LMFDB - Embedded newform 2646.2.h.p.667.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (of order $3$, degree $2$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.p.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} -1.00000 q^{8} +(1.84981 + 3.20397i) q^{10} +1.47710 q^{11} +(1.34981 + 2.33795i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.28799 + 5.69497i) q^{17} +(0.444368 - 0.769668i) q^{19} +(-1.84981 + 3.20397i) q^{20} +(0.738550 + 1.27921i) q^{22} -6.28799 q^{23} +8.68725 q^{25} +(-1.34981 + 2.33795i) q^{26} +(-1.25526 + 2.17417i) q^{29} +(3.40545 - 5.89841i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.28799 + 5.69497i) q^{34} +(-1.38874 + 2.40536i) q^{37} +0.888736 q^{38} -3.69963 q^{40} +(-2.05563 - 3.56046i) q^{41} +(0.00618986 - 0.0107211i) q^{43} +(-0.738550 + 1.27921i) q^{44} +(-3.14400 - 5.44556i) q^{46} +(3.49381 + 6.05146i) q^{47} +(4.34362 + 7.52338i) q^{50} -2.69963 q^{52} +(1.60507 + 2.78007i) q^{53} +5.46472 q^{55} -2.51052 q^{58} +(-3.45489 + 5.98404i) q^{59} +(-2.86652 - 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(4.99381 + 8.64953i) q^{65} +(4.73236 - 8.19669i) q^{67} -6.57598 q^{68} +5.46472 q^{71} +(6.03273 + 10.4490i) q^{73} -2.77747 q^{74} +(0.444368 + 0.769668i) q^{76} +(-5.72617 - 9.91802i) q^{79} +(-1.84981 - 3.20397i) q^{80} +(2.05563 - 3.56046i) q^{82} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +0.0123797 q^{86} -1.47710 q^{88} +(-4.43818 + 7.68715i) q^{89} +(3.14400 - 5.44556i) q^{92} +(-3.49381 + 6.05146i) q^{94} +(1.64400 - 2.84748i) q^{95} +(6.58836 - 11.4114i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} - 9 q^{37} + 6 q^{38} - 10 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 3 q^{47} + 2 q^{50} - 4 q^{52} - 9 q^{53} - 14 q^{55} + 10 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} + 8 q^{68} - 14 q^{71} + 25 q^{73} - 18 q^{74} + 3 q^{76} + 7 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} - 9 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8 + 5 * q^10 - 2 * q^11 + 2 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 - 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 - 2 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 - 9 * q^37 + 6 * q^38 - 10 * q^40 - 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 3 * q^47 + 2 * q^50 - 4 * q^52 - 9 * q^53 - 14 * q^55 + 10 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 + 8 * q^68 - 14 * q^71 + 25 * q^73 - 18 * q^74 + 3 * q^76 + 7 * q^79 - 5 * q^80 + 12 * q^82 + 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 - 9 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.69963			1.65452			0.827262	−	0.561816i	$-0.189897\pi$
$5$	3.69963			1.65452			0.827262	+	0.561816i	$0.189897\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.84981	+	3.20397i	0.584963	+	1.01318i
$11$	1.47710			0.445362			0.222681	−	0.974891i	$-0.428519\pi$
$11$	1.47710			0.445362			0.222681	+	0.974891i	$0.428519\pi$
$12$		0			0
$13$	1.34981	+	2.33795i	0.374371	+	0.648430i	0.990233	−	0.139425i	$-0.0445253\pi$
$13$	1.34981	+	2.33795i	0.374371	+	0.648430i	−0.615862	+	0.787854i	$0.711192\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	0.921268	+	0.388927i	$0.127154\pi$
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	−0.123813	+	0.992306i	$0.539512\pi$
$18$		0			0
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	−0.810541	−	0.585682i	$-0.800827\pi$
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	0.912486	+	0.409108i	$0.134160\pi$
$20$	−1.84981	+	3.20397i	−0.413631	+	0.716430i
$21$		0			0
$22$	0.738550	+	1.27921i	0.157459	+	0.272728i
$23$	−6.28799			−1.31114			−0.655568	−	0.755136i	$-0.727571\pi$
$23$	−6.28799			−1.31114			−0.655568	+	0.755136i	$0.727571\pi$
$24$		0			0
$25$	8.68725			1.73745
$26$	−1.34981	+	2.33795i	−0.264720	+	0.458509i
$27$		0			0
$28$		0			0
$29$	−1.25526	+	2.17417i	−0.233096	+	0.403734i	−0.958718	−	0.284360i	$-0.908219\pi$
$29$	−1.25526	+	2.17417i	−0.233096	+	0.403734i	0.725622	+	0.688094i	$0.241552\pi$
$30$		0			0
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	−0.379329	−	0.925262i	$-0.623845\pi$
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	0.990965	−	0.134123i	$-0.0428217\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−3.28799	+	5.69497i	−0.563886	+	0.976679i
$35$		0			0
$36$		0			0
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$	0.888736			0.144172
$39$		0			0
$40$	−3.69963			−0.584963
$41$	−2.05563	−	3.56046i	−0.321036	−	0.556050i	0.659666	−	0.751559i	$-0.270698\pi$
$41$	−2.05563	−	3.56046i	−0.321036	−	0.556050i	−0.980702	+	0.195508i	$0.937364\pi$
$42$		0			0
$43$	0.00618986	−	0.0107211i	0.000943944	−	0.00163496i	−0.865553	−	0.500817i	$-0.833033\pi$
$43$	0.00618986	−	0.0107211i	0.000943944	−	0.00163496i	0.866497	+	0.499182i	$0.166366\pi$
$44$	−0.738550	+	1.27921i	−0.111341	+	0.192848i
$45$		0			0
$46$	−3.14400	−	5.44556i	−0.463557	−	0.802904i
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	0.999938	+	0.0111494i	$0.00354904\pi$
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	−0.490313	+	0.871546i	$0.663118\pi$
$48$		0			0
$49$		0			0
$50$	4.34362	+	7.52338i	0.614281	+	1.06397i
$51$		0			0
$52$	−2.69963			−0.374371
$53$	1.60507	+	2.78007i	0.220474	+	0.381872i	0.954952	−	0.296760i	$-0.0959063\pi$
$53$	1.60507	+	2.78007i	0.220474	+	0.381872i	−0.734478	+	0.678632i	$0.762573\pi$
$54$		0			0
$55$	5.46472			0.736863
$56$		0			0
$57$		0			0
$58$	−2.51052			−0.329647
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	−0.998372	−	0.0570397i	$-0.981834\pi$
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	0.548584	+	0.836096i	$0.315167\pi$
$60$		0			0
$61$	−2.86652	−	4.96497i	−0.367021	−	0.635699i	0.622077	−	0.782956i	$-0.286289\pi$
$61$	−2.86652	−	4.96497i	−0.367021	−	0.635699i	−0.989098	+	0.147257i	$0.952956\pi$
$62$	6.81089			0.864984
$63$		0			0
$64$	1.00000			0.125000
$65$	4.99381	+	8.64953i	0.619406	+	1.07284i
$66$		0			0
$67$	4.73236	−	8.19669i	0.578150	−	1.00138i	−0.417542	−	0.908658i	$-0.637108\pi$
$67$	4.73236	−	8.19669i	0.578150	−	1.00138i	0.995692	−	0.0927271i	$-0.0295584\pi$
$68$	−6.57598			−0.797455
$69$		0			0
$70$		0			0
$71$	5.46472			0.648543			0.324271	−	0.945964i	$-0.394881\pi$
$71$	5.46472			0.648543			0.324271	+	0.945964i	$0.394881\pi$
$72$		0			0
$73$	6.03273	+	10.4490i	0.706078	+	1.22296i	0.966301	+	0.257414i	$0.0828705\pi$
$73$	6.03273	+	10.4490i	0.706078	+	1.22296i	−0.260223	+	0.965548i	$0.583796\pi$
$74$	−2.77747			−0.322875
$75$		0			0
$76$	0.444368	+	0.769668i	0.0509725	+	0.0882870i
$77$		0			0
$78$		0			0
$79$	−5.72617	−	9.91802i	−0.644244	−	1.11586i	−0.984475	−	0.175522i	$-0.943839\pi$
$79$	−5.72617	−	9.91802i	−0.644244	−	1.11586i	0.340231	−	0.940342i	$-0.389495\pi$
$80$	−1.84981	−	3.20397i	−0.206816	−	0.358215i
$81$		0			0
$82$	2.05563	−	3.56046i	0.227007	−	0.393187i
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	−0.716619	−	0.697465i	$-0.754311\pi$
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	0.962332	+	0.271878i	$0.0876447\pi$
$84$		0			0
$85$	12.1643	+	21.0693i	1.31941	+	2.28528i
$86$	0.0123797			0.00133494
$87$		0			0
$88$	−1.47710			−0.157459
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	−0.999429	−	0.0337963i	$-0.989240\pi$
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	0.528983	+	0.848633i	$0.322574\pi$
$90$		0			0
$91$		0			0
$92$	3.14400	−	5.44556i	0.327784	−	0.567739i
$93$		0			0
$94$	−3.49381	+	6.05146i	−0.360359	+	0.624160i
$95$	1.64400	−	2.84748i	0.168670	−	0.292146i
$96$		0			0
$97$	6.58836	−	11.4114i	0.668947	−	1.15865i	−0.309252	−	0.950980i	$-0.600079\pi$
$97$	6.58836	−	11.4114i	0.668947	−	1.15865i	0.978199	−	0.207670i	$-0.0665880\pi$
$98$		0			0
$99$		0			0
$100$	−4.34362	+	7.52338i	−0.434362	+	0.752338i
$101$	5.25457			0.522849			0.261425	−	0.965224i	$-0.415808\pi$
$101$	5.25457			0.522849			0.261425	+	0.965224i	$0.415808\pi$
$102$		0			0
$103$	−1.66621			−0.164176			−0.0820882	−	0.996625i	$-0.526159\pi$
$103$	−1.66621			−0.164176			−0.0820882	+	0.996625i	$0.526159\pi$
$104$	−1.34981	−	2.33795i	−0.132360	−	0.229255i
$105$		0			0
$106$	−1.60507	+	2.78007i	−0.155899	+	0.270024i
$107$	5.38255	−	9.32284i	0.520350	−	0.901273i	−0.479370	−	0.877613i	$-0.659135\pi$
$107$	5.38255	−	9.32284i	0.520350	−	0.901273i	0.999720	−	0.0236602i	$-0.00753198\pi$
$108$		0			0
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$	2.73236	+	4.73259i	0.260520	+	0.451234i
$111$		0			0
$112$		0			0
$113$	6.78180	+	11.7464i	0.637978	+	1.10501i	0.985876	+	0.167478i	$0.0535624\pi$
$113$	6.78180	+	11.7464i	0.637978	+	1.10501i	−0.347897	+	0.937533i	$0.613104\pi$
$114$		0			0
$115$	−23.2632			−2.16931
$116$	−1.25526	−	2.17417i	−0.116548	−	0.201867i
$117$		0			0
$118$	−6.90978			−0.636097
$119$		0			0
$120$		0			0
$121$	−8.81818			−0.801652
$122$	2.86652	−	4.96497i	0.259523	−	0.449507i
$123$		0			0
$124$	3.40545	+	5.89841i	0.305818	+	0.529692i
$125$	13.6414			1.22013
$126$		0			0
$127$	−2.85669			−0.253490			−0.126745	−	0.991935i	$-0.540453\pi$
$127$	−2.85669			−0.253490			−0.126745	+	0.991935i	$0.540453\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.99381	+	8.64953i	−0.437986	+	0.758614i
$131$	0.155687			0.0136024			0.00680122	−	0.999977i	$-0.497835\pi$
$131$	0.155687			0.0136024			0.00680122	+	0.999977i	$0.497835\pi$
$132$		0			0
$133$		0			0
$134$	9.46472			0.817627
$135$		0			0
$136$	−3.28799	−	5.69497i	−0.281943	−	0.488340i
$137$	3.41164			0.291476			0.145738	−	0.989323i	$-0.453444\pi$
$137$	3.41164			0.291476			0.145738	+	0.989323i	$0.453444\pi$
$138$		0			0
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	0.996259	+	0.0864229i	$0.0275436\pi$
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	−0.423285	+	0.905997i	$0.639123\pi$
$140$		0			0
$141$		0			0
$142$	2.73236	+	4.73259i	0.229295	+	0.397150i
$143$	1.99381	+	3.45338i	0.166731	+	0.288786i
$144$		0			0
$145$	−4.64400	+	8.04364i	−0.385663	+	0.667988i
$146$	−6.03273	+	10.4490i	−0.499272	+	0.864765i
$147$		0			0
$148$	−1.38874	−	2.40536i	−0.114153	−	0.197719i
$149$	−0.333792			−0.0273453			−0.0136727	−	0.999907i	$-0.504352\pi$
$149$	−0.333792			−0.0273453			−0.0136727	+	0.999907i	$0.504352\pi$
$150$		0			0
$151$	−19.9098			−1.62023			−0.810117	−	0.586268i	$-0.800597\pi$
$151$	−19.9098			−1.62023			−0.810117	+	0.586268i	$0.800597\pi$
$152$	−0.444368	+	0.769668i	−0.0360430	+	0.0624283i
$153$		0			0
$154$		0			0
$155$	12.5989	−	21.8219i	1.01197	−	1.75278i
$156$		0			0
$157$	−3.48143	+	6.03001i	−0.277848	+	0.481248i	−0.970850	−	0.239689i	$-0.922955\pi$
$157$	−3.48143	+	6.03001i	−0.277848	+	0.481248i	0.693001	+	0.720936i	$0.256288\pi$
$158$	5.72617	−	9.91802i	0.455550	−	0.789035i
$159$		0			0
$160$	1.84981	−	3.20397i	0.146241	−	0.253296i
$161$		0			0
$162$		0			0
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	−0.663486	−	0.748189i	$-0.730924\pi$
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	0.979693	+	0.200502i	$0.0642572\pi$
$164$	4.11126			0.321036
$165$		0			0
$166$	4.47710			0.347490
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	0.945906	+	0.324440i	$0.105176\pi$
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	−0.191979	+	0.981399i	$0.561491\pi$
$168$		0			0
$169$	2.85600	−	4.94674i	0.219693	−	0.380519i
$170$	−12.1643	+	21.0693i	−0.932963	+	1.61594i
$171$		0			0
$172$	0.00618986	+	0.0107211i	0.000471972	+	0.000817480i
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	−0.874080	−	0.485782i	$-0.838535\pi$
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	0.0163405	−	0.999866i	$-0.494798\pi$
$174$		0			0
$175$		0			0
$176$	−0.738550	−	1.27921i	−0.0556703	−	0.0964238i
$177$		0			0
$178$	−8.87636			−0.665311
$179$	−0.166896	−	0.289073i	−0.0124744	−	0.0216063i	0.859721	−	0.510764i	$-0.170637\pi$
$179$	−0.166896	−	0.289073i	−0.0124744	−	0.0216063i	−0.872195	+	0.489158i	$0.837304\pi$
$180$		0			0
$181$	−23.2422			−1.72758			−0.863789	−	0.503853i	$-0.831915\pi$
$181$	−23.2422			−1.72758			−0.863789	+	0.503853i	$0.831915\pi$
$182$		0			0
$183$		0			0
$184$	6.28799			0.463557
$185$	−5.13781	+	8.89894i	−0.377739	+	0.654263i
$186$		0			0
$187$	4.85669	+	8.41204i	0.355157	+	0.615149i
$188$	−6.98762			−0.509625
$189$		0			0
$190$	3.28799			0.238536
$191$	−8.16071	−	14.1348i	−0.590488	−	1.02276i	−0.994167	−	0.107854i	$-0.965602\pi$
$191$	−8.16071	−	14.1348i	−0.590488	−	1.02276i	0.403679	−	0.914901i	$-0.367731\pi$
$192$		0			0
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	−0.484400	−	0.874846i	$-0.660962\pi$
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	0.999839	−	0.0179200i	$-0.00570443\pi$
$194$	13.1767			0.946034
$195$		0			0
$196$		0			0
$197$	−2.42402			−0.172704			−0.0863520	−	0.996265i	$-0.527521\pi$
$197$	−2.42402			−0.172704			−0.0863520	+	0.996265i	$0.527521\pi$
$198$		0			0
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	0.953769	−	0.300541i	$-0.0971673\pi$
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	−0.737161	+	0.675717i	$0.763834\pi$
$200$	−8.68725			−0.614281
$201$		0			0
$202$	2.62729	+	4.55059i	0.184855	+	0.320179i
$203$		0			0
$204$		0			0
$205$	−7.60507	−	13.1724i	−0.531161	−	0.919999i
$206$	−0.833104	−	1.44298i	−0.0580451	−	0.100537i
$207$		0			0
$208$	1.34981	−	2.33795i	0.0935928	−	0.162107i
$209$	0.656376	−	1.13688i	0.0454025	−	0.0786394i
$210$		0			0
$211$	5.72253	+	9.91171i	0.393955	+	0.682350i	0.992967	−	0.118390i	$-0.0377732\pi$
$211$	5.72253	+	9.91171i	0.393955	+	0.682350i	−0.599012	+	0.800740i	$0.704440\pi$
$212$	−3.21015			−0.220474
$213$		0			0
$214$	10.7651			0.735887
$215$	0.0229002	−	0.0396643i	0.00156178	−	0.00270508i
$216$		0			0
$217$		0			0
$218$	0.0945538	−	0.163772i	0.00640399	−	0.0110920i
$219$		0			0
$220$	−2.73236	+	4.73259i	−0.184216	+	0.319071i
$221$	−8.87636	+	15.3743i	−0.597088	+	1.03419i
$222$		0			0
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	−0.719407	−	0.694589i	$-0.755586\pi$
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	0.961235	+	0.275730i	$0.0889196\pi$
$224$		0			0
$225$		0			0
$226$	−6.78180	+	11.7464i	−0.451119	+	0.781361i
$227$	13.6552			0.906328			0.453164	−	0.891427i	$-0.350295\pi$
$227$	13.6552			0.906328			0.453164	+	0.891427i	$0.350295\pi$
$228$		0			0
$229$	−17.3745			−1.14814			−0.574070	−	0.818807i	$-0.694636\pi$
$229$	−17.3745			−1.14814			−0.574070	+	0.818807i	$0.694636\pi$
$230$	−11.6316	−	20.1466i	−0.766966	−	1.32842i
$231$		0			0
$232$	1.25526	−	2.17417i	0.0824119	−	0.142742i
$233$	−7.62110	+	13.2001i	−0.499275	+	0.864769i	−1.00000		0.000837426i	$-0.999733\pi$
$233$	−7.62110	+	13.2001i	−0.499275	+	0.864769i	0.500725	+	0.865606i	$0.333067\pi$
$234$		0			0
$235$	12.9258	+	22.3881i	0.843186	+	1.46044i
$236$	−3.45489	−	5.98404i	−0.224894	−	0.389528i
$237$		0			0
$238$		0			0
$239$	−9.47524	−	16.4116i	−0.612902	−	1.06158i	−0.990749	−	0.135710i	$-0.956669\pi$
$239$	−9.47524	−	16.4116i	−0.612902	−	1.06158i	0.377846	−	0.925868i	$-0.376665\pi$
$240$		0			0
$241$	24.5054			1.57853			0.789267	−	0.614051i	$-0.210461\pi$
$241$	24.5054			1.57853			0.789267	+	0.614051i	$0.210461\pi$
$242$	−4.40909	−	7.63676i	−0.283427	−	0.490910i
$243$		0			0
$244$	5.73305			0.367021
$245$		0			0
$246$		0			0
$247$	2.39926			0.152661
$248$	−3.40545	+	5.89841i	−0.216246	+	0.374549i
$249$		0			0
$250$	6.82072	+	11.8138i	0.431380	+	0.747173i
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$	−1.42835	−	2.47397i	−0.0896224	−	0.155231i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.20877			−0.512049			−0.256025	−	0.966670i	$-0.582413\pi$
$257$	−8.20877			−0.512049			−0.256025	+	0.966670i	$0.582413\pi$
$258$		0			0
$259$		0			0
$260$	−9.98762			−0.619406
$261$		0			0
$262$	0.0778435	+	0.134829i	0.00480919	+	0.00832976i
$263$	5.34617			0.329659			0.164830	−	0.986322i	$-0.447293\pi$
$263$	5.34617			0.329659			0.164830	+	0.986322i	$0.447293\pi$
$264$		0			0
$265$	5.93818	+	10.2852i	0.364779	+	0.631816i
$266$		0			0
$267$		0			0
$268$	4.73236	+	8.19669i	0.289075	+	0.500692i
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	0.997187	+	0.0749550i	$0.0238813\pi$
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	−0.433681	+	0.901067i	$0.642785\pi$
$270$		0			0
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	−0.732447	−	0.680824i	$-0.761622\pi$
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	0.955834	+	0.293906i	$0.0949552\pi$
$272$	3.28799	−	5.69497i	0.199364	−	0.345308i
$273$		0			0
$274$	1.70582	+	2.95456i	0.103052	+	0.178492i
$275$	12.8319			0.773795
$276$		0			0
$277$	−9.09888			−0.546699			−0.273349	−	0.961915i	$-0.588132\pi$
$277$	−9.09888			−0.546699			−0.273349	+	0.961915i	$0.588132\pi$
$278$	−6.75526	+	11.7005i	−0.405154	+	0.701747i
$279$		0			0
$280$		0			0
$281$	−6.00433	+	10.3998i	−0.358188	+	0.620400i	−0.987658	−	0.156624i	$-0.949939\pi$
$281$	−6.00433	+	10.3998i	−0.358188	+	0.620400i	0.629470	+	0.777025i	$0.283272\pi$
$282$		0			0
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	−0.681861	−	0.731481i	$-0.738829\pi$
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	0.974412	+	0.224768i	$0.0721626\pi$
$284$	−2.73236	+	4.73259i	−0.162136	+	0.280827i
$285$		0			0
$286$	−1.99381	+	3.45338i	−0.117896	+	0.204203i
$287$		0			0
$288$		0			0
$289$	−13.1218	+	22.7276i	−0.771870	+	1.33692i
$290$	−9.28799			−0.545410
$291$		0			0
$292$	−12.0655			−0.706078
$293$	10.7101	+	18.5505i	0.625694	+	1.08373i	0.988406	+	0.151832i	$0.0485173\pi$
$293$	10.7101	+	18.5505i	0.625694	+	1.08373i	−0.362713	+	0.931901i	$0.618149\pi$
$294$		0			0
$295$	−12.7818	+	22.1387i	−0.744185	+	1.28897i
$296$	1.38874	−	2.40536i	0.0807186	−	0.139809i
$297$		0			0
$298$	−0.166896	−	0.289073i	−0.00966804	−	0.0167455i
$299$	−8.48762	−	14.7010i	−0.490852	−	0.850180i
$300$		0			0
$301$		0			0
$302$	−9.95489	−	17.2424i	−0.572839	−	0.992187i
$303$		0			0
$304$	−0.888736			−0.0509725
$305$	−10.6051	−	18.3685i	−0.607245	−	1.05178i
$306$		0			0
$307$	5.68725			0.324588			0.162294	−	0.986742i	$-0.448111\pi$
$307$	5.68725			0.324588			0.162294	+	0.986742i	$0.448111\pi$
$308$		0			0
$309$		0			0
$310$	25.1978			1.43114
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	−0.650655	−	0.759373i	$-0.725506\pi$
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	0.982964	+	0.183797i	$0.0588390\pi$
$312$		0			0
$313$	−13.3869	−	23.1868i	−0.756671	−	1.31059i	−0.944539	−	0.328398i	$-0.893491\pi$
$313$	−13.3869	−	23.1868i	−0.756671	−	1.31059i	0.187868	−	0.982194i	$-0.439842\pi$
$314$	−6.96286			−0.392937
$315$		0			0
$316$	11.4523			0.644244
$317$	0.951246	+	1.64761i	0.0534273	+	0.0925388i	0.891502	−	0.453016i	$-0.149652\pi$
$317$	0.951246	+	1.64761i	0.0534273	+	0.0925388i	−0.838075	+	0.545555i	$0.816319\pi$
$318$		0			0
$319$	−1.85414	+	3.21147i	−0.103812	+	0.179808i
$320$	3.69963			0.206816
$321$		0			0
$322$		0			0
$323$	5.84431			0.325186
$324$		0			0
$325$	11.7262	+	20.3103i	0.650451	+	1.12661i
$326$	8.07413			0.447184
$327$		0			0
$328$	2.05563	+	3.56046i	0.113503	+	0.196593i
$329$		0			0
$330$		0			0
$331$	−2.78366	−	4.82144i	−0.153004	−	0.265010i	0.779327	−	0.626618i	$-0.215561\pi$
$331$	−2.78366	−	4.82144i	−0.153004	−	0.265010i	−0.932330	+	0.361608i	$0.882228\pi$
$332$	2.23855	+	3.87728i	0.122856	+	0.212794i
$333$		0			0
$334$	−9.74288	+	16.8752i	−0.533107	+	0.923368i
$335$	17.5080	−	30.3247i	0.956563	−	1.65682i
$336$		0			0
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.799585	−	0.600553i	$-0.794947\pi$
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.120302	−	0.992737i	$-0.538386\pi$
$338$	5.71201			0.310692
$339$		0			0
$340$	−24.3287			−1.31941
$341$	5.03018	−	8.71253i	0.272400	−	0.471810i
$342$		0			0
$343$		0			0
$344$	−0.00618986	+	0.0107211i	−0.000333735	+	0.000578045i
$345$		0			0
$346$	11.2818	−	19.5407i	0.606513	−	1.05051i
$347$	−15.2033	+	26.3328i	−0.816154	+	1.41362i	0.0923418	+	0.995727i	$0.470565\pi$
$347$	−15.2033	+	26.3328i	−0.816154	+	1.41362i	−0.908496	+	0.417893i	$0.862769\pi$
$348$		0			0
$349$	6.29782	−	10.9082i	0.337115	−	0.583900i	−0.646774	−	0.762682i	$-0.723882\pi$
$349$	6.29782	−	10.9082i	0.337115	−	0.583900i	0.983889	+	0.178782i	$0.0572156\pi$
$350$		0			0
$351$		0			0
$352$	0.738550	−	1.27921i	0.0393648	−	0.0681819i
$353$	−7.53156			−0.400865			−0.200432	−	0.979708i	$-0.564235\pi$
$353$	−7.53156			−0.400865			−0.200432	+	0.979708i	$0.564235\pi$
$354$		0			0
$355$	20.2174			1.07303
$356$	−4.43818	−	7.68715i	−0.235223	−	0.407418i
$357$		0			0
$358$	0.166896	−	0.289073i	0.00882074	−	0.0152780i
$359$	3.44801	−	5.97213i	0.181979	−	0.315197i	−0.760575	−	0.649250i	$-0.775083\pi$
$359$	3.44801	−	5.97213i	0.181979	−	0.315197i	0.942554	+	0.334053i	$0.108416\pi$
$360$		0			0
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	−11.6211	−	20.1283i	−0.610791	−	1.05792i
$363$		0			0
$364$		0			0
$365$	22.3189	+	38.6574i	1.16822	+	2.02342i
$366$		0			0
$367$	−23.1236			−1.20704			−0.603522	−	0.797346i	$-0.706237\pi$
$367$	−23.1236			−1.20704			−0.603522	+	0.797346i	$0.706237\pi$
$368$	3.14400	+	5.44556i	0.163892	+	0.283869i
$369$		0			0
$370$	−10.2756			−0.534204
$371$		0			0
$372$		0			0
$373$	29.1643			1.51007			0.755036	−	0.655683i	$-0.227619\pi$
$373$	29.1643			1.51007			0.755036	+	0.655683i	$0.227619\pi$
$374$	−4.85669	+	8.41204i	−0.251134	+	0.434976i
$375$		0			0
$376$	−3.49381	−	6.05146i	−0.180180	−	0.312080i
$377$	−6.77747			−0.349058
$378$		0			0
$379$	−13.5622			−0.696645			−0.348322	−	0.937375i	$-0.613249\pi$
$379$	−13.5622			−0.696645			−0.348322	+	0.937375i	$0.613249\pi$
$380$	1.64400	+	2.84748i	0.0843352	+	0.146073i
$381$		0			0
$382$	8.16071	−	14.1348i	0.417538	−	0.723197i
$383$	−2.83565			−0.144895			−0.0724475	−	0.997372i	$-0.523081\pi$
$383$	−2.83565			−0.144895			−0.0724475	+	0.997372i	$0.523081\pi$
$384$		0			0
$385$		0			0
$386$	14.3214			0.728941
$387$		0			0
$388$	6.58836	+	11.4114i	0.334474	+	0.579325i
$389$	18.6080			0.943464			0.471732	−	0.881742i	$-0.343629\pi$
$389$	18.6080			0.943464			0.471732	+	0.881742i	$0.343629\pi$
$390$		0			0
$391$	−20.6749	−	35.8099i	−1.04557	−	1.81099i
$392$		0			0
$393$		0			0
$394$	−1.21201	−	2.09926i	−0.0610601	−	0.105759i
$395$	−21.1847	−	36.6930i	−1.06592	−	1.84622i
$396$		0			0
$397$	10.2880	−	17.8193i	0.516340	−	0.894326i	−0.483481	−	0.875355i	$-0.660628\pi$
$397$	10.2880	−	17.8193i	0.516340	−	0.894326i	0.999820	−	0.0189712i	$-0.00603907\pi$
$398$	−3.05563	+	5.29251i	−0.153165	+	0.265290i
$399$		0			0
$400$	−4.34362	−	7.52338i	−0.217181	−	0.376169i
$401$	6.75409			0.337283			0.168642	−	0.985677i	$-0.446062\pi$
$401$	6.75409			0.337283			0.168642	+	0.985677i	$0.446062\pi$
$402$		0			0
$403$	18.3869			0.915916
$404$	−2.62729	+	4.55059i	−0.130712	+	0.226400i
$405$		0			0
$406$		0			0
$407$	−2.05130	+	3.55296i	−0.101679	+	0.176114i
$408$		0			0
$409$	7.66071	−	13.2687i	0.378798	−	0.656097i	−0.612090	−	0.790788i	$-0.709671\pi$
$409$	7.66071	−	13.2687i	0.378798	−	0.656097i	0.990888	+	0.134691i	$0.0430043\pi$
$410$	7.60507	−	13.1724i	0.375588	−	0.650537i
$411$		0			0
$412$	0.833104	−	1.44298i	0.0410441	−	0.0710904i
$413$		0			0
$414$		0			0
$415$	8.28180	−	14.3445i	0.406538	−	0.704144i
$416$	2.69963			0.132360
$417$		0			0
$418$	1.31275			0.0642088
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	0.740949	−	0.671561i	$-0.234376\pi$
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	−0.952064	+	0.305900i	$0.901043\pi$
$420$		0			0
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.0834618	−	0.996511i	$-0.473402\pi$
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.821273	−	0.570536i	$-0.193264\pi$
$422$	−5.72253	+	9.91171i	−0.278568	+	0.482494i
$423$		0			0
$424$	−1.60507	−	2.78007i	−0.0779493	−	0.135012i
$425$	28.5636	+	49.4736i	1.38554	+	2.39982i
$426$		0			0
$427$		0			0
$428$	5.38255	+	9.32284i	0.260175	+	0.450637i
$429$		0			0
$430$	0.0458003			0.00220869
$431$	4.71015	+	8.15822i	0.226880	+	0.392967i	0.956882	−	0.290478i	$-0.0938142\pi$
$431$	4.71015	+	8.15822i	0.226880	+	0.392967i	−0.730002	+	0.683445i	$0.760481\pi$
$432$		0			0
$433$	0.208771			0.0100329			0.00501645	−	0.999987i	$-0.498403\pi$
$433$	0.208771			0.0100329			0.00501645	+	0.999987i	$0.498403\pi$
$434$		0			0
$435$		0			0
$436$	0.189108			0.00905662
$437$	−2.79418	+	4.83967i	−0.133664	+	0.231513i
$438$		0			0
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	0.722231	−	0.691652i	$-0.243117\pi$
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	−0.960104	+	0.279645i	$0.909783\pi$
$440$	−5.46472			−0.260520
$441$		0			0
$442$	−17.7527			−0.844410
$443$	−7.84981	−	13.5963i	−0.372956	−	0.645979i	0.617063	−	0.786914i	$-0.288322\pi$
$443$	−7.84981	−	13.5963i	−0.372956	−	0.645979i	−0.990019	+	0.140935i	$0.954989\pi$
$444$		0			0
$445$	−16.4196	+	28.4396i	−0.778364	+	1.34817i
$446$	7.22253			0.341997
$447$		0			0
$448$		0			0
$449$	−33.6253			−1.58688			−0.793439	−	0.608650i	$-0.791712\pi$
$449$	−33.6253			−1.58688			−0.793439	+	0.608650i	$0.791712\pi$
$450$		0			0
$451$	−3.03637	−	5.25915i	−0.142977	−	0.247644i
$452$	−13.5636			−0.637978
$453$		0			0
$454$	6.82760	+	11.8258i	0.320435	+	0.555010i
$455$		0			0
$456$		0			0
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	−0.940239	−	0.340516i	$-0.889398\pi$
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	0.175224	−	0.984529i	$-0.443935\pi$
$458$	−8.68725	−	15.0468i	−0.405928	−	0.703089i
$459$		0			0
$460$	11.6316	−	20.1466i	0.542327	−	0.939338i
$461$	−2.07165	+	3.58821i	−0.0964865	+	0.167120i	−0.910228	−	0.414107i	$-0.864094\pi$
$461$	−2.07165	+	3.58821i	−0.0964865	+	0.167120i	0.813742	+	0.581227i	$0.197427\pi$
$462$		0			0
$463$	−8.34176	−	14.4484i	−0.387675	−	0.671472i	0.604462	−	0.796634i	$-0.293388\pi$
$463$	−8.34176	−	14.4484i	−0.387675	−	0.671472i	−0.992136	+	0.125162i	$0.960055\pi$
$464$	2.51052			0.116548
$465$		0			0
$466$	−15.2422			−0.706081
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	−0.278918	−	0.960315i	$-0.589976\pi$
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	0.971116	−	0.238608i	$-0.0766909\pi$
$468$		0			0
$469$		0			0
$470$	−12.9258	+	22.3881i	−0.596223	+	1.03269i
$471$		0			0
$472$	3.45489	−	5.98404i	0.159024	−	0.275438i
$473$	0.00914304	−	0.0158362i	0.000420397	−	0.000728149i
$474$		0			0
$475$	3.86033	−	6.68630i	0.177124	−	0.306788i
$476$		0			0
$477$		0			0
$478$	9.47524	−	16.4116i	0.433387	−	0.750649i
$479$	−2.95930			−0.135214			−0.0676068	−	0.997712i	$-0.521536\pi$
$479$	−2.95930			−0.135214			−0.0676068	+	0.997712i	$0.521536\pi$
$480$		0			0
$481$	−7.49814			−0.341886
$482$	12.2527	+	21.2223i	0.558096	+	0.966650i
$483$		0			0
$484$	4.40909	−	7.63676i	0.200413	−	0.347126i
$485$	24.3745	−	42.2179i	1.10679	−	1.91701i
$486$		0			0
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	−0.986345	−	0.164691i	$-0.947337\pi$
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	0.350546	−	0.936546i	$-0.385996\pi$
$488$	2.86652	+	4.96497i	0.129761	+	0.224753i
$489$		0			0
$490$		0			0
$491$	−17.0734	−	29.5721i	−0.770513	−	1.33457i	−0.937282	−	0.348572i	$-0.886667\pi$
$491$	−17.0734	−	29.5721i	−0.770513	−	1.33457i	0.166769	−	0.985996i	$-0.446667\pi$
$492$		0			0
$493$	−16.5091			−0.743534
$494$	1.19963	+	2.07782i	0.0539738	+	0.0934854i
$495$		0			0
$496$	−6.81089			−0.305818
$497$		0			0
$498$		0			0
$499$	−2.28071			−0.102099			−0.0510493	−	0.998696i	$-0.516257\pi$
$499$	−2.28071			−0.102099			−0.0510493	+	0.998696i	$0.516257\pi$
$500$	−6.82072	+	11.8138i	−0.305032	+	0.528331i
$501$		0			0
$502$	−6.06182	−	10.4994i	−0.270552	−	0.468610i
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$	−4.64400	−	8.04364i	−0.206451	−	0.357583i
$507$		0			0
$508$	1.42835	−	2.47397i	0.0633726	−	0.109765i
$509$	25.6181			1.13550			0.567750	−	0.823201i	$-0.307814\pi$
$509$	25.6181			1.13550			0.567750	+	0.823201i	$0.307814\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−4.10439	−	7.10900i	−0.181037	−	0.313565i
$515$	−6.16435			−0.271634
$516$		0			0
$517$	5.16071	+	8.93861i	0.226968	+	0.393119i
$518$		0			0
$519$		0			0
$520$	−4.99381	−	8.64953i	−0.218993	−	0.379307i
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.805130	−	0.593099i	$-0.797904\pi$
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.111073	−	0.993812i	$-0.535429\pi$
$522$		0			0
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	−0.985301	−	0.170827i	$-0.945356\pi$
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	0.640591	+	0.767882i	$0.278689\pi$
$524$	−0.0778435	+	0.134829i	−0.00340061	+	0.00589003i
$525$		0			0
$526$	2.67309	+	4.62992i	0.116552	+	0.201874i
$527$	44.7883			1.95101
$528$		0			0
$529$	16.5388			0.719080
$530$	−5.93818	+	10.2852i	−0.257938	+	0.446762i
$531$		0			0
$532$		0			0
$533$	5.54944	−	9.61192i	0.240373	−	0.416338i
$534$		0			0
$535$	19.9134	−	34.4911i	0.860932	−	1.49118i
$536$	−4.73236	+	8.19669i	−0.204407	+	0.354043i
$537$		0			0
$538$	−9.24219	+	16.0079i	−0.398459	+	0.690152i
$539$		0			0
$540$		0			0
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$	7.35483			0.315917
$543$		0			0
$544$	6.57598			0.281943
$545$	−0.349814	−	0.605896i	−0.0149844	−	0.0259537i
$546$		0			0
$547$	20.3356	−	35.2222i	0.869486	−	1.50599i	0.00696400	−	0.999976i	$-0.497783\pi$
$547$	20.3356	−	35.2222i	0.869486	−	1.50599i	0.862522	−	0.506019i	$-0.168883\pi$
$548$	−1.70582	+	2.95456i	−0.0728689	+	0.126213i
$549$		0			0
$550$	6.41597	+	11.1128i	0.273578	+	0.473851i
$551$	1.11559	+	1.93227i	0.0475259	+	0.0823173i
$552$		0			0
$553$		0			0
$554$	−4.54944	−	7.87987i	−0.193287	−	0.334783i
$555$		0			0
$556$	−13.5105			−0.572974
$557$	−6.68794	−	11.5838i	−0.283377	−	0.490823i	0.688837	−	0.724916i	$-0.258121\pi$
$557$	−6.68794	−	11.5838i	−0.283377	−	0.490823i	−0.972214	+	0.234093i	$0.924788\pi$
$558$		0			0
$559$	0.0334206			0.00141354
$560$		0			0
$561$		0			0
$562$	−12.0087			−0.506555
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	−0.281355	−	0.959604i	$-0.590784\pi$
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	0.971719	−	0.236141i	$-0.0758828\pi$
$564$		0			0
$565$	25.0901	+	43.4574i	1.05555	+	1.82827i
$566$	9.84294			0.413729
$567$		0			0
$568$	−5.46472			−0.229295
$569$	−8.36398	−	14.4868i	−0.350636	−	0.607320i	0.635725	−	0.771916i	$-0.280701\pi$
$569$	−8.36398	−	14.4868i	−0.350636	−	0.607320i	−0.986361	+	0.164596i	$0.947368\pi$
$570$		0			0
$571$	13.7367	−	23.7926i	0.574863	−	0.995691i	−0.421194	−	0.906971i	$-0.638389\pi$
$571$	13.7367	−	23.7926i	0.574863	−	0.995691i	0.996057	−	0.0887207i	$-0.0282778\pi$
$572$	−3.98762			−0.166731
$573$		0			0
$574$		0			0
$575$	−54.6253			−2.27803
$576$		0			0
$577$	−1.41714	−	2.45455i	−0.0589962	−	0.102184i	0.835019	−	0.550221i	$-0.185457\pi$
$577$	−1.41714	−	2.45455i	−0.0589962	−	0.102184i	−0.894015	+	0.448037i	$0.852123\pi$
$578$	−26.2436			−1.09159
$579$		0			0
$580$	−4.64400	−	8.04364i	−0.192831	−	0.333994i
$581$		0			0
$582$		0			0
$583$	2.37085	+	4.10644i	0.0981908	+	0.170071i
$584$	−6.03273	−	10.4490i	−0.249636	−	0.432383i
$585$		0			0
$586$	−10.7101	+	18.5505i	−0.442432	+	0.766315i
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	−0.910404	−	0.413720i	$-0.864229\pi$
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	0.813494	+	0.581573i	$0.197563\pi$
$588$		0			0
$589$	−3.02654	−	5.24212i	−0.124706	−	0.215998i
$590$	−25.5636			−1.05244
$591$		0			0
$592$	2.77747			0.114153
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	−0.852671	−	0.522449i	$-0.825019\pi$
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	0.878789	+	0.477210i	$0.158352\pi$
$594$		0			0
$595$		0			0
$596$	0.166896	−	0.289073i	0.00683634	−	0.0118409i
$597$		0			0
$598$	8.48762	−	14.7010i	0.347085	−	0.601168i
$599$	21.9258	−	37.9766i	0.895864	−	1.55168i	0.0631320	−	0.998005i	$-0.479891\pi$
$599$	21.9258	−	37.9766i	0.895864	−	1.55168i	0.832732	−	0.553676i	$-0.186776\pi$
$600$		0			0
$601$	6.71634	−	11.6330i	0.273965	−	0.474522i	−0.695908	−	0.718131i	$-0.744998\pi$
$601$	6.71634	−	11.6330i	0.273965	−	0.474522i	0.969874	+	0.243609i	$0.0783314\pi$
$602$		0			0
$603$		0			0
$604$	9.95489	−	17.2424i	0.405059	−	0.701582i
$605$	−32.6240			−1.32635
$606$		0			0
$607$	4.58465			0.186085			0.0930425	−	0.995662i	$-0.470341\pi$
$607$	4.58465			0.186085			0.0930425	+	0.995662i	$0.470341\pi$
$608$	−0.444368	−	0.769668i	−0.0180215	−	0.0312142i
$609$		0			0
$610$	10.6051	−	18.3685i	0.429387	−	0.743720i
$611$	−9.43199	+	16.3367i	−0.381577	+	0.660911i
$612$		0			0
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$	2.84362	+	4.92530i	0.114759	+	0.198769i
$615$		0			0
$616$		0			0
$617$	−6.00433	−	10.3998i	−0.241725	−	0.418680i	0.719481	−	0.694513i	$-0.244380\pi$
$617$	−6.00433	−	10.3998i	−0.241725	−	0.418680i	−0.961206	+	0.275832i	$0.911047\pi$
$618$		0			0
$619$	17.5636			0.705941			0.352970	−	0.935634i	$-0.385172\pi$
$619$	17.5636			0.705941			0.352970	+	0.935634i	$0.385172\pi$
$620$	12.5989	+	21.8219i	0.505983	+	0.876389i
$621$		0			0
$622$	11.7207			0.469956
$623$		0			0
$624$		0			0
$625$	7.03204			0.281282
$626$	13.3869	−	23.1868i	0.535047	−	0.926729i
$627$		0			0
$628$	−3.48143	−	6.03001i	−0.138924	−	0.240624i
$629$	−18.2646			−0.728258
$630$		0			0
$631$	−44.9381			−1.78896			−0.894479	−	0.447110i	$-0.852453\pi$
$631$	−44.9381			−1.78896			−0.894479	+	0.447110i	$0.852453\pi$
$632$	5.72617	+	9.91802i	0.227775	+	0.394518i
$633$		0			0
$634$	−0.951246	+	1.64761i	−0.0377788	+	0.0654348i
$635$	−10.5687			−0.419406
$636$		0			0
$637$		0			0
$638$	−3.70829			−0.146813
$639$		0			0
$640$	1.84981	+	3.20397i	0.0731203	+	0.126648i
$641$	28.9839			1.14480			0.572398	−	0.819976i	$-0.306013\pi$
$641$	28.9839			1.14480			0.572398	+	0.819976i	$0.306013\pi$
$642$		0			0
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	0.722258	−	0.691623i	$-0.243104\pi$
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	−0.960093	+	0.279682i	$0.909771\pi$
$644$		0			0
$645$		0			0
$646$	2.92216	+	5.06132i	0.114971	+	0.199135i
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	0.951423	+	0.307887i	$0.0996219\pi$
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	−0.209073	+	0.977900i	$0.567045\pi$
$648$		0			0
$649$	−5.10322	+	8.83903i	−0.200319	+	0.346962i
$650$	−11.7262	+	20.3103i	−0.459938	+	0.796636i
$651$		0			0
$652$	4.03706	+	6.99240i	0.158104	+	0.273843i
$653$	−37.4079			−1.46388			−0.731942	−	0.681366i	$-0.761386\pi$
$653$	−37.4079			−1.46388			−0.731942	+	0.681366i	$0.761386\pi$
$654$		0			0
$655$	0.575984			0.0225056
$656$	−2.05563	+	3.56046i	−0.0802589	+	0.139013i
$657$		0			0
$658$		0			0
$659$	−14.9356	+	25.8693i	−0.581810	+	1.00772i	0.413455	+	0.910524i	$0.364322\pi$
$659$	−14.9356	+	25.8693i	−0.581810	+	1.00772i	−0.995265	+	0.0971993i	$0.969012\pi$
$660$		0			0
$661$	2.80401	−	4.85669i	0.109063	−	0.188904i	−0.806328	−	0.591469i	$-0.798548\pi$
$661$	2.80401	−	4.85669i	0.109063	−	0.188904i	0.915391	+	0.402566i	$0.131881\pi$
$662$	2.78366	−	4.82144i	0.108190	−	0.187391i
$663$		0			0
$664$	−2.23855	+	3.87728i	−0.0868726	+	0.150468i
$665$		0			0
$666$		0			0
$667$	7.89307	−	13.6712i	0.305621	−	0.529351i
$668$	−19.4858			−0.753927
$669$		0			0
$670$	35.0159			1.35278
$671$	−4.23414	−	7.33375i	−0.163457	−	0.283116i
$672$		0			0
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	−0.942575	−	0.333994i	$-0.891603\pi$
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$674$	16.8869	−	29.2489i	0.650458	−	1.12663i
$675$		0			0
$676$	2.85600	+	4.94674i	0.109846	+	0.190259i
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	0.739949	−	0.672663i	$-0.234850\pi$
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	−0.952518	+	0.304483i	$0.901516\pi$
$678$		0			0
$679$		0			0
$680$	−12.1643	−	21.0693i	−0.466481	−	0.807970i
$681$		0			0
$682$	10.0604			0.385231
$683$	4.41961	+	7.65499i	0.169112	+	0.292910i	0.938108	−	0.346343i	$-0.112577\pi$
$683$	4.41961	+	7.65499i	0.169112	+	0.292910i	−0.768996	+	0.639253i	$0.779243\pi$
$684$		0			0
$685$	12.6218			0.482254
$686$		0			0
$687$		0			0
$688$	−0.0123797			−0.000471972
$689$	−4.33310	+	7.50516i	−0.165078	+	0.285924i
$690$		0			0
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	0.999643	−	0.0267023i	$-0.00850061\pi$
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	−0.522947	+	0.852365i	$0.675167\pi$
$692$	22.5636			0.857740
$693$		0			0
$694$	−30.4065			−1.15422
$695$	24.9920	+	43.2873i	0.947999	+	1.64198i
$696$		0			0
$697$	13.5178	−	23.4135i	0.512023	−	0.886850i
$698$	12.5956			0.476752
$699$		0			0
$700$		0			0
$701$	43.4858			1.64243			0.821217	−	0.570616i	$-0.193295\pi$
$701$	43.4858			1.64243			0.821217	+	0.570616i	$0.193295\pi$
$702$		0			0
$703$	1.23422	+	2.13773i	0.0465495	+	0.0806260i
$704$	1.47710			0.0556703
$705$		0			0
$706$	−3.76578	−	6.52252i	−0.141727	−	0.245478i
$707$		0			0
$708$		0			0
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	0.996606	−	0.0823158i	$-0.0262316\pi$
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	−0.569591	+	0.821928i	$0.692898\pi$
$710$	10.1087	+	17.5088i	0.379373	+	0.657094i
$711$		0			0
$712$	4.43818	−	7.68715i	0.166328	−	0.288088i
$713$	−21.4134	+	37.0891i	−0.801939	+	1.38900i
$714$		0			0
$715$	7.37636	+	12.7762i	0.275860	+	0.477804i
$716$	0.333792			0.0124744
$717$		0			0
$718$	6.89602			0.257357
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	−0.730571	−	0.682836i	$-0.760746\pi$
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	0.956639	+	0.291275i	$0.0940796\pi$
$720$		0			0
$721$		0			0
$722$	−9.10507	+	15.7705i	−0.338856	+	0.586915i
$723$		0			0
$724$	11.6211	−	20.1283i	0.431895	−	0.748063i
$725$	−10.9048	+	18.8876i	−0.404993	+	0.701468i
$726$		0			0
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	0.0189562	+	0.999820i	$0.493966\pi$
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	−0.875348	+	0.483494i	$0.839368\pi$
$728$		0			0
$729$		0			0
$730$	−22.3189	+	38.6574i	−0.826058	+	1.43077i
$731$	0.0814088			0.00301101
$732$		0			0
$733$	36.0297			1.33079			0.665394	−	0.746493i	$-0.268264\pi$
$733$	36.0297			1.33079			0.665394	+	0.746493i	$0.268264\pi$
$734$	−11.5618	−	20.0257i	−0.426755	−	0.739161i
$735$		0			0
$736$	−3.14400	+	5.44556i	−0.115889	+	0.200726i
$737$	6.99017	−	12.1073i	0.257486	−	0.445979i
$738$		0			0
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	0.877694	+	0.479221i	$0.159081\pi$
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	−0.0238296	+	0.999716i	$0.507586\pi$
$740$	−5.13781	−	8.89894i	−0.188870	−	0.327132i
$741$		0			0
$742$		0			0
$743$	−0.598884	−	1.03730i	−0.0219709	−	0.0380548i	0.854831	−	0.518907i	$-0.173661\pi$
$743$	−0.598884	−	1.03730i	−0.0219709	−	0.0380548i	−0.876802	+	0.480852i	$0.840327\pi$
$744$		0			0
$745$	−1.23491			−0.0452435
$746$	14.5822	+	25.2571i	0.533891	+	0.924727i
$747$		0			0
$748$	−9.71339			−0.355157
$749$		0			0
$750$		0			0
$751$	48.1199			1.75592			0.877961	−	0.478733i	$-0.158904\pi$
$751$	48.1199			1.75592			0.877961	+	0.478733i	$0.158904\pi$
$752$	3.49381	−	6.05146i	0.127406	−	0.220674i
$753$		0			0
$754$	−3.38874	−	5.86946i	−0.123410	−	0.213753i
$755$	−73.6588			−2.68072
$756$		0			0
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$	−6.78111	−	11.7452i	−0.246301	−	0.426606i
$759$		0			0
$760$	−1.64400	+	2.84748i	−0.0596340	+	0.103289i
$761$	−37.5402			−1.36083			−0.680416	−	0.732826i	$-0.738201\pi$
$761$	−37.5402			−1.36083			−0.680416	+	0.732826i	$0.738201\pi$
$762$		0			0
$763$		0			0
$764$	16.3214			0.590488
$765$		0			0
$766$	−1.41783	−	2.45575i	−0.0512281	−	0.0887297i
$767$	−18.6538			−0.673551
$768$		0			0
$769$	13.4592	+	23.3121i	0.485352	+	0.840654i	0.999858	−	0.0168324i	$-0.00535818\pi$
$769$	13.4592	+	23.3121i	0.485352	+	0.840654i	−0.514506	+	0.857486i	$0.672025\pi$
$770$		0			0
$771$		0			0
$772$	7.16071	+	12.4027i	0.257719	+	0.446383i
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.823245	+	0.567687i	$0.192162\pi$
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.0800089	+	0.996794i	$0.474505\pi$
$774$		0			0
$775$	29.5840	−	51.2409i	1.06269	−	1.84063i
$776$	−6.58836	+	11.4114i	−0.236508	+	0.409645i
$777$		0			0
$778$	9.30401	+	16.1150i	0.333565	+	0.577752i
$779$	−3.65383			−0.130912
$780$		0			0
$781$	8.07194			0.288837
$782$	20.6749	−	35.8099i	0.739332	−	1.28056i
$783$		0			0
$784$		0			0
$785$	−12.8800	+	22.3088i	−0.459707	+	0.796236i
$786$		0			0
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	−0.880430	−	0.474176i	$-0.842746\pi$
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	0.850863	+	0.525387i	$0.176080\pi$
$788$	1.21201	−	2.09926i	0.0431760	−	0.0747830i
$789$		0			0
$790$	21.1847	−	36.6930i	0.753718	−	1.30548i
$791$		0			0
$792$		0			0
$793$	7.73855	−	13.4036i	0.274804	−	0.475974i
$794$	20.5760			0.730214
$795$		0			0
$796$	−6.11126			−0.216608
$797$	−15.3702	−	26.6219i	−0.544439	−	0.942996i	−0.998642	−	0.0520981i	$-0.983409\pi$
$797$	−15.3702	−	26.6219i	−0.544439	−	0.942996i	0.454203	−	0.890898i	$-0.349924\pi$
$798$		0			0
$799$	−22.9752	+	39.7943i	−0.812806	+	1.40782i
$800$	4.34362	−	7.52338i	0.153570	−	0.265992i
$801$		0			0
$802$	3.37704	+	5.84921i	0.119248	+	0.206543i
$803$	8.91095	+	15.4342i	0.314461	+	0.544662i
$804$		0			0
$805$		0			0
$806$	9.19344	+	15.9235i	0.323825	+	0.560881i
$807$		0			0
$808$	−5.25457			−0.184855
$809$	1.44251	+	2.49850i	0.0507159	+	0.0878425i	0.890269	−	0.455435i	$-0.150516\pi$
$809$	1.44251	+	2.49850i	0.0507159	+	0.0878425i	−0.839553	+	0.543278i	$0.817183\pi$
$810$		0			0
$811$	−28.5461			−1.00239			−0.501195	−	0.865334i	$-0.667106\pi$
$811$	−28.5461			−1.00239			−0.501195	+	0.865334i	$0.667106\pi$
$812$		0			0
$813$		0			0
$814$	−4.10260			−0.143796
$815$	14.9356	−	25.8693i	0.523172	−	0.906161i
$816$		0			0
$817$	−0.00550115	−	0.00952827i	−0.000192461	−	0.000333352i
$818$	15.3214			0.535701
$819$		0			0
$820$	15.2101			0.531161
$821$	3.98329	+	6.89926i	0.139018	+	0.240786i	0.927125	−	0.374752i	$-0.122272\pi$
$821$	3.98329	+	6.89926i	0.139018	+	0.240786i	−0.788107	+	0.615538i	$0.788939\pi$
$822$		0			0
$823$	−20.2731	+	35.1140i	−0.706675	+	1.22400i	0.259409	+	0.965768i	$0.416472\pi$
$823$	−20.2731	+	35.1140i	−0.706675	+	1.22400i	−0.966084	+	0.258229i	$0.916861\pi$
$824$	1.66621			0.0580451
$825$		0			0
$826$		0			0
$827$	−1.22115			−0.0424636			−0.0212318	−	0.999775i	$-0.506759\pi$
$827$	−1.22115			−0.0424636			−0.0212318	+	0.999775i	$0.506759\pi$
$828$		0			0
$829$	7.07530	+	12.2548i	0.245735	+	0.425626i	0.962338	−	0.271856i	$-0.0876373\pi$
$829$	7.07530	+	12.2548i	0.245735	+	0.425626i	−0.716603	+	0.697481i	$0.754304\pi$
$830$	16.5636			0.574931
$831$		0			0
$832$	1.34981	+	2.33795i	0.0467964	+	0.0810537i
$833$		0			0
$834$		0			0
$835$	36.0450	+	62.4318i	1.24739	+	2.16054i
$836$	0.656376	+	1.13688i	0.0227012	+	0.0393197i
$837$		0			0
$838$	4.32141	−	7.48491i	0.149281	−	0.258562i
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	−0.844642	−	0.535332i	$-0.820187\pi$
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	0.885932	+	0.463815i	$0.153520\pi$
$840$		0			0
$841$	11.3486	+	19.6564i	0.391333	+	0.677808i
$842$	37.1272			1.27949
$843$		0			0
$844$	−11.4451			−0.393955
$845$	10.5662	−	18.3011i	0.363487	−	0.629577i
$846$		0			0
$847$		0			0
$848$	1.60507	−	2.78007i	0.0551185	−	0.0954680i
$849$		0			0
$850$	−28.5636	+	49.4736i	−0.979724	+	1.69693i
$851$	8.73236	−	15.1249i	0.299341	−	0.518475i
$852$		0			0
$853$	8.33998	−	14.4453i	0.285556	−	0.494597i	−0.687188	−	0.726479i	$-0.741155\pi$
$853$	8.33998	−	14.4453i	0.285556	−	0.494597i	0.972744	+	0.231883i	$0.0744886\pi$
$854$		0			0
$855$		0			0
$856$	−5.38255	+	9.32284i	−0.183972	+	0.318648i
$857$	−13.8516			−0.473162			−0.236581	−	0.971612i	$-0.576027\pi$
$857$	−13.8516			−0.473162			−0.236581	+	0.971612i	$0.576027\pi$
$858$		0			0
$859$	−48.4944			−1.65461			−0.827304	−	0.561754i	$-0.810127\pi$
$859$	−48.4944			−1.65461			−0.827304	+	0.561754i	$0.810127\pi$
$860$	0.0229002	+	0.0396643i	0.000780889	+	0.00135254i
$861$		0			0
$862$	−4.71015	+	8.15822i	−0.160428	+	0.277870i
$863$	−2.96541	+	5.13624i	−0.100944	+	0.174840i	−0.912074	−	0.410026i	$-0.865520\pi$
$863$	−2.96541	+	5.13624i	−0.100944	+	0.174840i	0.811130	+	0.584866i	$0.198853\pi$
$864$		0			0
$865$	−41.7385	−	72.2932i	−1.41915	−	2.45804i
$866$	0.104386	+	0.180801i	0.00354717	+	0.00614387i
$867$		0			0
$868$		0			0
$869$	−8.45813	−	14.6499i	−0.286922	−	0.496964i
$870$		0			0
$871$	25.5512			0.865770
$872$	0.0945538	+	0.163772i	0.00320200	+	0.00554602i
$873$		0			0
$874$	−5.58836			−0.189029
$875$		0			0
$876$		0			0
$877$	3.92944			0.132688			0.0663439	−	0.997797i	$-0.478867\pi$
$877$	3.92944			0.132688			0.0663439	+	0.997797i	$0.478867\pi$
$878$	4.98398	−	8.63250i	0.168201	−	0.291333i
$879$		0			0
$880$	−2.73236	−	4.73259i	−0.0921078	−	0.159535i
$881$	37.6552			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$881$	37.6552			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$882$		0			0
$883$	−53.2334			−1.79145			−0.895723	−	0.444613i	$-0.853341\pi$
$883$	−53.2334			−1.79145			−0.895723	+	0.444613i	$0.853341\pi$
$884$	−8.87636	−	15.3743i	−0.298544	−	0.517094i
$885$		0			0
$886$	7.84981	−	13.5963i	0.263720	−	0.456776i
$887$	−36.9876			−1.24192			−0.620961	−	0.783841i	$-0.713258\pi$
$887$	−36.9876			−1.24192			−0.620961	+	0.783841i	$0.713258\pi$
$888$		0			0
$889$		0			0
$890$	−32.8392			−1.10077
$891$		0			0
$892$	3.61126	+	6.25489i	0.120914	+	0.209429i
$893$	6.21015			0.207815
$894$		0			0
$895$	−0.617454	−	1.06946i	−0.0206392	−	0.0357482i
$896$		0			0
$897$		0			0
$898$	−16.8127	−	29.1204i	−0.561046	−	0.971761i
$899$	8.54944	+	14.8081i	0.285140	+	0.493877i
$900$		0			0
$901$	−10.5549	+	18.2817i	−0.351636	+	0.609052i
$902$	3.03637	−	5.25915i	0.101100	−	0.175111i
$903$		0			0
$904$	−6.78180	−	11.7464i	−0.225559	−	0.390680i
$905$	−85.9875			−2.85832
$906$		0			0
$907$	−39.0159			−1.29550			−0.647752	−	0.761852i	$-0.724291\pi$
$907$	−39.0159			−1.29550			−0.647752	+	0.761852i	$0.724291\pi$
$908$	−6.82760	+	11.8258i	−0.226582	+	0.392451i
$909$		0			0
$910$		0			0
$911$	12.8090	−	22.1859i	0.424382	−	0.735052i	−0.571980	−	0.820267i	$-0.693825\pi$
$911$	12.8090	−	22.1859i	0.424382	−	0.735052i	0.996363	+	0.0852158i	$0.0271580\pi$
$912$		0			0
$913$	3.30656	−	5.72713i	0.109431	−	0.189540i
$914$	16.3541	−	28.3262i	0.540947	−	0.936948i
$915$		0			0
$916$	8.68725	−	15.0468i	0.287035	−	0.497159i
$917$		0			0
$918$		0			0
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	−0.643637	−	0.765331i	$-0.722575\pi$
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	0.984615	+	0.174740i	$0.0559086\pi$
$920$	23.2632			0.766966
$921$		0			0
$922$	−4.14331			−0.136453
$923$	7.37636	+	12.7762i	0.242796	+	0.420535i
$924$		0			0
$925$	−12.0643	+	20.8960i	−0.396672	+	0.687055i
$926$	8.34176	−	14.4484i	0.274127	−	0.474803i
$927$		0			0
$928$	1.25526	+	2.17417i	0.0412059	+	0.0713708i
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	0.895073	−	0.445920i	$-0.147123\pi$
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	−0.833715	+	0.552196i	$0.813790\pi$
$930$		0			0
$931$		0			0
$932$	−7.62110	−	13.2001i	−0.249637	−	0.432384i
$933$		0			0
$934$	29.9171			0.978916
$935$	17.9680	+	31.1214i	0.587615	+	1.01778i
$936$		0			0
$937$	27.1345			0.886445			0.443223	−	0.896412i	$-0.353835\pi$
$937$	27.1345			0.886445			0.443223	+	0.896412i	$0.353835\pi$
$938$		0			0
$939$		0			0
$940$	−25.8516			−0.843186
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	−0.912983	−	0.407998i	$-0.866227\pi$
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	0.809828	+	0.586667i	$0.199560\pi$
$942$		0			0
$943$	12.9258	+	22.3881i	0.420922	+	0.729058i
$944$	6.90978			0.224894
$945$		0			0
$946$	0.0182861			0.000594531
$947$	15.6396	+	27.0886i	0.508218	+	0.880260i	0.999955	+	0.00951587i	$0.00302904\pi$
$947$	15.6396	+	27.0886i	0.508218	+	0.880260i	−0.491736	+	0.870744i	$0.663638\pi$
$948$		0			0
$949$	−16.2861	+	28.2084i	−0.528670	+	0.915684i
$950$	7.72067			0.250492
$951$		0			0
$952$		0			0
$953$	−4.28937			−0.138946			−0.0694732	−	0.997584i	$-0.522132\pi$
$953$	−4.28937			−0.138946			−0.0694732	+	0.997584i	$0.522132\pi$
$954$		0			0
$955$	−30.1916	−	52.2933i	−0.976977	−	1.69217i
$956$	18.9505			0.612902
$957$		0			0
$958$	−1.47965	−	2.56283i	−0.0478053	−	0.0828011i
$959$		0			0
$960$		0			0
$961$	−7.69413	−	13.3266i	−0.248198	−	0.429891i
$962$	−3.74907	−	6.49358i	−0.120875	−	0.209361i
$963$		0			0
$964$	−12.2527	+	21.2223i	−0.394633	+	0.683525i
$965$	26.4920	−	45.8854i	0.852806	−	1.47710i
$966$		0			0
$967$	−7.59201	−	13.1497i	−0.244142	−	0.422867i	0.717748	−	0.696303i	$-0.245173\pi$
$967$	−7.59201	−	13.1497i	−0.244142	−	0.422867i	−0.961890	+	0.273436i	$0.911840\pi$
$968$	8.81818			0.283427
$969$		0			0
$970$	48.7490			1.56524
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	−0.838796	−	0.544445i	$-0.816740\pi$
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	0.890902	+	0.454196i	$0.150074\pi$
$972$		0			0
$973$		0			0
$974$	14.0309	−	24.3022i	0.449578	−	0.778692i
$975$		0			0
$976$	−2.86652	+	4.96497i	−0.0917552	+	0.158925i
$977$	7.77197	−	13.4614i	0.248647	−	0.430670i	−0.714503	−	0.699632i	$-0.753347\pi$
$977$	7.77197	−	13.4614i	0.248647	−	0.430670i	0.963151	+	0.268962i	$0.0866806\pi$
$978$		0			0
$979$	−6.55563	+	11.3547i	−0.209519	+	0.362897i
$980$		0			0
$981$		0			0
$982$	17.0734	−	29.5721i	0.544835	−	0.943682i
$983$	12.3832			0.394961			0.197481	−	0.980307i	$-0.436724\pi$
$983$	12.3832			0.394961			0.197481	+	0.980307i	$0.436724\pi$
$984$		0			0
$985$	−8.96796			−0.285743
$986$	−8.25457	−	14.2973i	−0.262879	−	0.455320i
$987$		0			0
$988$	−1.19963	+	2.07782i	−0.0381653	+	0.0661042i
$989$	−0.0389218	+	0.0674145i	−0.00123764	+	0.00214366i
$990$		0			0
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	0.808321	−	0.588742i	$-0.200377\pi$
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	−0.914026	+	0.405656i	$0.867043\pi$
$992$	−3.40545	−	5.89841i	−0.108123	−	0.187275i
$993$		0			0
$994$		0			0
$995$	11.3047	+	19.5803i	0.358383	+	0.620738i
$996$		0			0
$997$	−4.80208			−0.152083			−0.0760417	−	0.997105i	$-0.524228\pi$
$997$	−4.80208			−0.152083			−0.0760417	+	0.997105i	$0.524228\pi$
$998$	−1.14035	−	1.97515i	−0.0360973	−	0.0625223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.p.667.3		6
3.2	odd	2		882.2.h.o.79.3		6
7.2	even	3		2646.2.f.n.883.1		6
7.3	odd	6		378.2.e.c.235.3		6
7.4	even	3		2646.2.e.o.2125.1		6
7.5	odd	6		2646.2.f.o.883.3		6
7.6	odd	2		378.2.h.d.289.1		6
9.4	even	3		2646.2.e.o.1549.1		6
9.5	odd	6		882.2.e.p.373.3		6
21.2	odd	6		882.2.f.m.295.1		6
21.5	even	6		882.2.f.l.295.3		6
21.11	odd	6		882.2.e.p.655.3		6
21.17	even	6		126.2.e.d.25.1	✓	6
21.20	even	2		126.2.h.c.79.1	yes	6
28.3	even	6		3024.2.q.h.2881.3		6
28.27	even	2		3024.2.t.g.289.1		6
63.2	odd	6		7938.2.a.by.1.1		3
63.4	even	3	inner	2646.2.h.p.361.3		6
63.5	even	6		882.2.f.l.589.3		6
63.13	odd	6		378.2.e.c.37.3		6
63.16	even	3		7938.2.a.bx.1.3		3
63.20	even	6		1134.2.g.k.163.1		6
63.23	odd	6		882.2.f.m.589.1		6
63.31	odd	6		378.2.h.d.361.1		6
63.32	odd	6		882.2.h.o.67.3		6
63.34	odd	6		1134.2.g.n.163.3		6
63.38	even	6		1134.2.g.k.487.1		6
63.40	odd	6		2646.2.f.o.1765.3		6
63.41	even	6		126.2.e.d.121.1	yes	6
63.47	even	6		7938.2.a.cb.1.3		3
63.52	odd	6		1134.2.g.n.487.3		6
63.58	even	3		2646.2.f.n.1765.1		6
63.59	even	6		126.2.h.c.67.1	yes	6
63.61	odd	6		7938.2.a.bu.1.1		3
84.59	odd	6		1008.2.q.h.529.3		6
84.83	odd	2		1008.2.t.g.961.3		6
252.31	even	6		3024.2.t.g.1873.1		6
252.59	odd	6		1008.2.t.g.193.3		6
252.139	even	6		3024.2.q.h.2305.3		6
252.167	odd	6		1008.2.q.h.625.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	21.17	even	6
126.2.e.d.121.1	yes	6	63.41	even	6
126.2.h.c.67.1	yes	6	63.59	even	6
126.2.h.c.79.1	yes	6	21.20	even	2
378.2.e.c.37.3		6	63.13	odd	6
378.2.e.c.235.3		6	7.3	odd	6
378.2.h.d.289.1		6	7.6	odd	2
378.2.h.d.361.1		6	63.31	odd	6
882.2.e.p.373.3		6	9.5	odd	6
882.2.e.p.655.3		6	21.11	odd	6
882.2.f.l.295.3		6	21.5	even	6
882.2.f.l.589.3		6	63.5	even	6
882.2.f.m.295.1		6	21.2	odd	6
882.2.f.m.589.1		6	63.23	odd	6
882.2.h.o.67.3		6	63.32	odd	6
882.2.h.o.79.3		6	3.2	odd	2
1008.2.q.h.529.3		6	84.59	odd	6
1008.2.q.h.625.3		6	252.167	odd	6
1008.2.t.g.193.3		6	252.59	odd	6
1008.2.t.g.961.3		6	84.83	odd	2
1134.2.g.k.163.1		6	63.20	even	6
1134.2.g.k.487.1		6	63.38	even	6
1134.2.g.n.163.3		6	63.34	odd	6
1134.2.g.n.487.3		6	63.52	odd	6
2646.2.e.o.1549.1		6	9.4	even	3
2646.2.e.o.2125.1		6	7.4	even	3
2646.2.f.n.883.1		6	7.2	even	3
2646.2.f.n.1765.1		6	63.58	even	3
2646.2.f.o.883.3		6	7.5	odd	6
2646.2.f.o.1765.3		6	63.40	odd	6
2646.2.h.p.361.3		6	63.4	even	3	inner
2646.2.h.p.667.3		6	1.1	even	1	trivial
3024.2.q.h.2305.3		6	252.139	even	6
3024.2.q.h.2881.3		6	28.3	even	6
3024.2.t.g.289.1		6	28.27	even	2
3024.2.t.g.1873.1		6	252.31	even	6
7938.2.a.bu.1.1		3	63.61	odd	6
7938.2.a.bx.1.3		3	63.16	even	3
7938.2.a.by.1.1		3	63.2	odd	6
7938.2.a.cb.1.3		3	63.47	even	6

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} -1.00000 q^{8} +(1.84981 + 3.20397i) q^{10} +1.47710 q^{11} +(1.34981 + 2.33795i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.28799 + 5.69497i) q^{17} +(0.444368 - 0.769668i) q^{19} +(-1.84981 + 3.20397i) q^{20} +(0.738550 + 1.27921i) q^{22} -6.28799 q^{23} +8.68725 q^{25} +(-1.34981 + 2.33795i) q^{26} +(-1.25526 + 2.17417i) q^{29} +(3.40545 - 5.89841i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.28799 + 5.69497i) q^{34} +(-1.38874 + 2.40536i) q^{37} +0.888736 q^{38} -3.69963 q^{40} +(-2.05563 - 3.56046i) q^{41} +(0.00618986 - 0.0107211i) q^{43} +(-0.738550 + 1.27921i) q^{44} +(-3.14400 - 5.44556i) q^{46} +(3.49381 + 6.05146i) q^{47} +(4.34362 + 7.52338i) q^{50} -2.69963 q^{52} +(1.60507 + 2.78007i) q^{53} +5.46472 q^{55} -2.51052 q^{58} +(-3.45489 + 5.98404i) q^{59} +(-2.86652 - 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(4.99381 + 8.64953i) q^{65} +(4.73236 - 8.19669i) q^{67} -6.57598 q^{68} +5.46472 q^{71} +(6.03273 + 10.4490i) q^{73} -2.77747 q^{74} +(0.444368 + 0.769668i) q^{76} +(-5.72617 - 9.91802i) q^{79} +(-1.84981 - 3.20397i) q^{80} +(2.05563 - 3.56046i) q^{82} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +0.0123797 q^{86} -1.47710 q^{88} +(-4.43818 + 7.68715i) q^{89} +(3.14400 - 5.44556i) q^{92} +(-3.49381 + 6.05146i) q^{94} +(1.64400 - 2.84748i) q^{95} +(6.58836 - 11.4114i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} - 9 q^{37} + 6 q^{38} - 10 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 3 q^{47} + 2 q^{50} - 4 q^{52} - 9 q^{53} - 14 q^{55} + 10 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} + 8 q^{68} - 14 q^{71} + 25 q^{73} - 18 q^{74} + 3 q^{76} + 7 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} - 9 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8 + 5 * q^10 - 2 * q^11 + 2 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 - 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 - 2 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 - 9 * q^37 + 6 * q^38 - 10 * q^40 - 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 3 * q^47 + 2 * q^50 - 4 * q^52 - 9 * q^53 - 14 * q^55 + 10 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 + 8 * q^68 - 14 * q^71 + 25 * q^73 - 18 * q^74 + 3 * q^76 + 7 * q^79 - 5 * q^80 + 12 * q^82 + 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 - 9 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Introduction

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