636			0.868180	+	0.496249i	$0.165290\pi$
$912$		0			0
$913$	−6.27723	+	10.8725i	−0.207746	+	0.359826i
$914$		0			0
$915$	18.0581	+	31.2775i	0.596982	+	1.03400i
$916$		0			0
$917$	−11.4535	+	35.1275i	−0.378228	+	1.16001i
$918$		0			0
$919$	−19.1566	−	33.1802i	−0.631918	−	1.09451i	−0.987159	−	0.159739i	$-0.948935\pi$
$919$	−19.1566	−	33.1802i	−0.631918	−	1.09451i	0.355241	−	0.934775i	$-0.384399\pi$
$920$		0			0
$921$	−16.5458	+	28.6581i	−0.545202	+	0.944317i
$922$		0			0
$923$	−14.5671			−0.479481
$924$		0			0
$925$	−27.9749			−0.919808
$926$		0			0
$927$	2.15856	−	3.73874i	0.0708964	−	0.122796i
$928$		0			0
$929$	−17.4401	−	30.2071i	−0.572191	−	0.991064i	−0.996341	−	0.0854720i	$-0.972760\pi$
$929$	−17.4401	−	30.2071i	−0.572191	−	0.991064i	0.424149	−	0.905592i	$-0.360573\pi$
$930$		0			0
$931$	−11.4963	+	5.09020i	−0.376775	+	0.166825i
$932$		0			0
$933$	−12.1401	−	21.0273i	−0.397449	−	0.688401i
$934$		0			0
$935$	4.81845	−	8.34580i	0.157580	−	0.272937i
$936$		0			0
$937$	−15.4087			−0.503379			−0.251690	−	0.967808i	$-0.580986\pi$
$937$	−15.4087			−0.503379			−0.251690	+	0.967808i	$0.580986\pi$
$938$		0			0
$939$	0.563973			0.0184046
$940$		0			0
$941$	13.8505	−	23.9897i	0.451513	−	0.782043i	−0.546967	−	0.837154i	$-0.684218\pi$
$941$	13.8505	−	23.9897i	0.451513	−	0.782043i	0.998480	+	0.0551107i	$0.0175512\pi$
$942$		0			0
$943$	38.4835	+	66.6554i	1.25320	+	2.17060i
$944$		0			0
$945$	2.81845	−	8.64408i	0.0916841	−	0.281192i
$946$		0			0
$947$	−2.01457	−	3.48933i	−0.0654646	−	0.113388i	0.831435	−	0.555621i	$-0.187520\pi$
$947$	−2.01457	−	3.48933i	−0.0654646	−	0.113388i	−0.896900	+	0.442233i	$0.854186\pi$
$948$		0			0
$949$	−19.0731	+	33.0356i	−0.619139	+	1.07238i
$950$		0			0
$951$	3.91714			0.127022
$952$		0			0
$953$	−42.4395			−1.37475			−0.687376	−	0.726302i	$-0.741237\pi$
$953$	−42.4395			−1.37475			−0.687376	+	0.726302i	$0.741237\pi$
$954$		0			0
$955$	−5.40133	+	9.35537i	−0.174783	+	0.302733i
$956$		0			0
$957$	2.31606	+	4.01153i	0.0748675	+	0.129674i
$958$		0			0
$959$	15.5735	−	3.29355i	0.502896	−	0.106354i
$960$		0			0
$961$	6.37312	+	11.0386i	0.205584	+	0.356083i
$962$		0			0
$963$	−5.29478	+	9.17083i	−0.170622	+	0.295526i
$964$		0			0
$965$	−8.61863			−0.277444
$966$		0			0
$967$	−4.40435			−0.141634			−0.0708172	−	0.997489i	$-0.522561\pi$
$967$	−4.40435			−0.141634			−0.0708172	+	0.997489i	$0.522561\pi$
$968$		0			0
$969$	−2.51844	+	4.36206i	−0.0809038	+	0.140130i
$970$		0			0
$971$	−0.216109	−	0.374312i	−0.00693528	−	0.0120123i	0.862537	−	0.505994i	$-0.168874\pi$
$971$	−0.216109	−	0.374312i	−0.00693528	−	0.0120123i	−0.869472	+	0.493982i	$0.835541\pi$
$972$		0			0
$973$	23.7831	+	26.4684i	0.762451	+	0.848538i
$974$		0			0
$975$	14.5458	+	25.1940i	0.465837	+	0.806854i
$976$		0			0
$977$	−8.57544	+	14.8531i	−0.274353	+	0.475193i	−0.969972	−	0.243218i	$-0.921797\pi$
$977$	−8.57544	+	14.8531i	−0.274353	+	0.475193i	0.695619	+	0.718411i	$0.255130\pi$
$978$		0			0
$979$	−7.41776			−0.237073
$980$		0			0
$981$	4.48934			0.143333
$982$		0			0
$983$	−11.2802	+	19.5379i	−0.359783	+	0.623162i	−0.987924	−	0.154937i	$-0.950483\pi$
$983$	−11.2802	+	19.5379i	−0.359783	+	0.623162i	0.628141	+	0.778099i	$0.283816\pi$
$984$		0			0
$985$	12.9555	+	22.4397i	0.412798	+	0.714987i
$986$		0			0
$987$	2.83010	+	3.14964i	0.0900831	+	0.100254i
$988$		0			0
$989$	−0.634710	−	1.09935i	−0.0201826	−	0.0349573i
$990$		0			0
$991$	23.4175	−	40.5603i	0.743882	−	1.28844i	−0.206833	−	0.978376i	$-0.566316\pi$
$991$	23.4175	−	40.5603i	0.743882	−	1.28844i	0.950715	−	0.310065i	$-0.100351\pi$
$992$		0			0
$993$	−4.72491			−0.149940
$994$		0			0
$995$	−38.6759			−1.22611
$996$		0			0
$997$	2.56156	−	4.43676i	0.0811255	−	0.140513i	−0.822608	−	0.568609i	$-0.807482\pi$
$997$	2.56156	−	4.43676i	0.0811255	−	0.140513i	0.903734	+	0.428095i	$0.140815\pi$
$998$		0			0
$999$	2.05422	+	3.55802i	0.0649928	+	0.112571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1848.2.bg.f.529.1	✓	8
7.2	even	3	inner	1848.2.bg.f.793.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1848.2.bg.f.529.1	✓	8	1.1	even	1	trivial
1848.2.bg.f.793.1	yes	8	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1848.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.71822 - 2.97604i) q^{5} +(1.76833 + 1.96799i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.71822 - 2.97604i) q^{5} +(1.76833 + 1.96799i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -4.27244 q^{13} +3.43644 q^{15} +(1.40216 - 2.42862i) q^{17} +(0.898054 + 1.55548i) q^{19} +(-2.58850 + 0.547425i) q^{21} +(3.98655 + 6.90491i) q^{23} +(-3.40455 + 5.89686i) q^{25} +1.00000 q^{27} -4.63211 q^{29} +(2.13622 - 3.70004i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(2.81845 - 8.64408i) q^{35} +(2.05422 + 3.55802i) q^{37} +(2.13622 - 3.70004i) q^{39} +9.65333 q^{41} -0.159213 q^{43} +(-1.71822 + 2.97604i) q^{45} +(-0.800217 - 1.38602i) q^{47} +(-0.745994 + 6.96014i) q^{49} +(1.40216 + 2.42862i) q^{51} +(5.99066 - 10.3761i) q^{53} +3.43644 q^{55} -1.79611 q^{57} +(2.72233 - 4.71521i) q^{59} +(5.25489 + 9.10173i) q^{61} +(0.820165 - 2.51542i) q^{63} +(7.34099 + 12.7150i) q^{65} +(-7.73666 + 13.4003i) q^{67} -7.97311 q^{69} +3.40954 q^{71} +(4.46421 - 7.73224i) q^{73} +(-3.40455 - 5.89686i) q^{75} +(-2.58850 + 0.547425i) q^{77} +(7.57266 + 13.1162i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.5545 q^{83} -9.63690 q^{85} +(2.31606 - 4.01153i) q^{87} +(3.70888 + 6.42397i) q^{89} +(-7.55510 - 8.40814i) q^{91} +(2.13622 + 3.70004i) q^{93} +(3.08611 - 5.34529i) q^{95} +2.74399 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + q^7 - 4 * q^9	\( 8 q - 4 q^{3} + q^{7} - 4 q^{9} - 4 q^{11} - 14 q^{13} - q^{17} + 2 q^{19} + q^{21} + 5 q^{23} - 4 q^{25} + 8 q^{27} - 34 q^{29} + 7 q^{31} - 4 q^{33} + 10 q^{35} + 10 q^{37} + 7 q^{39} + 24 q^{41} - 16 q^{43} + 11 q^{47} + 5 q^{49} - q^{51} + 14 q^{53} - 4 q^{57} + q^{59} + 2 q^{61} - 2 q^{63} + 8 q^{65} - 17 q^{67} - 10 q^{69} - 54 q^{71} + 11 q^{73} - 4 q^{75} + q^{77} + 23 q^{79} - 4 q^{81} + 16 q^{83} - 52 q^{85} + 17 q^{87} - 18 q^{89} - 3 q^{91} + 7 q^{93} + 14 q^{95} + 14 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + q^7 - 4 * q^9 - 4 * q^11 - 14 * q^13 - q^17 + 2 * q^19 + q^21 + 5 * q^23 - 4 * q^25 + 8 * q^27 - 34 * q^29 + 7 * q^31 - 4 * q^33 + 10 * q^35 + 10 * q^37 + 7 * q^39 + 24 * q^41 - 16 * q^43 + 11 * q^47 + 5 * q^49 - q^51 + 14 * q^53 - 4 * q^57 + q^59 + 2 * q^61 - 2 * q^63 + 8 * q^65 - 17 * q^67 - 10 * q^69 - 54 * q^71 + 11 * q^73 - 4 * q^75 + q^77 + 23 * q^79 - 4 * q^81 + 16 * q^83 - 52 * q^85 + 17 * q^87 - 18 * q^89 - 3 * q^91 + 7 * q^93 + 14 * q^95 + 14 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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