LMFDB - Embedded newform 504.2.r.d.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.4
Root			$-0.577806 - 2.22188i$ of defining polynomial
Character	$\chi$	$=$	504.169
Dual form			504.2.r.d.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71311 + 0.255482i) q^{3} +(1.81197 + 3.13842i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.86946 + 0.875335i) q^{9} +O(q^{10})$	\(q+(1.71311 + 0.255482i) q^{3} +(1.81197 + 3.13842i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.86946 + 0.875335i) q^{9} +(-1.95863 + 3.39245i) q^{11} +(-2.53644 - 4.39324i) q^{13} +(2.30228 + 5.83936i) q^{15} +1.03225 q^{17} -2.50895 q^{19} +(-1.07781 + 1.35585i) q^{21} +(-2.47895 - 4.29366i) q^{23} +(-4.06644 + 7.04328i) q^{25} +(4.69205 + 2.23263i) q^{27} +(4.60288 - 7.97242i) q^{29} +(0.422194 + 0.731261i) q^{31} +(-4.22205 + 5.31123i) q^{33} -3.62393 q^{35} +4.84439 q^{37} +(-3.22279 - 8.17410i) q^{39} +(2.07362 + 3.59161i) q^{41} +(2.20174 - 3.81352i) q^{43} +(2.45219 + 10.5916i) q^{45} +(3.93758 - 6.82008i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(1.76835 + 0.263721i) q^{51} +12.2786 q^{53} -14.1959 q^{55} +(-4.29809 - 0.640990i) q^{57} +(5.60288 + 9.70447i) q^{59} +(-0.208348 + 0.360870i) q^{61} +(-2.19279 + 2.04736i) q^{63} +(9.19188 - 15.9208i) q^{65} +(-5.02507 - 8.70368i) q^{67} +(-3.14974 - 7.98882i) q^{69} -5.05162 q^{71} +7.20723 q^{73} +(-8.76567 + 11.0270i) q^{75} +(-1.95863 - 3.39245i) q^{77} +(-7.56570 + 13.1042i) q^{79} +(7.46758 + 5.02347i) q^{81} +(-0.932821 + 1.61569i) q^{83} +(1.87040 + 3.23963i) q^{85} +(9.92202 - 12.4816i) q^{87} -0.669401 q^{89} +5.07288 q^{91} +(0.536438 + 1.36059i) q^{93} +(-4.54612 - 7.87412i) q^{95} +(-7.63513 + 13.2244i) q^{97} +(-8.58974 + 8.02003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9	$ 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{15} - 16 q^{17} - 4 q^{19} - q^{21} - 5 q^{23} - 14 q^{25} + 5 q^{27} + q^{29} + 11 q^{31} - 8 q^{35} + 54 q^{37} - 12 q^{39} + 2 q^{41} - 11 q^{43} + 26 q^{45} + 7 q^{47} - 4 q^{49} + 17 q^{51} - 8 q^{53} + 12 q^{55} - 13 q^{57} + 9 q^{59} - 7 q^{61} - 5 q^{63} - 9 q^{65} - 12 q^{67} + 4 q^{69} - 24 q^{71} + 26 q^{73} - 23 q^{75} - 6 q^{77} - 22 q^{79} + 34 q^{81} - 6 q^{83} - 11 q^{85} + 37 q^{87} - 28 q^{89} + 6 q^{91} - 13 q^{93} - 23 q^{95} - q^{97} - 42 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9 - 6 * q^11 - 3 * q^13 + 4 * q^15 - 16 * q^17 - 4 * q^19 - q^21 - 5 * q^23 - 14 * q^25 + 5 * q^27 + q^29 + 11 * q^31 - 8 * q^35 + 54 * q^37 - 12 * q^39 + 2 * q^41 - 11 * q^43 + 26 * q^45 + 7 * q^47 - 4 * q^49 + 17 * q^51 - 8 * q^53 + 12 * q^55 - 13 * q^57 + 9 * q^59 - 7 * q^61 - 5 * q^63 - 9 * q^65 - 12 * q^67 + 4 * q^69 - 24 * q^71 + 26 * q^73 - 23 * q^75 - 6 * q^77 - 22 * q^79 + 34 * q^81 - 6 * q^83 - 11 * q^85 + 37 * q^87 - 28 * q^89 + 6 * q^91 - 13 * q^93 - 23 * q^95 - q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.71311	+	0.255482i	0.989062	+	0.147503i
$3$	1.71311	+	0.255482i	0.989062	+	0.147503i
$4$		0			0
$5$	1.81197	+	3.13842i	0.810336	+	1.40354i	0.912629	+	0.408788i	$0.134049\pi$
$5$	1.81197	+	3.13842i	0.810336	+	1.40354i	−0.102294	+	0.994754i	$0.532618\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	2.86946	+	0.875335i	0.956486	+	0.291778i
$10$		0			0
$11$	−1.95863	+	3.39245i	−0.590550	+	1.02286i	0.403609	+	0.914932i	$0.367756\pi$
$11$	−1.95863	+	3.39245i	−0.590550	+	1.02286i	−0.994158	+	0.107930i	$0.965578\pi$
$12$		0			0
$13$	−2.53644	−	4.39324i	−0.703481	−	1.21847i	−0.967237	−	0.253876i	$-0.918295\pi$
$13$	−2.53644	−	4.39324i	−0.703481	−	1.21847i	0.263755	−	0.964590i	$-0.415039\pi$
$14$		0			0
$15$	2.30228	+	5.83936i	0.594446	+	1.50772i
$16$		0			0
$17$	1.03225			0.250357			0.125178	−	0.992134i	$-0.460050\pi$
$17$	1.03225			0.250357			0.125178	+	0.992134i	$0.460050\pi$
$18$		0			0
$19$	−2.50895			−0.575592			−0.287796	−	0.957692i	$-0.592922\pi$
$19$	−2.50895			−0.575592			−0.287796	+	0.957692i	$0.592922\pi$
$20$		0			0
$21$	−1.07781	+	1.35585i	−0.235197	+	0.295871i
$22$		0			0
$23$	−2.47895	−	4.29366i	−0.516896	−	0.895290i	−0.999807	−	0.0196209i	$-0.993754\pi$
$23$	−2.47895	−	4.29366i	−0.516896	−	0.895290i	0.482912	−	0.875669i	$-0.339579\pi$
$24$		0			0
$25$	−4.06644	+	7.04328i	−0.813288	+	1.40866i
$26$		0			0
$27$	4.69205	+	2.23263i	0.902986	+	0.429671i
$28$		0			0
$29$	4.60288	−	7.97242i	0.854733	−	1.48044i	−0.0221599	−	0.999754i	$-0.507054\pi$
$29$	4.60288	−	7.97242i	0.854733	−	1.48044i	0.876893	−	0.480686i	$-0.159612\pi$
$30$		0			0
$31$	0.422194	+	0.731261i	0.0758282	+	0.131338i	0.901446	−	0.432891i	$-0.142507\pi$
$31$	0.422194	+	0.731261i	0.0758282	+	0.131338i	−0.825618	+	0.564230i	$0.809173\pi$
$32$		0			0
$33$	−4.22205	+	5.31123i	−0.734965	+	0.924566i
$34$		0			0
$35$	−3.62393			−0.612556
$36$		0			0
$37$	4.84439			0.796412			0.398206	−	0.917296i	$-0.369633\pi$
$37$	4.84439			0.796412			0.398206	+	0.917296i	$0.369633\pi$
$38$		0			0
$39$	−3.22279	−	8.17410i	−0.516060	−	1.30890i
$40$		0			0
$41$	2.07362	+	3.59161i	0.323844	+	0.560915i	0.981278	−	0.192598i	$-0.0616912\pi$
$41$	2.07362	+	3.59161i	0.323844	+	0.560915i	−0.657433	+	0.753513i	$0.728358\pi$
$42$		0			0
$43$	2.20174	−	3.81352i	0.335762	−	0.581557i	−0.647869	−	0.761752i	$-0.724340\pi$
$43$	2.20174	−	3.81352i	0.335762	−	0.581557i	0.983631	+	0.180195i	$0.0576729\pi$
$44$		0			0
$45$	2.45219	+	10.5916i	0.365552	+	1.57891i
$46$		0			0
$47$	3.93758	−	6.82008i	0.574355	−	0.994812i	−0.421757	−	0.906709i	$-0.638586\pi$
$47$	3.93758	−	6.82008i	0.574355	−	0.994812i	0.996111	−	0.0881025i	$-0.0280803\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	1.76835	+	0.263721i	0.247619	+	0.0369283i
$52$		0			0
$53$	12.2786			1.68660			0.843300	−	0.537443i	$-0.180610\pi$
$53$	12.2786			1.68660			0.843300	+	0.537443i	$0.180610\pi$
$54$		0			0
$55$	−14.1959			−1.91417
$56$		0			0
$57$	−4.29809	−	0.640990i	−0.569296	−	0.0849013i
$58$		0			0
$59$	5.60288	+	9.70447i	0.729432	+	1.26341i	0.957123	+	0.289681i	$0.0935491\pi$
$59$	5.60288	+	9.70447i	0.729432	+	1.26341i	−0.227691	+	0.973733i	$0.573118\pi$
$60$		0			0
$61$	−0.208348	+	0.360870i	−0.0266763	+	0.0462047i	−0.879055	−	0.476720i	$-0.841826\pi$
$61$	−0.208348	+	0.360870i	−0.0266763	+	0.0462047i	0.852379	+	0.522924i	$0.175159\pi$
$62$		0			0
$63$	−2.19279	+	2.04736i	−0.276266	+	0.257943i
$64$		0			0
$65$	9.19188	−	15.9208i	1.14011	−	1.97473i
$66$		0			0
$67$	−5.02507	−	8.70368i	−0.613910	−	1.06332i	−0.990575	−	0.136974i	$-0.956262\pi$
$67$	−5.02507	−	8.70368i	−0.613910	−	1.06332i	0.376665	−	0.926350i	$-0.377071\pi$
$68$		0			0
$69$	−3.14974	−	7.98882i	−0.379184	−	0.961741i
$70$		0			0
$71$	−5.05162			−0.599517			−0.299759	−	0.954015i	$-0.596906\pi$
$71$	−5.05162			−0.599517			−0.299759	+	0.954015i	$0.596906\pi$
$72$		0			0
$73$	7.20723			0.843543			0.421771	−	0.906702i	$-0.361408\pi$
$73$	7.20723			0.843543			0.421771	+	0.906702i	$0.361408\pi$
$74$		0			0
$75$	−8.76567	+	11.0270i	−1.01217	+	1.27329i
$76$		0			0
$77$	−1.95863	−	3.39245i	−0.223207	−	0.386606i
$78$		0			0
$79$	−7.56570	+	13.1042i	−0.851208	+	1.47433i	0.0289116	+	0.999582i	$0.490796\pi$
$79$	−7.56570	+	13.1042i	−0.851208	+	1.47433i	−0.880119	+	0.474753i	$0.842537\pi$
$80$		0			0
$81$	7.46758	+	5.02347i	0.829731	+	0.558164i
$82$		0			0
$83$	−0.932821	+	1.61569i	−0.102390	+	0.177345i	−0.912669	−	0.408699i	$-0.865982\pi$
$83$	−0.932821	+	1.61569i	−0.102390	+	0.177345i	0.810279	+	0.586045i	$0.199316\pi$
$84$		0			0
$85$	1.87040	+	3.23963i	0.202873	+	0.351387i
$86$		0			0
$87$	9.92202	−	12.4816i	1.06375	−	1.33817i
$88$		0			0
$89$	−0.669401			−0.0709564			−0.0354782	−	0.999370i	$-0.511295\pi$
$89$	−0.669401			−0.0709564			−0.0354782	+	0.999370i	$0.511295\pi$
$90$		0			0
$91$	5.07288			0.531782
$92$		0			0
$93$	0.536438	+	1.36059i	0.0556260	+	0.141087i
$94$		0			0
$95$	−4.54612	−	7.87412i	−0.466423	−	0.807868i
$96$		0			0
$97$	−7.63513	+	13.2244i	−0.775230	+	1.34274i	0.159436	+	0.987208i	$0.449032\pi$
$97$	−7.63513	+	13.2244i	−0.775230	+	1.34274i	−0.934665	+	0.355529i	$0.884301\pi$
$98$		0			0
$99$	−8.58974	+	8.02003i	−0.863301	+	0.806044i
$100$		0			0
$101$	5.87840	−	10.1817i	0.584923	−	1.01312i	−0.409962	−	0.912103i	$-0.634458\pi$
$101$	5.87840	−	10.1817i	0.584923	−	1.01312i	0.994885	−	0.101014i	$-0.0322087\pi$
$102$		0			0
$103$	−5.51538	−	9.55293i	−0.543447	−	0.941278i	−0.998703	−	0.0509171i	$-0.983786\pi$
$103$	−5.51538	−	9.55293i	−0.543447	−	0.941278i	0.455256	−	0.890361i	$-0.349548\pi$
$104$		0			0
$105$	−6.20818	−	0.925849i	−0.605856	−	0.0903536i
$106$		0			0
$107$	−0.842907			−0.0814869			−0.0407434	−	0.999170i	$-0.512973\pi$
$107$	−0.842907			−0.0814869			−0.0407434	+	0.999170i	$0.512973\pi$
$108$		0			0
$109$	−17.1875			−1.64627			−0.823133	−	0.567849i	$-0.807776\pi$
$109$	−17.1875			−1.64627			−0.823133	+	0.567849i	$0.807776\pi$
$110$		0			0
$111$	8.29894	+	1.23765i	0.787701	+	0.117473i
$112$		0			0
$113$	−4.54538	−	7.87284i	−0.427594	−	0.740614i	0.569065	−	0.822293i	$-0.307305\pi$
$113$	−4.54538	−	7.87284i	−0.427594	−	0.740614i	−0.996659	+	0.0816784i	$0.973972\pi$
$114$		0			0
$115$	8.98353	−	15.5599i	0.837718	−	1.45097i
$116$		0			0
$117$	−3.43265	−	14.8264i	−0.317348	−	1.37071i
$118$		0			0
$119$	−0.516124	+	0.893953i	−0.0473130	+	0.0819486i
$120$		0			0
$121$	−2.17248	−	3.76284i	−0.197498	−	0.342076i
$122$		0			0
$123$	2.63473	+	6.68258i	0.237566	+	0.602548i
$124$		0			0
$125$	−11.3533			−1.01547
$126$		0			0
$127$	−14.4859			−1.28541			−0.642706	−	0.766113i	$-0.722188\pi$
$127$	−14.4859			−1.28541			−0.642706	+	0.766113i	$0.722188\pi$
$128$		0			0
$129$	4.74609	−	5.97046i	0.417870	−	0.525670i
$130$		0			0
$131$	−4.03476	−	6.98840i	−0.352518	−	0.610580i	0.634172	−	0.773192i	$-0.281341\pi$
$131$	−4.03476	−	6.98840i	−0.352518	−	0.610580i	−0.986690	+	0.162613i	$0.948008\pi$
$132$		0			0
$133$	1.25447	−	2.17281i	0.108777	−	0.188407i
$134$		0			0
$135$	1.49490	+	18.7711i	0.128660	+	1.61556i
$136$		0			0
$137$	−9.85792	+	17.0744i	−0.842219	+	1.45877i	0.0457961	+	0.998951i	$0.485418\pi$
$137$	−9.85792	+	17.0744i	−0.842219	+	1.45877i	−0.888015	+	0.459815i	$0.847916\pi$
$138$		0			0
$139$	−8.35960	−	14.4792i	−0.709052	−	1.22811i	−0.965209	−	0.261479i	$-0.915790\pi$
$139$	−8.35960	−	14.4792i	−0.709052	−	1.22811i	0.256157	−	0.966635i	$-0.417543\pi$
$140$		0			0
$141$	8.48789	−	10.6775i	0.714809	−	0.899211i
$142$		0			0
$143$	19.8718			1.66176
$144$		0			0
$145$	33.3610			2.77048
$146$		0			0
$147$	−0.635299	−	1.61133i	−0.0523986	−	0.132901i
$148$		0			0
$149$	−9.16439	−	15.8732i	−0.750776	−	1.30038i	−0.947447	−	0.319912i	$-0.896347\pi$
$149$	−9.16439	−	15.8732i	−0.750776	−	1.30038i	0.196671	−	0.980469i	$-0.436987\pi$
$150$		0			0
$151$	7.23100	−	12.5245i	0.588450	−	1.01923i	−0.405985	−	0.913880i	$-0.633072\pi$
$151$	7.23100	−	12.5245i	0.588450	−	1.01923i	0.994436	−	0.105346i	$-0.0335951\pi$
$152$		0			0
$153$	2.96199	+	0.903563i	0.239463	+	0.0730487i
$154$		0			0
$155$	−1.53000	+	2.65004i	−0.122893	+	0.212856i
$156$		0			0
$157$	−1.92387	−	3.33225i	−0.153542	−	0.265942i	0.778985	−	0.627042i	$-0.215735\pi$
$157$	−1.92387	−	3.33225i	−0.153542	−	0.265942i	−0.932527	+	0.361100i	$0.882401\pi$
$158$		0			0
$159$	21.0346	+	3.13697i	1.66815	+	0.248778i
$160$		0			0
$161$	4.95789			0.390737
$162$		0			0
$163$	13.0322			1.02076			0.510382	−	0.859948i	$-0.329504\pi$
$163$	13.0322			1.02076			0.510382	+	0.859948i	$0.329504\pi$
$164$		0			0
$165$	−24.3191	−	3.62679i	−1.89324	−	0.282346i
$166$		0			0
$167$	3.04538	+	5.27476i	0.235659	+	0.408173i	0.959464	−	0.281831i	$-0.0909418\pi$
$167$	3.04538	+	5.27476i	0.235659	+	0.408173i	−0.723805	+	0.690005i	$0.757609\pi$
$168$		0			0
$169$	−6.36704	+	11.0280i	−0.489772	+	0.848310i
$170$		0			0
$171$	−7.19932	−	2.19617i	−0.550546	−	0.167945i
$172$		0			0
$173$	−5.89855	+	10.2166i	−0.448458	+	0.776752i	−0.998286	−	0.0585258i	$-0.981360\pi$
$173$	−5.89855	+	10.2166i	−0.448458	+	0.776752i	0.549828	+	0.835278i	$0.314693\pi$
$174$		0			0
$175$	−4.06644	−	7.04328i	−0.307394	−	0.532422i
$176$		0			0
$177$	7.11900	+	18.0562i	0.535097	+	1.35719i
$178$		0			0
$179$	1.06148			0.0793389			0.0396694	−	0.999213i	$-0.487370\pi$
$179$	1.06148			0.0793389			0.0396694	+	0.999213i	$0.487370\pi$
$180$		0			0
$181$	−16.0384			−1.19212			−0.596062	−	0.802938i	$-0.703269\pi$
$181$	−16.0384			−1.19212			−0.596062	+	0.802938i	$0.703269\pi$
$182$		0			0
$183$	−0.449118	+	0.564979i	−0.0331998	+	0.0417644i
$184$		0			0
$185$	8.77786	+	15.2037i	0.645361	+	1.11780i
$186$		0			0
$187$	−2.02179	+	3.50185i	−0.147848	+	0.256081i
$188$		0			0
$189$	−4.27954	+	2.94712i	−0.311291	+	0.214371i
$190$		0			0
$191$	−11.9676	+	20.7285i	−0.865944	+	1.49986i	0.000163629		1.00000i	$0.499948\pi$
$191$	−11.9676	+	20.7285i	−0.865944	+	1.49986i	−0.866107	+	0.499858i	$0.833385\pi$
$192$		0			0
$193$	−6.60707	−	11.4438i	−0.475587	−	0.823741i	0.524022	−	0.851705i	$-0.324431\pi$
$193$	−6.60707	−	11.4438i	−0.475587	−	0.823741i	−0.999609	+	0.0279638i	$0.991098\pi$
$194$		0			0
$195$	19.8141	−	24.9256i	1.41892	−	1.78496i
$196$		0			0
$197$	−25.0403			−1.78405			−0.892023	−	0.451990i	$-0.850714\pi$
$197$	−25.0403			−1.78405			−0.892023	+	0.451990i	$0.850714\pi$
$198$		0			0
$199$	8.28159			0.587066			0.293533	−	0.955949i	$-0.405169\pi$
$199$	8.28159			0.587066			0.293533	+	0.955949i	$0.405169\pi$
$200$		0			0
$201$	−6.38484	−	16.1941i	−0.450352	−	1.14225i
$202$		0			0
$203$	4.60288	+	7.97242i	0.323059	+	0.559554i
$204$		0			0
$205$	−7.51464	+	13.0157i	−0.524845	+	0.909059i
$206$		0			0
$207$	−3.35484	−	14.4904i	−0.233178	−	1.00715i
$208$		0			0
$209$	4.91410	−	8.51148i	0.339916	−	0.588751i
$210$		0			0
$211$	−1.79752	−	3.11340i	−0.123747	−	0.214335i	0.797496	−	0.603325i	$-0.206158\pi$
$211$	−1.79752	−	3.11340i	−0.123747	−	0.214335i	−0.921242	+	0.388989i	$0.872824\pi$
$212$		0			0
$213$	−8.65396	−	1.29060i	−0.592959	−	0.0884303i
$214$		0			0
$215$	15.9579			1.08832
$216$		0			0
$217$	−0.844387			−0.0573207
$218$		0			0
$219$	12.3468	+	1.84132i	0.834316	+	0.124425i
$220$		0			0
$221$	−2.61823	−	4.53491i	−0.176121	−	0.305051i
$222$		0			0
$223$	−5.08601	+	8.80923i	−0.340585	+	0.589910i	−0.984541	−	0.175152i	$-0.943958\pi$
$223$	−5.08601	+	8.80923i	−0.340585	+	0.589910i	0.643957	+	0.765062i	$0.277292\pi$
$224$		0			0
$225$	−17.8337	+	16.6509i	−1.18891	+	1.11006i
$226$		0			0
$227$	−6.95054	+	12.0387i	−0.461324	+	0.799036i	−0.999027	−	0.0440980i	$-0.985959\pi$
$227$	−6.95054	+	12.0387i	−0.461324	+	0.799036i	0.537704	+	0.843134i	$0.319292\pi$
$228$		0			0
$229$	2.84347	+	4.92504i	0.187902	+	0.325456i	0.944551	−	0.328366i	$-0.106498\pi$
$229$	2.84347	+	4.92504i	0.187902	+	0.325456i	−0.756649	+	0.653822i	$0.773165\pi$
$230$		0			0
$231$	−2.48863	−	6.31202i	−0.163740	−	0.415300i
$232$		0			0
$233$	19.4775			1.27601			0.638006	−	0.770031i	$-0.279759\pi$
$233$	19.4775			1.27601			0.638006	+	0.770031i	$0.279759\pi$
$234$		0			0
$235$	28.5390			1.86168
$236$		0			0
$237$	−16.3087	+	20.5159i	−1.05936	+	1.33265i
$238$		0			0
$239$	−2.50000	−	4.33013i	−0.161712	−	0.280093i	0.773771	−	0.633465i	$-0.218368\pi$
$239$	−2.50000	−	4.33013i	−0.161712	−	0.280093i	−0.935483	+	0.353373i	$0.885035\pi$
$240$		0			0
$241$	−5.14080	+	8.90412i	−0.331148	+	0.573565i	−0.982737	−	0.185007i	$-0.940769\pi$
$241$	−5.14080	+	8.90412i	−0.331148	+	0.573565i	0.651589	+	0.758572i	$0.274103\pi$
$242$		0			0
$243$	11.5093	+	10.5136i	0.738325	+	0.674446i
$244$		0			0
$245$	1.81197	−	3.13842i	0.115762	−	0.200506i
$246$		0			0
$247$	6.36379	+	11.0224i	0.404918	+	0.701339i
$248$		0			0
$249$	−2.01080	+	2.52953i	−0.127429	+	0.160303i
$250$		0			0
$251$	−0.829685			−0.0523693			−0.0261846	−	0.999657i	$-0.508336\pi$
$251$	−0.829685			−0.0523693			−0.0261846	+	0.999657i	$0.508336\pi$
$252$		0			0
$253$	19.4214			1.22101
$254$		0			0
$255$	2.37652	+	6.02767i	0.148824	+	0.377467i
$256$		0			0
$257$	6.87516	+	11.9081i	0.428860	+	0.742808i	0.996772	−	0.0802814i	$-0.0255819\pi$
$257$	6.87516	+	11.9081i	0.428860	+	0.742808i	−0.567912	+	0.823089i	$0.692249\pi$
$258$		0			0
$259$	−2.42219	+	4.19536i	−0.150508	+	0.260687i
$260$		0			0
$261$	20.1863	−	18.8475i	1.24950	−	1.16663i
$262$		0			0
$263$	−12.9285	+	22.3929i	−0.797208	+	1.38081i	0.124219	+	0.992255i	$0.460357\pi$
$263$	−12.9285	+	22.3929i	−0.797208	+	1.38081i	−0.921427	+	0.388550i	$0.872976\pi$
$264$		0			0
$265$	22.2485	+	38.5355i	1.36671	+	2.36721i
$266$		0			0
$267$	−1.14675	−	0.171020i	−0.0701802	−	0.0104662i
$268$		0			0
$269$	9.32410			0.568500			0.284250	−	0.958750i	$-0.408255\pi$
$269$	9.32410			0.568500			0.284250	+	0.958750i	$0.408255\pi$
$270$		0			0
$271$	25.7421			1.56372			0.781861	−	0.623453i	$-0.214271\pi$
$271$	25.7421			1.56372			0.781861	+	0.623453i	$0.214271\pi$
$272$		0			0
$273$	8.69037	+	1.29603i	0.525965	+	0.0784392i
$274$		0			0
$275$	−15.9293	−	27.5904i	−0.960574	−	1.66376i
$276$		0			0
$277$	5.06570	−	8.77405i	0.304368	−	0.527181i	−0.672752	−	0.739868i	$-0.734888\pi$
$277$	5.06570	−	8.77405i	0.304368	−	0.527181i	0.977120	+	0.212686i	$0.0682213\pi$
$278$		0			0
$279$	0.571369	+	2.46788i	0.0342070	+	0.147748i
$280$		0			0
$281$	3.47969	−	6.02699i	0.207581	−	0.359540i	−0.743371	−	0.668879i	$-0.766774\pi$
$281$	3.47969	−	6.02699i	0.207581	−	0.359540i	0.950952	+	0.309339i	$0.100108\pi$
$282$		0			0
$283$	3.95920	+	6.85753i	0.235350	+	0.407638i	0.959374	−	0.282136i	$-0.0910430\pi$
$283$	3.95920	+	6.85753i	0.235350	+	0.407638i	−0.724024	+	0.689774i	$0.757710\pi$
$284$		0			0
$285$	−5.77629	−	14.6506i	−0.342158	−	0.867829i
$286$		0			0
$287$	−4.14723			−0.244803
$288$		0			0
$289$	−15.9345			−0.937321
$290$		0			0
$291$	−16.4584	+	20.7042i	−0.964807	+	1.21370i
$292$		0			0
$293$	5.63128	+	9.75367i	0.328983	+	0.569815i	0.982310	−	0.187260i	$-0.0599608\pi$
$293$	5.63128	+	9.75367i	0.328983	+	0.569815i	−0.653327	+	0.757076i	$0.726627\pi$
$294$		0			0
$295$	−20.3044	+	35.1683i	−1.18217	+	2.04758i
$296$		0			0
$297$	−16.7641	+	11.5446i	−0.972752	+	0.669888i
$298$		0			0
$299$	−12.5754	+	21.7812i	−0.727253	+	1.25964i
$300$		0			0
$301$	2.20174	+	3.81352i	0.126906	+	0.219808i
$302$		0			0
$303$	12.6716	−	15.9405i	0.727962	−	0.915757i
$304$		0			0
$305$	−1.51008			−0.0864669
$306$		0			0
$307$	23.0142			1.31349			0.656744	−	0.754113i	$-0.271933\pi$
$307$	23.0142			1.31349			0.656744	+	0.754113i	$0.271933\pi$
$308$		0			0
$309$	−7.00783	−	17.7742i	−0.398662	−	1.01114i
$310$		0			0
$311$	6.78832	+	11.7577i	0.384930	+	0.666719i	0.991760	−	0.128114i	$-0.0408922\pi$
$311$	6.78832	+	11.7577i	0.384930	+	0.666719i	−0.606829	+	0.794832i	$0.707559\pi$
$312$		0			0
$313$	8.92362	−	15.4562i	0.504393	−	0.873634i	−0.495595	−	0.868554i	$-0.665050\pi$
$313$	8.92362	−	15.4562i	0.504393	−	0.873634i	0.999987	−	0.00507958i	$-0.00161689\pi$
$314$		0			0
$315$	−10.3987	−	3.17215i	−0.585901	−	0.178731i
$316$		0			0
$317$	9.69755	−	16.7966i	0.544669	−	0.943394i	−0.453959	−	0.891022i	$-0.649989\pi$
$317$	9.69755	−	16.7966i	0.544669	−	0.943394i	0.998628	−	0.0523711i	$-0.0166779\pi$
$318$		0			0
$319$	18.0307	+	31.2301i	1.00952	+	1.74855i
$320$		0			0
$321$	−1.44399	−	0.215347i	−0.0805956	−	0.0120195i
$322$		0			0
$323$	−2.58986			−0.144103
$324$		0			0
$325$	41.2571			2.28853
$326$		0			0
$327$	−29.4440	−	4.39110i	−1.62826	−	0.242828i
$328$		0			0
$329$	3.93758	+	6.82008i	0.217086	+	0.376003i
$330$		0			0
$331$	−7.28729	+	12.6220i	−0.400546	+	0.693765i	−0.993792	−	0.111256i	$-0.964513\pi$
$331$	−7.28729	+	12.6220i	−0.400546	+	0.693765i	0.593246	+	0.805021i	$0.297846\pi$
$332$		0			0
$333$	13.9008	+	4.24046i	0.761757	+	0.232376i
$334$		0			0
$335$	18.2105	−	31.5415i	0.994946	−	1.72330i
$336$		0			0
$337$	−13.8962	−	24.0689i	−0.756975	−	1.31112i	−0.944387	−	0.328837i	$-0.893343\pi$
$337$	−13.8962	−	24.0689i	−0.756975	−	1.31112i	0.187412	−	0.982281i	$-0.439990\pi$
$338$		0			0
$339$	−5.77535	−	14.6483i	−0.313674	−	0.795584i
$340$		0			0
$341$	−3.30769			−0.179121
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	19.3650	−	24.3607i	1.04258	−	1.31153i
$346$		0			0
$347$	−7.45604	−	12.9142i	−0.400261	−	0.693273i	0.593496	−	0.804837i	$-0.297747\pi$
$347$	−7.45604	−	12.9142i	−0.400261	−	0.693273i	−0.993757	+	0.111564i	$0.964414\pi$
$348$		0			0
$349$	10.9579	−	18.9796i	0.586562	−	1.01596i	−0.408116	−	0.912930i	$-0.633814\pi$
$349$	10.9579	−	18.9796i	0.586562	−	1.01596i	0.994679	−	0.103026i	$-0.0328525\pi$
$350$		0			0
$351$	−2.09260	−	26.2762i	−0.111695	−	1.40252i
$352$		0			0
$353$	−7.73100	+	13.3905i	−0.411480	+	0.712703i	−0.995052	−	0.0993578i	$-0.968321\pi$
$353$	−7.73100	+	13.3905i	−0.411480	+	0.712703i	0.583572	+	0.812061i	$0.301654\pi$
$354$		0			0
$355$	−9.15337	−	15.8541i	−0.485810	−	0.841448i
$356$		0			0
$357$	−1.11256	+	1.39958i	−0.0588831	+	0.0740734i
$358$		0			0
$359$	7.56506			0.399269			0.199634	−	0.979870i	$-0.436025\pi$
$359$	7.56506			0.399269			0.199634	+	0.979870i	$0.436025\pi$
$360$		0			0
$361$	−12.7052			−0.668694
$362$		0			0
$363$	−2.76034	−	7.00117i	−0.144880	−	0.367466i
$364$		0			0
$365$	13.0593	+	22.6193i	0.683553	+	1.18395i
$366$		0			0
$367$	14.5046	−	25.1227i	0.757133	−	1.31139i	−0.187174	−	0.982327i	$-0.559933\pi$
$367$	14.5046	−	25.1227i	0.757133	−	1.31139i	0.944307	−	0.329066i	$-0.106734\pi$
$368$		0			0
$369$	2.80630	+	12.1211i	0.146090	+	0.630998i
$370$		0			0
$371$	−6.13932	+	10.6336i	−0.318737	+	0.552069i
$372$		0			0
$373$	−0.655525	−	1.13540i	−0.0339418	−	0.0587889i	0.848556	−	0.529106i	$-0.177473\pi$
$373$	−0.655525	−	1.13540i	−0.0339418	−	0.0587889i	−0.882497	+	0.470317i	$0.844139\pi$
$374$		0			0
$375$	−19.4495	−	2.90057i	−1.00437	−	0.149785i
$376$		0			0
$377$	−46.6997			−2.40515
$378$		0			0
$379$	−15.7015			−0.806531			−0.403265	−	0.915083i	$-0.632125\pi$
$379$	−15.7015			−0.806531			−0.403265	+	0.915083i	$0.632125\pi$
$380$		0			0
$381$	−24.8158	−	3.70088i	−1.27135	−	0.189602i
$382$		0			0
$383$	10.4804	+	18.1525i	0.535522	+	0.927551i	0.999138	+	0.0415148i	$0.0132184\pi$
$383$	10.4804	+	18.1525i	0.535522	+	0.927551i	−0.463616	+	0.886036i	$0.653448\pi$
$384$		0			0
$385$	7.09795	−	12.2940i	0.361745	−	0.626561i
$386$		0			0
$387$	9.65590	−	9.01548i	0.490837	−	0.458283i
$388$		0			0
$389$	−5.80937	+	10.0621i	−0.294547	+	0.510170i	−0.974879	−	0.222733i	$-0.928502\pi$
$389$	−5.80937	+	10.0621i	−0.294547	+	0.510170i	0.680333	+	0.732904i	$0.261835\pi$
$390$		0			0
$391$	−2.55889	−	4.43212i	−0.129409	−	0.224142i
$392$		0			0
$393$	−5.12655	−	13.0027i	−0.258600	−	0.655898i
$394$		0			0
$395$	−54.8351			−2.75906
$396$		0			0
$397$	−35.5217			−1.78278			−0.891390	−	0.453237i	$-0.850269\pi$
$397$	−35.5217			−1.78278			−0.891390	+	0.453237i	$0.850269\pi$
$398$		0			0
$399$	2.70416	−	3.40176i	0.135377	−	0.170301i
$400$		0			0
$401$	2.45388	+	4.25024i	0.122541	+	0.212247i	0.920769	−	0.390108i	$-0.127562\pi$
$401$	2.45388	+	4.25024i	0.122541	+	0.212247i	−0.798228	+	0.602355i	$0.794229\pi$
$402$		0			0
$403$	2.14174	−	3.70960i	0.106687	−	0.184788i
$404$		0			0
$405$	−2.23475	+	32.5387i	−0.111046	+	1.61686i
$406$		0			0
$407$	−9.48837	+	16.4343i	−0.470321	+	0.814620i
$408$		0			0
$409$	−2.21561	−	3.83756i	−0.109555	−	0.189755i	0.806035	−	0.591868i	$-0.201609\pi$
$409$	−2.21561	−	3.83756i	−0.109555	−	0.189755i	−0.915590	+	0.402113i	$0.868276\pi$
$410$		0			0
$411$	−21.2499	+	26.7317i	−1.04818	+	1.31858i
$412$		0			0
$413$	−11.2058			−0.551399
$414$		0			0
$415$	−6.76096			−0.331882
$416$		0			0
$417$	−10.6217	−	26.9402i	−0.520146	−	1.31927i
$418$		0			0
$419$	−17.7719	−	30.7819i	−0.868216	−	1.50379i	−0.863818	−	0.503803i	$-0.831934\pi$
$419$	−17.7719	−	30.7819i	−0.868216	−	1.50379i	−0.00439727	−	0.999990i	$-0.501400\pi$
$420$		0			0
$421$	1.81923	−	3.15100i	0.0886639	−	0.153570i	−0.818283	−	0.574816i	$-0.805074\pi$
$421$	1.81923	−	3.15100i	0.0886639	−	0.153570i	0.906947	+	0.421246i	$0.138407\pi$
$422$		0			0
$423$	17.2686	−	16.1232i	0.839627	−	0.783939i
$424$		0			0
$425$	−4.19757	+	7.27041i	−0.203612	+	0.352667i
$426$		0			0
$427$	−0.208348	−	0.360870i	−0.0100827	−	0.0174637i
$428$		0			0
$429$	34.0425	+	5.07688i	1.64359	+	0.245114i
$430$		0			0
$431$	10.9303			0.526495			0.263247	−	0.964728i	$-0.415206\pi$
$431$	10.9303			0.526495			0.263247	+	0.964728i	$0.415206\pi$
$432$		0			0
$433$	15.3189			0.736180			0.368090	−	0.929790i	$-0.380012\pi$
$433$	15.3189			0.736180			0.368090	+	0.929790i	$0.380012\pi$
$434$		0			0
$435$	57.1509	+	8.52314i	2.74018	+	0.408653i
$436$		0			0
$437$	6.21954	+	10.7726i	0.297521	+	0.515322i
$438$		0			0
$439$	−5.30117	+	9.18189i	−0.253011	+	0.438228i	−0.964353	−	0.264618i	$-0.914754\pi$
$439$	−5.30117	+	9.18189i	−0.253011	+	0.438228i	0.711343	+	0.702846i	$0.248087\pi$
$440$		0			0
$441$	−0.676667	−	2.92269i	−0.0322222	−	0.139176i
$442$		0			0
$443$	10.0680	−	17.4383i	0.478347	−	0.828521i	−0.521345	−	0.853346i	$-0.674570\pi$
$443$	10.0680	−	17.4383i	0.478347	−	0.828521i	0.999692	+	0.0248251i	$0.00790288\pi$
$444$		0			0
$445$	−1.21293	−	2.10086i	−0.0574985	−	0.0995903i
$446$		0			0
$447$	−11.6442	−	29.5338i	−0.550754	−	1.39690i
$448$		0			0
$449$	−2.74616			−0.129599			−0.0647997	−	0.997898i	$-0.520641\pi$
$449$	−2.74616			−0.129599			−0.0647997	+	0.997898i	$0.520641\pi$
$450$		0			0
$451$	−16.2458			−0.764985
$452$		0			0
$453$	15.5872	−	19.6083i	0.732352	−	0.921279i
$454$		0			0
$455$	9.19188	+	15.9208i	0.430922	+	0.746379i
$456$		0			0
$457$	−12.7715	+	22.1208i	−0.597423	+	1.03477i	0.395777	+	0.918347i	$0.370475\pi$
$457$	−12.7715	+	22.1208i	−0.597423	+	1.03477i	−0.993200	+	0.116421i	$0.962858\pi$
$458$		0			0
$459$	4.84336	+	2.30463i	0.226069	+	0.107571i
$460$		0			0
$461$	8.82316	−	15.2822i	0.410936	−	0.711761i	−0.584057	−	0.811713i	$-0.698535\pi$
$461$	8.82316	−	15.2822i	0.410936	−	0.711761i	0.994992	+	0.0999516i	$0.0318688\pi$
$462$		0			0
$463$	−13.2501	−	22.9499i	−0.615785	−	1.06657i	−0.990246	−	0.139328i	$-0.955506\pi$
$463$	−13.2501	−	22.9499i	−0.615785	−	1.06657i	0.374461	−	0.927242i	$-0.377828\pi$
$464$		0			0
$465$	−3.29809	+	4.14891i	−0.152945	+	0.192401i
$466$		0			0
$467$	20.1735			0.933519			0.466759	−	0.884384i	$-0.345421\pi$
$467$	20.1735			0.933519			0.466759	+	0.884384i	$0.345421\pi$
$468$		0			0
$469$	10.0501			0.464072
$470$		0			0
$471$	−2.44447	−	6.20001i	−0.112635	−	0.285681i
$472$		0			0
$473$	8.62479	+	14.9386i	0.396568	+	0.686876i
$474$		0			0
$475$	10.2025	−	17.6712i	0.468122	−	0.810811i
$476$		0			0
$477$	35.2330	+	10.7479i	1.61321	+	0.492113i
$478$		0			0
$479$	4.92470	−	8.52984i	0.225015	−	0.389738i	−0.731309	−	0.682047i	$-0.761090\pi$
$479$	4.92470	−	8.52984i	0.225015	−	0.389738i	0.956324	+	0.292309i	$0.0944234\pi$
$480$		0			0
$481$	−12.2875	−	21.2826i	−0.560261	−	0.970401i
$482$		0			0
$483$	8.49339	+	1.26665i	0.386463	+	0.0576346i
$484$		0			0
$485$	−55.3383			−2.51278
$486$		0			0
$487$	10.0278			0.454403			0.227202	−	0.973848i	$-0.427042\pi$
$487$	10.0278			0.454403			0.227202	+	0.973848i	$0.427042\pi$
$488$		0			0
$489$	22.3256	+	3.32950i	1.00960	+	0.150565i
$490$		0			0
$491$	0.610055	+	1.05665i	0.0275314	+	0.0476858i	0.879463	−	0.475968i	$-0.157902\pi$
$491$	0.610055	+	1.05665i	0.0275314	+	0.0476858i	−0.851931	+	0.523653i	$0.824569\pi$
$492$		0			0
$493$	4.75131	−	8.22951i	0.213988	−	0.370639i
$494$		0			0
$495$	−40.7345	−	12.4262i	−1.83088	−	0.558514i
$496$		0			0
$497$	2.52581	−	4.37483i	0.113298	−	0.196238i
$498$		0			0
$499$	−10.3222	−	17.8786i	−0.462086	−	0.800356i	0.536979	−	0.843596i	$-0.319566\pi$
$499$	−10.3222	−	17.8786i	−0.462086	−	0.800356i	−0.999065	+	0.0432393i	$0.986232\pi$
$500$		0			0
$501$	3.86946	+	9.81426i	0.172875	+	0.438469i
$502$		0			0
$503$	8.85094			0.394644			0.197322	−	0.980339i	$-0.436776\pi$
$503$	8.85094			0.394644			0.197322	+	0.980339i	$0.436776\pi$
$504$		0			0
$505$	42.6059			1.89594
$506$		0			0
$507$	−13.7249	+	17.2655i	−0.609543	+	0.766788i
$508$		0			0
$509$	12.8460	+	22.2499i	0.569388	+	0.986209i	0.996627	+	0.0820702i	$0.0261532\pi$
$509$	12.8460	+	22.2499i	0.569388	+	0.986209i	−0.427238	+	0.904139i	$0.640513\pi$
$510$		0			0
$511$	−3.60362	+	6.24165i	−0.159415	+	0.276114i
$512$		0			0
$513$	−11.7721	−	5.60156i	−0.519751	−	0.247315i
$514$		0			0
$515$	19.9874	−	34.6191i	0.880749	−	1.52550i
$516$		0			0
$517$	15.4245	+	26.7161i	0.678370	+	1.17497i
$518$		0			0
$519$	−12.7150	+	15.9951i	−0.558126	+	0.702107i
$520$		0			0
$521$	−14.6797			−0.643129			−0.321565	−	0.946888i	$-0.604209\pi$
$521$	−14.6797			−0.643129			−0.321565	+	0.946888i	$0.604209\pi$
$522$		0			0
$523$	20.7922			0.909182			0.454591	−	0.890700i	$-0.349786\pi$
$523$	20.7922			0.909182			0.454591	+	0.890700i	$0.349786\pi$
$524$		0			0
$525$	−5.16681	−	13.1048i	−0.225498	−	0.571939i
$526$		0			0
$527$	0.435809	+	0.754843i	0.0189841	+	0.0328815i
$528$		0			0
$529$	−0.790345	+	1.36892i	−0.0343628	+	0.0595181i
$530$		0			0
$531$	7.58256	+	32.7510i	0.329055	+	1.42127i
$532$		0			0
$533$	10.5192	−	18.2198i	0.455637	−	0.789187i
$534$		0			0
$535$	−1.52732	−	2.64539i	−0.0660317	−	0.114370i
$536$		0			0
$537$	1.81843	+	0.271189i	0.0784710	+	0.0117027i
$538$		0			0
$539$	3.91726			0.168728
$540$		0			0
$541$	−30.9593			−1.33104			−0.665521	−	0.746379i	$-0.731791\pi$
$541$	−30.9593			−1.33104			−0.665521	+	0.746379i	$0.731791\pi$
$542$		0			0
$543$	−27.4755	−	4.09752i	−1.17909	−	0.175841i
$544$		0			0
$545$	−31.1432	−	53.9416i	−1.33403	−	2.31060i
$546$		0			0
$547$	5.80535	−	10.0552i	0.248219	−	0.429928i	−0.714813	−	0.699316i	$-0.753488\pi$
$547$	5.80535	−	10.0552i	0.248219	−	0.429928i	0.963032	+	0.269388i	$0.0868214\pi$
$548$		0			0
$549$	−0.913729	+	0.853127i	−0.0389970	+	0.0364106i
$550$		0			0
$551$	−11.5484	+	20.0024i	−0.491977	+	0.852130i
$552$		0			0
$553$	−7.56570	−	13.1042i	−0.321726	−	0.557246i
$554$		0			0
$555$	11.1531	+	28.2881i	0.473424	+	1.20076i
$556$		0			0
$557$	19.0116			0.805546			0.402773	−	0.915300i	$-0.368046\pi$
$557$	19.0116			0.805546			0.402773	+	0.915300i	$0.368046\pi$
$558$		0			0
$559$	−22.3383			−0.944809
$560$		0			0
$561$	−4.35821	+	5.48251i	−0.184004	+	0.231472i
$562$		0			0
$563$	10.7959	+	18.6990i	0.454992	+	0.788069i	0.998688	−	0.0512136i	$-0.0163089\pi$
$563$	10.7959	+	18.6990i	0.454992	+	0.788069i	−0.543696	+	0.839282i	$0.682976\pi$
$564$		0			0
$565$	16.4722	−	28.5306i	0.692989	−	1.20029i
$566$		0			0
$567$	−8.08424	+	3.95538i	−0.339506	+	0.166110i
$568$		0			0
$569$	−9.28858	+	16.0883i	−0.389397	+	0.674456i	−0.992369	−	0.123307i	$-0.960650\pi$
$569$	−9.28858	+	16.0883i	−0.389397	+	0.674456i	0.602971	+	0.797763i	$0.293983\pi$
$570$		0			0
$571$	4.42902	+	7.67130i	0.185349	+	0.321034i	0.943694	−	0.330820i	$-0.107325\pi$
$571$	4.42902	+	7.67130i	0.185349	+	0.321034i	−0.758345	+	0.651853i	$0.773992\pi$
$572$		0			0
$573$	−25.7975	+	32.4525i	−1.07770	+	1.35572i
$574$		0			0
$575$	40.3219			1.68154
$576$		0			0
$577$	−3.76684			−0.156816			−0.0784078	−	0.996921i	$-0.524984\pi$
$577$	−3.76684			−0.156816			−0.0784078	+	0.996921i	$0.524984\pi$
$578$		0			0
$579$	−8.39492	−	21.2924i	−0.348881	−	0.884881i
$580$		0			0
$581$	−0.932821	−	1.61569i	−0.0386999	−	0.0670302i
$582$		0			0
$583$	−24.0493	+	41.6546i	−0.996021	+	1.72516i
$584$		0			0
$585$	40.3117	−	37.6381i	1.66669	−	1.55614i
$586$		0			0
$587$	−8.37616	+	14.5079i	−0.345721	+	0.598806i	−0.985484	−	0.169766i	$-0.945699\pi$
$587$	−8.37616	+	14.5079i	−0.345721	+	0.598806i	0.639763	+	0.768572i	$0.279032\pi$
$588$		0			0
$589$	−1.05926	−	1.83469i	−0.0436461	−	0.0755973i
$590$		0			0
$591$	−42.8966	−	6.39734i	−1.76453	−	0.263151i
$592$		0			0
$593$	30.3776			1.24746			0.623729	−	0.781640i	$-0.285617\pi$
$593$	30.3776			1.24746			0.623729	+	0.781640i	$0.285617\pi$
$594$		0			0
$595$	−3.74080			−0.153358
$596$		0			0
$597$	14.1872	+	2.11580i	0.580645	+	0.0865938i
$598$		0			0
$599$	−8.97578	−	15.5465i	−0.366741	−	0.635213i	0.622313	−	0.782768i	$-0.286193\pi$
$599$	−8.97578	−	15.5465i	−0.366741	−	0.635213i	−0.989054	+	0.147555i	$0.952860\pi$
$600$		0			0
$601$	2.66678	−	4.61900i	0.108780	−	0.188413i	−0.806496	−	0.591239i	$-0.798639\pi$
$601$	2.66678	−	4.61900i	0.108780	−	0.188413i	0.915276	+	0.402826i	$0.131972\pi$
$602$		0			0
$603$	−6.80060	−	29.3735i	−0.276942	−	1.19618i
$604$		0			0
$605$	7.87291	−	13.6363i	0.320079	−	0.554393i
$606$		0			0
$607$	9.11826	+	15.7933i	0.370099	+	0.641030i	0.989580	−	0.143981i	$-0.0459905\pi$
$607$	9.11826	+	15.7933i	0.370099	+	0.641030i	−0.619482	+	0.785011i	$0.712657\pi$
$608$		0			0
$609$	5.84840	+	14.8335i	0.236989	+	0.601085i
$610$		0			0
$611$	−39.9497			−1.61619
$612$		0			0
$613$	24.2030			0.977550			0.488775	−	0.872410i	$-0.337444\pi$
$613$	24.2030			0.977550			0.488775	+	0.872410i	$0.337444\pi$
$614$		0			0
$615$	−16.1987	+	20.3775i	−0.653193	+	0.821699i
$616$		0			0
$617$	3.15635	+	5.46696i	0.127070	+	0.220092i	0.922540	−	0.385901i	$-0.126109\pi$
$617$	3.15635	+	5.46696i	0.127070	+	0.220092i	−0.795470	+	0.605993i	$0.792776\pi$
$618$		0			0
$619$	−7.03450	+	12.1841i	−0.282740	+	0.489721i	−0.972059	−	0.234738i	$-0.924577\pi$
$619$	−7.03450	+	12.1841i	−0.282740	+	0.489721i	0.689318	+	0.724459i	$0.257910\pi$
$620$		0			0
$621$	−2.04516	−	25.6807i	−0.0820696	−	1.03053i
$622$		0			0
$623$	0.334701	−	0.579718i	0.0134095	−	0.0232259i
$624$		0			0
$625$	−0.239656	−	0.415097i	−0.00958625	−	0.0166039i
$626$		0			0
$627$	10.5929	−	13.3256i	0.423040	−	0.532173i
$628$		0			0
$629$	5.00061			0.199387
$630$		0			0
$631$	−1.75345			−0.0698036			−0.0349018	−	0.999391i	$-0.511112\pi$
$631$	−1.75345			−0.0698036			−0.0349018	+	0.999391i	$0.511112\pi$
$632$		0			0
$633$	−2.28393	−	5.79282i	−0.0907780	−	0.230244i
$634$		0			0
$635$	−26.2479	−	45.4627i	−1.04162	−	1.80413i
$636$		0			0
$637$	−2.53644	+	4.39324i	−0.100497	+	0.174066i
$638$		0			0
$639$	−14.4954	−	4.42186i	−0.573430	−	0.174926i
$640$		0			0
$641$	−13.6942	+	23.7191i	−0.540889	+	0.936847i	0.457964	+	0.888971i	$0.348579\pi$
$641$	−13.6942	+	23.7191i	−0.540889	+	0.936847i	−0.998853	+	0.0478765i	$0.984755\pi$
$642$		0			0
$643$	21.3323	+	36.9486i	0.841263	+	1.45711i	0.888827	+	0.458242i	$0.151521\pi$
$643$	21.3323	+	36.9486i	0.841263	+	1.45711i	−0.0475644	+	0.998868i	$0.515146\pi$
$644$		0			0
$645$	27.3375	+	4.07695i	1.07641	+	0.160530i
$646$		0			0
$647$	45.7615			1.79907			0.899536	−	0.436847i	$-0.143905\pi$
$647$	45.7615			1.79907			0.899536	+	0.436847i	$0.143905\pi$
$648$		0			0
$649$	−43.8959			−1.72306
$650$		0			0
$651$	−1.44652	−	0.215726i	−0.0566938	−	0.00845496i
$652$		0			0
$653$	0.388265	+	0.672494i	0.0151940	+	0.0263167i	0.873522	−	0.486784i	$-0.161830\pi$
$653$	0.388265	+	0.672494i	0.0151940	+	0.0263167i	−0.858328	+	0.513101i	$0.828497\pi$
$654$		0			0
$655$	14.6217	−	25.3255i	0.571316	−	0.989549i
$656$		0			0
$657$	20.6809	+	6.30874i	0.806837	+	0.246127i
$658$		0			0
$659$	5.97934	−	10.3565i	0.232922	−	0.403433i	−0.725745	−	0.687964i	$-0.758505\pi$
$659$	5.97934	−	10.3565i	0.232922	−	0.403433i	0.958667	+	0.284531i	$0.0918380\pi$
$660$		0			0
$661$	−6.31373	−	10.9357i	−0.245576	−	0.425350i	0.716718	−	0.697364i	$-0.245644\pi$
$661$	−6.31373	−	10.9357i	−0.245576	−	0.425350i	−0.962293	+	0.272014i	$0.912310\pi$
$662$		0			0
$663$	−3.32672	−	8.43770i	−0.129199	−	0.327693i
$664$		0			0
$665$	9.09225			0.352582
$666$		0			0
$667$	−45.6411			−1.76723
$668$		0			0
$669$	−10.9635	+	13.7918i	−0.423872	+	0.533220i
$670$		0			0
$671$	−0.816155	−	1.41362i	−0.0315073	−	0.0545723i
$672$		0			0
$673$	−14.5735	+	25.2421i	−0.561768	+	0.973011i	0.435574	+	0.900153i	$0.356545\pi$
$673$	−14.5735	+	25.2421i	−0.561768	+	0.973011i	−0.997342	+	0.0728584i	$0.976788\pi$
$674$		0			0
$675$	−34.8050	+	23.9685i	−1.33965	+	0.922550i
$676$		0			0
$677$	3.92732	−	6.80232i	0.150939	−	0.261435i	−0.780634	−	0.624989i	$-0.785104\pi$
$677$	3.92732	−	6.80232i	0.150939	−	0.261435i	0.931573	+	0.363554i	$0.118437\pi$
$678$		0			0
$679$	−7.63513	−	13.2244i	−0.293009	−	0.507507i
$680$		0			0
$681$	−14.9827	+	18.8478i	−0.574137	+	0.722249i
$682$		0			0
$683$	8.87441			0.339570			0.169785	−	0.985481i	$-0.445693\pi$
$683$	8.87441			0.339570			0.169785	+	0.985481i	$0.445693\pi$
$684$		0			0
$685$	−71.4488			−2.72992
$686$		0			0
$687$	3.61291	+	9.16357i	0.137841	+	0.349612i
$688$		0			0
$689$	−31.1440	−	53.9430i	−1.18649	−	2.05506i
$690$		0			0
$691$	1.82008	−	3.15248i	0.0692392	−	0.119926i	−0.829327	−	0.558763i	$-0.811276\pi$
$691$	1.82008	−	3.15248i	0.0692392	−	0.119926i	0.898567	+	0.438837i	$0.144609\pi$
$692$		0			0
$693$	−2.65068	−	11.4490i	−0.100691	−	0.434910i
$694$		0			0
$695$	30.2946	−	52.4718i	1.14914	−	1.99037i
$696$		0			0
$697$	2.14049	+	3.70743i	0.0810767	+	0.140429i
$698$		0			0
$699$	33.3670	+	4.97615i	1.26206	+	0.188215i
$700$		0			0
$701$	18.1003			0.683638			0.341819	−	0.939766i	$-0.388957\pi$
$701$	18.1003			0.683638			0.341819	+	0.939766i	$0.388957\pi$
$702$		0			0
$703$	−12.1543			−0.458408
$704$		0			0
$705$	48.8903	+	7.29120i	1.84132	+	0.274603i
$706$		0			0
$707$	5.87840	+	10.1817i	0.221080	+	0.382922i
$708$		0			0
$709$	−17.5624	+	30.4191i	−0.659572	+	1.14241i	0.321155	+	0.947027i	$0.395929\pi$
$709$	−17.5624	+	30.4191i	−0.659572	+	1.14241i	−0.980727	+	0.195385i	$0.937404\pi$
$710$		0			0
$711$	−33.1800	+	30.9794i	−1.24435	+	1.16182i
$712$		0			0
$713$	2.09319	−	3.62551i	0.0783906	−	0.135776i
$714$		0			0
$715$	36.0070	+	62.3660i	1.34659	+	2.33235i
$716$		0			0
$717$	−3.17649	−	8.05667i	−0.118628	−	0.300882i
$718$		0			0
$719$	−23.8092			−0.887933			−0.443966	−	0.896044i	$-0.646429\pi$
$719$	−23.8092			−0.887933			−0.443966	+	0.896044i	$0.646429\pi$
$720$		0			0
$721$	11.0308			0.410807
$722$		0			0
$723$	−11.0816	+	13.9403i	−0.412128	+	0.518446i
$724$		0			0
$725$	37.4346	+	64.8387i	1.39029	+	2.40805i
$726$		0			0
$727$	−1.29251	+	2.23869i	−0.0479364	+	0.0830283i	−0.888998	−	0.457911i	$-0.848598\pi$
$727$	−1.29251	+	2.23869i	−0.0479364	+	0.0830283i	0.841062	+	0.540939i	$0.181931\pi$
$728$		0			0
$729$	17.0307	+	20.9513i	0.630766	+	0.775973i
$730$		0			0
$731$	2.27274	−	3.93650i	0.0840603	−	0.145597i
$732$		0			0
$733$	11.7493	+	20.3505i	0.433972	+	0.751661i	0.997211	−	0.0746325i	$-0.0237784\pi$
$733$	11.7493	+	20.3505i	0.433972	+	0.751661i	−0.563239	+	0.826294i	$0.690445\pi$
$734$		0			0
$735$	3.90590	−	4.91351i	0.144071	−	0.181238i
$736$		0			0
$737$	39.3691			1.45018
$738$		0			0
$739$	16.9236			0.622544			0.311272	−	0.950321i	$-0.399245\pi$
$739$	16.9236			0.622544			0.311272	+	0.950321i	$0.399245\pi$
$740$		0			0
$741$	8.08581	+	20.5084i	0.297040	+	0.753394i
$742$		0			0
$743$	−4.39163	−	7.60652i	−0.161113	−	0.279056i	0.774155	−	0.632996i	$-0.218175\pi$
$743$	−4.39163	−	7.60652i	−0.161113	−	0.279056i	−0.935268	+	0.353940i	$0.884842\pi$
$744$		0			0
$745$	33.2111	−	57.5233i	1.21676	−	2.10749i
$746$		0			0
$747$	−4.09096	+	3.81963i	−0.149680	+	0.139753i
$748$		0			0
$749$	0.421453	−	0.729979i	0.0153996	−	0.0266728i
$750$		0			0
$751$	−0.983876	−	1.70412i	−0.0359021	−	0.0621843i	0.847516	−	0.530770i	$-0.178097\pi$
$751$	−0.983876	−	1.70412i	−0.0359021	−	0.0621843i	−0.883418	+	0.468585i	$0.844764\pi$
$752$		0			0
$753$	−1.42134	−	0.211970i	−0.0517964	−	0.00772460i
$754$		0			0
$755$	52.4093			1.90737
$756$		0			0
$757$	−10.3423			−0.375899			−0.187949	−	0.982179i	$-0.560184\pi$
$757$	−10.3423			−0.375899			−0.187949	+	0.982179i	$0.560184\pi$
$758$		0			0
$759$	33.2708	+	4.96181i	1.20766	+	0.180102i
$760$		0			0
$761$	7.88205	+	13.6521i	0.285724	+	0.494889i	0.972785	−	0.231711i	$-0.0744325\pi$
$761$	7.88205	+	13.6521i	0.285724	+	0.494889i	−0.687060	+	0.726600i	$0.741099\pi$
$762$		0			0
$763$	8.59376	−	14.8848i	0.311115	−	0.538867i
$764$		0			0
$765$	2.53127	+	10.9332i	0.0915184	+	0.395290i
$766$		0			0
$767$	28.4227	−	49.2296i	1.02628	−	1.77758i
$768$		0			0
$769$	22.1895	+	38.4333i	0.800172	+	1.38594i	0.919502	+	0.393084i	$0.128592\pi$
$769$	22.1895	+	38.4333i	0.800172	+	1.38594i	−0.119330	+	0.992855i	$0.538075\pi$
$770$		0			0
$771$	8.73555	+	22.1563i	0.314603	+	0.797941i
$772$		0			0
$773$	−25.5222			−0.917969			−0.458984	−	0.888444i	$-0.651787\pi$
$773$	−25.5222			−0.917969			−0.458984	+	0.888444i	$0.651787\pi$
$774$		0			0
$775$	−6.86730			−0.246681
$776$		0			0
$777$	−5.22131	+	6.56827i	−0.187314	+	0.235635i
$778$		0			0
$779$	−5.20259	−	9.01116i	−0.186402	−	0.322858i
$780$		0			0
$781$	9.89427	−	17.1374i	0.354045	−	0.613223i
$782$		0			0
$783$	39.3964	−	27.1304i	1.40791	−	0.969563i
$784$		0			0
$785$	6.97199	−	12.0758i	0.248841	−	0.431005i
$786$		0			0
$787$	−12.2841	−	21.2767i	−0.437882	−	0.758434i	0.559644	−	0.828733i	$-0.310938\pi$
$787$	−12.2841	−	21.2767i	−0.437882	−	0.758434i	−0.997526	+	0.0702995i	$0.977605\pi$
$788$		0			0
$789$	−27.8689	+	35.0584i	−0.992160	+	1.24811i
$790$		0			0
$791$	9.09077			0.323231
$792$		0			0
$793$	2.11385			0.0750650
$794$		0			0
$795$	28.2688	+	71.6994i	1.00259	+	2.54291i
$796$		0			0
$797$	18.6983	+	32.3864i	0.662328	+	1.14719i	0.980002	+	0.198986i	$0.0637649\pi$
$797$	18.6983	+	32.3864i	0.662328	+	1.14719i	−0.317674	+	0.948200i	$0.602902\pi$
$798$		0			0
$799$	4.06456	−	7.04002i	0.143794	−	0.249058i
$800$		0			0
$801$	−1.92082	−	0.585950i	−0.0678688	−	0.0207035i
$802$		0			0
$803$	−14.1163	+	24.4502i	−0.498154	+	0.862828i
$804$		0			0
$805$	8.98353	+	15.5599i	0.316628	+	0.548415i
$806$		0			0
$807$	15.9732	+	2.38214i	0.562282	+	0.0838553i
$808$		0			0
$809$	12.6565			0.444980			0.222490	−	0.974935i	$-0.428582\pi$
$809$	12.6565			0.444980			0.222490	+	0.974935i	$0.428582\pi$
$810$		0			0
$811$	−42.2499			−1.48360			−0.741798	−	0.670624i	$-0.766027\pi$
$811$	−42.2499			−1.48360			−0.741798	+	0.670624i	$0.766027\pi$
$812$		0			0
$813$	44.0989	+	6.57664i	1.54662	+	0.230653i
$814$		0			0
$815$	23.6140	+	40.9006i	0.827162	+	1.43269i
$816$		0			0
$817$	−5.52404	+	9.56792i	−0.193262	+	0.334739i
$818$		0			0
$819$	14.5564	+	4.44046i	0.508642	+	0.155162i
$820$		0			0
$821$	−19.7218	+	34.1591i	−0.688295	+	1.19216i	0.284094	+	0.958797i	$0.408307\pi$
$821$	−19.7218	+	34.1591i	−0.688295	+	1.19216i	−0.972389	+	0.233366i	$0.925026\pi$
$822$		0			0
$823$	1.33208	+	2.30723i	0.0464334	+	0.0804249i	0.888308	−	0.459248i	$-0.151881\pi$
$823$	1.33208	+	2.30723i	0.0464334	+	0.0804249i	−0.841875	+	0.539673i	$0.818548\pi$
$824$		0			0
$825$	−20.2397	−	51.3349i	−0.704657	−	1.78725i
$826$		0			0
$827$	−2.13009			−0.0740704			−0.0370352	−	0.999314i	$-0.511791\pi$
$827$	−2.13009			−0.0740704			−0.0370352	+	0.999314i	$0.511791\pi$
$828$		0			0
$829$	−7.61167			−0.264364			−0.132182	−	0.991225i	$-0.542198\pi$
$829$	−7.61167			−0.264364			−0.132182	+	0.991225i	$0.542198\pi$
$830$		0			0
$831$	10.9197	−	13.7367i	0.378800	−	0.476520i
$832$		0			0
$833$	−0.516124	−	0.893953i	−0.0178826	−	0.0309736i
$834$		0			0
$835$	−11.0363	+	19.1154i	−0.381926	+	0.661515i
$836$		0			0
$837$	0.348316	+	4.37372i	0.0120395	+	0.151178i
$838$		0			0
$839$	−19.9543	+	34.5618i	−0.688898	+	1.19321i	0.283297	+	0.959032i	$0.408572\pi$
$839$	−19.9543	+	34.5618i	−0.688898	+	1.19321i	−0.972195	+	0.234174i	$0.924762\pi$
$840$		0			0
$841$	−27.8730	−	48.2774i	−0.961136	−	1.66474i
$842$		0			0
$843$	7.50086	−	9.43588i	0.258343	−	0.324989i
$844$		0			0
$845$	−46.1474			−1.58752
$846$		0			0
$847$	4.34495			0.149294
$848$		0			0
$849$	5.03055	+	12.7592i	0.172648	+	0.437894i
$850$		0			0
$851$	−12.0090	−	20.8002i	−0.411662	−	0.713020i
$852$		0			0
$853$	24.1004	−	41.7431i	0.825182	−	1.42926i	−0.0765985	−	0.997062i	$-0.524406\pi$
$853$	24.1004	−	41.7431i	0.825182	−	1.42926i	0.901780	−	0.432195i	$-0.142261\pi$
$854$		0			0
$855$	−6.15242	−	26.5738i	−0.210408	−	0.908806i
$856$		0			0
$857$	−20.3367	+	35.2242i	−0.694688	+	1.20324i	0.275598	+	0.961273i	$0.411124\pi$
$857$	−20.3367	+	35.2242i	−0.694688	+	1.20324i	−0.970286	+	0.241962i	$0.922209\pi$
$858$		0			0
$859$	5.05826	+	8.76116i	0.172586	+	0.298927i	0.939323	−	0.343034i	$-0.111455\pi$
$859$	5.05826	+	8.76116i	0.172586	+	0.298927i	−0.766737	+	0.641961i	$0.778121\pi$
$860$		0			0
$861$	−7.10465	−	1.05954i	−0.242126	−	0.0361091i
$862$		0			0
$863$	16.5930			0.564832			0.282416	−	0.959292i	$-0.408864\pi$
$863$	16.5930			0.564832			0.282416	+	0.959292i	$0.408864\pi$
$864$		0			0
$865$	−42.7518			−1.45361
$866$		0			0
$867$	−27.2974	−	4.07097i	−0.927069	−	0.138257i
$868$		0			0
$869$	−29.6368	−	51.3325i	−1.00536	−	1.74134i
$870$		0			0
$871$	−25.4916	+	44.1527i	−0.863749	+	1.49606i
$872$		0			0
$873$	−33.4845	+	31.2636i	−1.13328	+	1.05811i
$874$		0			0
$875$	5.67667	−	9.83228i	0.191906	−	0.332392i
$876$		0			0
$877$	−18.9649	−	32.8482i	−0.640399	−	1.10920i	−0.985344	−	0.170581i	$-0.945436\pi$
$877$	−18.9649	−	32.8482i	−0.640399	−	1.10920i	0.344945	−	0.938623i	$-0.387898\pi$
$878$		0			0
$879$	7.15509	+	18.1477i	0.241335	+	0.612108i
$880$		0			0
$881$	20.9737			0.706623			0.353312	−	0.935506i	$-0.385056\pi$
$881$	20.9737			0.706623			0.353312	+	0.935506i	$0.385056\pi$
$882$		0			0
$883$	39.6536			1.33445			0.667225	−	0.744856i	$-0.267482\pi$
$883$	39.6536			1.33445			0.667225	+	0.744856i	$0.267482\pi$
$884$		0			0
$885$	−43.7685	+	55.0596i	−1.47126	+	1.85081i
$886$		0			0
$887$	−11.6160	−	20.1195i	−0.390028	−	0.675548i	0.602425	−	0.798175i	$-0.294201\pi$
$887$	−11.6160	−	20.1195i	−0.390028	−	0.675548i	−0.992453	+	0.122628i	$0.960868\pi$
$888$		0			0
$889$	7.24293	−	12.5451i	0.242920	−	0.420750i
$890$		0			0
$891$	−31.6681	+	15.4943i	−1.06092	+	0.519077i
$892$		0			0
$893$	−9.87917	+	17.1112i	−0.330594	+	0.572605i
$894$		0			0
$895$	1.92337	+	3.33137i	0.0642911	+	0.111355i
$896$		0			0
$897$	−27.1077	+	34.1007i	−0.905098	+	1.13859i
$898$		0			0
$899$	7.77322			0.259251
$900$		0			0
$901$	12.6746			0.422252
$902$		0			0
$903$	2.79752	+	7.09547i	0.0930957	+	0.236122i
$904$		0			0
$905$	−29.0610	−	50.3352i	−0.966021	−	1.67320i
$906$		0			0
$907$	21.1911	−	36.7041i	0.703640	−	1.21874i	−0.263540	−	0.964649i	$-0.584890\pi$
$907$	21.1911	−	36.7041i	0.703640	−	1.21874i	0.967180	−	0.254092i	$-0.0817766\pi$
$908$		0			0
$909$	25.7802	−	24.0704i	0.855076	−	0.798364i
$910$		0			0
$911$	−9.66820	+	16.7458i	−0.320322	+	0.554814i	−0.980554	−	0.196248i	$-0.937124\pi$
$911$	−9.66820	+	16.7458i	−0.320322	+	0.554814i	0.660233	+	0.751061i	$0.270458\pi$
$912$		0			0
$913$	−3.65411	−	6.32910i	−0.120933	−	0.209463i
$914$		0			0
$915$	−2.58693	−	0.385798i	−0.0855211	−	0.0127541i
$916$		0			0
$917$	8.06951			0.266479
$918$		0			0
$919$	28.4866			0.939685			0.469842	−	0.882750i	$-0.344311\pi$
$919$	28.4866			0.939685			0.469842	+	0.882750i	$0.344311\pi$
$920$		0			0
$921$	39.4257	+	5.87971i	1.29912	+	0.193743i
$922$		0			0
$923$	12.8131	+	22.1930i	0.421749	+	0.730491i
$924$		0			0
$925$	−19.6994	+	34.1204i	−0.647712	+	1.12187i
$926$		0			0
$927$	−7.46416	−	32.2395i	−0.245155	−	1.05888i
$928$		0			0
$929$	12.5930	−	21.8117i	0.413163	−	0.715620i	−0.582070	−	0.813139i	$-0.697757\pi$
$929$	12.5930	−	21.8117i	0.413163	−	0.715620i	0.995234	+	0.0975184i	$0.0310905\pi$
$930$		0			0
$931$	1.25447	+	2.17281i	0.0411137	+	0.0712110i
$932$		0			0
$933$	8.62522	+	21.8765i	0.282377	+	0.716204i
$934$		0			0
$935$	−14.6537			−0.479227
$936$		0			0
$937$	−17.4922			−0.571445			−0.285722	−	0.958312i	$-0.592234\pi$
$937$	−17.4922			−0.571445			−0.285722	+	0.958312i	$0.592234\pi$
$938$		0			0
$939$	19.2359	−	24.1982i	0.627739	−	0.789678i
$940$		0			0
$941$	15.9577	+	27.6396i	0.520207	+	0.901025i	0.999724	+	0.0234921i	$0.00747845\pi$
$941$	15.9577	+	27.6396i	0.520207	+	0.901025i	−0.479517	+	0.877532i	$0.659188\pi$
$942$		0			0
$943$	10.2808	−	17.8068i	0.334788	−	0.579869i
$944$		0			0
$945$	−17.0037	−	8.09092i	−0.553129	−	0.263197i
$946$		0			0
$947$	8.04820	−	13.9399i	0.261531	−	0.452986i	−0.705118	−	0.709090i	$-0.749106\pi$
$947$	8.04820	−	13.9399i	0.261531	−	0.452986i	0.966649	+	0.256105i	$0.0824392\pi$
$948$		0			0
$949$	−18.2807	−	31.6631i	−0.593417	−	1.02783i
$950$		0			0
$951$	20.9042	−	26.2969i	0.677864	−	0.852734i
$952$		0			0
$953$	24.0358			0.778595			0.389298	−	0.921112i	$-0.372718\pi$
$953$	24.0358			0.778595			0.389298	+	0.921112i	$0.372718\pi$
$954$		0			0
$955$	−86.7394			−2.80682
$956$		0			0
$957$	22.9097	+	58.1069i	0.740567	+	1.87833i
$958$		0			0
$959$	−9.85792	−	17.0744i	−0.318329	−	0.551362i
$960$		0			0
$961$	15.1435	−	26.2293i	0.488500	−	0.846107i
$962$		0			0
$963$	−2.41869	−	0.737826i	−0.0779411	−	0.0237761i
$964$		0			0
$965$	23.9436	−	41.4715i	0.770770	−	1.33501i
$966$		0			0
$967$	6.29484	+	10.9030i	0.202428	+	0.350616i	0.949310	−	0.314340i	$-0.101783\pi$
$967$	6.29484	+	10.9030i	0.202428	+	0.350616i	−0.746882	+	0.664957i	$0.768450\pi$
$968$		0			0
$969$	−4.43670	−	0.661661i	−0.142527	−	0.0212556i
$970$		0			0
$971$	30.7939			0.988223			0.494112	−	0.869398i	$-0.335493\pi$
$971$	30.7939			0.988223			0.494112	+	0.869398i	$0.335493\pi$
$972$		0			0
$973$	16.7192			0.535993
$974$		0			0
$975$	70.6777	+	10.5404i	2.26350	+	0.337564i
$976$		0			0
$977$	3.78282	+	6.55204i	0.121023	+	0.209618i	0.920171	−	0.391516i	$-0.128049\pi$
$977$	3.78282	+	6.55204i	0.121023	+	0.209618i	−0.799148	+	0.601134i	$0.794716\pi$
$978$		0			0
$979$	1.31111	−	2.27091i	0.0419033	−	0.0725786i
$980$		0			0
$981$	−49.3189	−	15.0448i	−1.57463	−	0.480344i
$982$		0			0
$983$	−13.3823	+	23.1789i	−0.426830	+	0.739292i	−0.996589	−	0.0825201i	$-0.973703\pi$
$983$	−13.3823	+	23.1789i	−0.426830	+	0.739292i	0.569759	+	0.821812i	$0.307036\pi$
$984$		0			0
$985$	−45.3721	−	78.5868i	−1.44568	−	2.50398i
$986$		0			0
$987$	5.00308	+	12.6895i	0.159250	+	0.403911i
$988$		0			0
$989$	−21.8320			−0.694216
$990$		0			0
$991$	−48.6851			−1.54653			−0.773266	−	0.634082i	$-0.781378\pi$
$991$	−48.6851			−1.54653			−0.773266	+	0.634082i	$0.781378\pi$
$992$		0			0
$993$	−15.7086	+	19.7610i	−0.498496	+	0.627095i
$994$		0			0
$995$	15.0060	+	25.9911i	0.475721	+	0.823973i
$996$		0			0
$997$	−17.0635	+	29.5548i	−0.540406	+	0.936011i	0.458474	+	0.888708i	$0.348396\pi$
$997$	−17.0635	+	29.5548i	−0.540406	+	0.936011i	−0.998881	+	0.0473036i	$0.984937\pi$
$998$		0			0
$999$	22.7301	+	10.8157i	0.719149	+	0.342195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.d.169.4	✓	8
3.2	odd	2		1512.2.r.d.505.2		8
4.3	odd	2		1008.2.r.m.673.1		8
9.2	odd	6		4536.2.a.ba.1.3		4
9.4	even	3	inner	504.2.r.d.337.4	yes	8
9.5	odd	6		1512.2.r.d.1009.2		8
9.7	even	3		4536.2.a.x.1.2		4
12.11	even	2		3024.2.r.l.2017.2		8
36.7	odd	6		9072.2.a.ce.1.2		4
36.11	even	6		9072.2.a.cl.1.3		4
36.23	even	6		3024.2.r.l.1009.2		8
36.31	odd	6		1008.2.r.m.337.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.d.169.4	✓	8	1.1	even	1	trivial
504.2.r.d.337.4	yes	8	9.4	even	3	inner
1008.2.r.m.337.1		8	36.31	odd	6
1008.2.r.m.673.1		8	4.3	odd	2
1512.2.r.d.505.2		8	3.2	odd	2
1512.2.r.d.1009.2		8	9.5	odd	6
3024.2.r.l.1009.2		8	36.23	even	6
3024.2.r.l.2017.2		8	12.11	even	2
4536.2.a.x.1.2		4	9.7	even	3
4536.2.a.ba.1.3		4	9.2	odd	6
9072.2.a.ce.1.2		4	36.7	odd	6
9072.2.a.cl.1.3		4	36.11	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71311 + 0.255482i) q^{3} +(1.81197 + 3.13842i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.86946 + 0.875335i) q^{9} +O(q^{10})\)	\(q+(1.71311 + 0.255482i) q^{3} +(1.81197 + 3.13842i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.86946 + 0.875335i) q^{9} +(-1.95863 + 3.39245i) q^{11} +(-2.53644 - 4.39324i) q^{13} +(2.30228 + 5.83936i) q^{15} +1.03225 q^{17} -2.50895 q^{19} +(-1.07781 + 1.35585i) q^{21} +(-2.47895 - 4.29366i) q^{23} +(-4.06644 + 7.04328i) q^{25} +(4.69205 + 2.23263i) q^{27} +(4.60288 - 7.97242i) q^{29} +(0.422194 + 0.731261i) q^{31} +(-4.22205 + 5.31123i) q^{33} -3.62393 q^{35} +4.84439 q^{37} +(-3.22279 - 8.17410i) q^{39} +(2.07362 + 3.59161i) q^{41} +(2.20174 - 3.81352i) q^{43} +(2.45219 + 10.5916i) q^{45} +(3.93758 - 6.82008i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(1.76835 + 0.263721i) q^{51} +12.2786 q^{53} -14.1959 q^{55} +(-4.29809 - 0.640990i) q^{57} +(5.60288 + 9.70447i) q^{59} +(-0.208348 + 0.360870i) q^{61} +(-2.19279 + 2.04736i) q^{63} +(9.19188 - 15.9208i) q^{65} +(-5.02507 - 8.70368i) q^{67} +(-3.14974 - 7.98882i) q^{69} -5.05162 q^{71} +7.20723 q^{73} +(-8.76567 + 11.0270i) q^{75} +(-1.95863 - 3.39245i) q^{77} +(-7.56570 + 13.1042i) q^{79} +(7.46758 + 5.02347i) q^{81} +(-0.932821 + 1.61569i) q^{83} +(1.87040 + 3.23963i) q^{85} +(9.92202 - 12.4816i) q^{87} -0.669401 q^{89} +5.07288 q^{91} +(0.536438 + 1.36059i) q^{93} +(-4.54612 - 7.87412i) q^{95} +(-7.63513 + 13.2244i) q^{97} +(-8.58974 + 8.02003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9	\( 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{15} - 16 q^{17} - 4 q^{19} - q^{21} - 5 q^{23} - 14 q^{25} + 5 q^{27} + q^{29} + 11 q^{31} - 8 q^{35} + 54 q^{37} - 12 q^{39} + 2 q^{41} - 11 q^{43} + 26 q^{45} + 7 q^{47} - 4 q^{49} + 17 q^{51} - 8 q^{53} + 12 q^{55} - 13 q^{57} + 9 q^{59} - 7 q^{61} - 5 q^{63} - 9 q^{65} - 12 q^{67} + 4 q^{69} - 24 q^{71} + 26 q^{73} - 23 q^{75} - 6 q^{77} - 22 q^{79} + 34 q^{81} - 6 q^{83} - 11 q^{85} + 37 q^{87} - 28 q^{89} + 6 q^{91} - 13 q^{93} - 23 q^{95} - q^{97} - 42 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9 - 6 * q^11 - 3 * q^13 + 4 * q^15 - 16 * q^17 - 4 * q^19 - q^21 - 5 * q^23 - 14 * q^25 + 5 * q^27 + q^29 + 11 * q^31 - 8 * q^35 + 54 * q^37 - 12 * q^39 + 2 * q^41 - 11 * q^43 + 26 * q^45 + 7 * q^47 - 4 * q^49 + 17 * q^51 - 8 * q^53 + 12 * q^55 - 13 * q^57 + 9 * q^59 - 7 * q^61 - 5 * q^63 - 9 * q^65 - 12 * q^67 + 4 * q^69 - 24 * q^71 + 26 * q^73 - 23 * q^75 - 6 * q^77 - 22 * q^79 + 34 * q^81 - 6 * q^83 - 11 * q^85 + 37 * q^87 - 28 * q^89 + 6 * q^91 - 13 * q^93 - 23 * q^95 - q^97 - 42 * q^99

Introduction

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