LMFDB - Embedded newform 624.2.bv.g.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.649638144.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 $ x^8 - 14x^6 + 75x^4 - 170*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$-1.42055 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.2.bv.g.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +1.28657i q^{5} +(-1.69781 - 0.980228i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +1.28657i q^{5} +(-1.69781 - 0.980228i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-4.77611 + 2.75749i) q^{11} +(-1.70297 + 3.17803i) q^{13} +(-1.11420 + 0.643285i) q^{15} +(0.911235 - 1.57830i) q^{17} +(-7.00452 - 4.04406i) q^{19} -1.96046i q^{21} +(3.48954 + 6.04406i) q^{23} +3.34474 q^{25} -1.00000 q^{27} +(1.11420 + 1.92986i) q^{29} +4.44548i q^{31} +(-4.77611 - 2.75749i) q^{33} +(1.26113 - 2.18435i) q^{35} +(-2.42621 + 1.40077i) q^{37} +(-3.60374 + 0.114203i) q^{39} +(-3.96940 + 2.29173i) q^{41} +(2.69781 - 4.67274i) q^{43} +(-1.11420 - 0.643285i) q^{45} -5.05816i q^{47} +(-1.57830 - 2.73370i) q^{49} +1.82247 q^{51} -2.44649 q^{53} +(-3.54770 - 6.14480i) q^{55} -8.08812i q^{57} +(8.69251 + 5.01862i) q^{59} +(-6.45364 + 11.1780i) q^{61} +(1.69781 - 0.980228i) q^{63} +(-4.08877 - 2.19099i) q^{65} +(-2.07379 + 1.19730i) q^{67} +(-3.48954 + 6.04406i) q^{69} +(13.0926 + 7.55904i) q^{71} +2.62301i q^{73} +(1.67237 + 2.89663i) q^{75} +10.8119 q^{77} -6.15661 q^{79} +(-0.500000 - 0.866025i) q^{81} +5.59406i q^{83} +(2.03060 + 1.17237i) q^{85} +(-1.11420 + 1.92986i) q^{87} +(13.0163 - 7.51498i) q^{89} +(6.00651 - 3.72638i) q^{91} +(-3.84990 + 2.22274i) q^{93} +(5.20297 - 9.01181i) q^{95} +(-12.0783 - 6.97341i) q^{97} -5.51498i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51} + 4 q^{53} + 10 q^{55} + 36 q^{59} + 2 q^{61} - 28 q^{65} - 36 q^{67} - 2 q^{69} - 6 q^{71} - 2 q^{75} + 56 q^{77} + 12 q^{79} - 4 q^{81} + 24 q^{85} - 6 q^{87} - 12 q^{89} - 38 q^{91} - 6 q^{93} + 34 q^{95} - 66 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 + 12 * q^17 - 6 * q^19 + 2 * q^23 - 4 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^33 - 10 * q^35 - 24 * q^41 + 8 * q^43 - 6 * q^45 + 18 * q^49 + 24 * q^51 + 4 * q^53 + 10 * q^55 + 36 * q^59 + 2 * q^61 - 28 * q^65 - 36 * q^67 - 2 * q^69 - 6 * q^71 - 2 * q^75 + 56 * q^77 + 12 * q^79 - 4 * q^81 + 24 * q^85 - 6 * q^87 - 12 * q^89 - 38 * q^91 - 6 * q^93 + 34 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$			1.28657i			0.575372i	0.957725	+	0.287686i	$0.0928859\pi$
$5$			1.28657i			0.575372i	−0.957725	+	0.287686i	$0.907114\pi$
$6$		0			0
$7$	−1.69781	−	0.980228i	−0.641710	−	0.370492i	0.143563	−	0.989641i	$-0.454144\pi$
$7$	−1.69781	−	0.980228i	−0.641710	−	0.370492i	−0.785273	+	0.619150i	$0.787477\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−4.77611	+	2.75749i	−1.44005	+	0.831414i	−0.997852	−	0.0655030i	$-0.979135\pi$
$11$	−4.77611	+	2.75749i	−1.44005	+	0.831414i	−0.442199	+	0.896917i	$0.645801\pi$
$12$		0			0
$13$	−1.70297	+	3.17803i	−0.472318	+	0.881428i
$13$	−1.70297	+	3.17803i	−0.472318	+	0.881428i
$14$		0			0
$15$	−1.11420	+	0.643285i	−0.287686	+	0.166096i
$16$		0			0
$17$	0.911235	−	1.57830i	0.221007	−	0.382795i	−0.734107	−	0.679034i	$-0.762399\pi$
$17$	0.911235	−	1.57830i	0.221007	−	0.382795i	0.955114	+	0.296239i	$0.0957323\pi$
$18$		0			0
$19$	−7.00452	−	4.04406i	−1.60695	−	0.927771i	−0.990048	−	0.140728i	$-0.955056\pi$
$19$	−7.00452	−	4.04406i	−1.60695	−	0.927771i	−0.616898	−	0.787043i	$-0.711611\pi$
$20$		0			0
$21$		−	1.96046i		−	0.427807i
$22$		0			0
$23$	3.48954	+	6.04406i	0.727619	+	1.26027i	0.957887	+	0.287146i	$0.0927065\pi$
$23$	3.48954	+	6.04406i	0.727619	+	1.26027i	−0.230268	+	0.973127i	$0.573960\pi$
$24$		0			0
$25$	3.34474			0.668947
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	1.11420	+	1.92986i	0.206902	+	0.358365i	0.950737	−	0.309998i	$-0.100328\pi$
$29$	1.11420	+	1.92986i	0.206902	+	0.358365i	−0.743835	+	0.668363i	$0.766995\pi$
$30$		0			0
$31$			4.44548i			0.798432i	0.916857	+	0.399216i	$0.130718\pi$
$31$			4.44548i			0.798432i	−0.916857	+	0.399216i	$0.869282\pi$
$32$		0			0
$33$	−4.77611	−	2.75749i	−0.831414	−	0.480017i
$34$		0			0
$35$	1.26113	−	2.18435i	0.213170	−	0.369222i
$36$		0			0
$37$	−2.42621	+	1.40077i	−0.398867	+	0.230286i	−0.685995	−	0.727606i	$-0.740633\pi$
$37$	−2.42621	+	1.40077i	−0.398867	+	0.230286i	0.287128	+	0.957892i	$0.407299\pi$
$38$		0			0
$39$	−3.60374	+	0.114203i	−0.577061	+	0.0182871i
$40$		0			0
$41$	−3.96940	+	2.29173i	−0.619916	+	0.357909i	−0.776836	−	0.629703i	$-0.783177\pi$
$41$	−3.96940	+	2.29173i	−0.619916	+	0.357909i	0.156920	+	0.987611i	$0.449843\pi$
$42$		0			0
$43$	2.69781	−	4.67274i	0.411411	−	0.712586i	−0.583633	−	0.812018i	$-0.698369\pi$
$43$	2.69781	−	4.67274i	0.411411	−	0.712586i	0.995044	+	0.0994321i	$0.0317026\pi$
$44$		0			0
$45$	−1.11420	−	0.643285i	−0.166096	−	0.0958953i
$46$		0			0
$47$		−	5.05816i		−	0.737809i	−0.929467	−	0.368905i	$-0.879733\pi$
$47$		−	5.05816i		−	0.737809i	0.929467	−	0.368905i	$-0.120267\pi$
$48$		0			0
$49$	−1.57830	−	2.73370i	−0.225472	−	0.390529i
$50$		0			0
$51$	1.82247			0.255197
$52$		0			0
$53$	−2.44649			−0.336051			−0.168025	−	0.985783i	$-0.553739\pi$
$53$	−2.44649			−0.336051			−0.168025	+	0.985783i	$0.553739\pi$
$54$		0			0
$55$	−3.54770	−	6.14480i	−0.478372	−	0.828565i
$56$		0			0
$57$		−	8.08812i		−	1.07130i
$58$		0			0
$59$	8.69251	+	5.01862i	1.13167	+	0.653369i	0.944354	−	0.328931i	$-0.106688\pi$
$59$	8.69251	+	5.01862i	1.13167	+	0.653369i	0.187314	+	0.982300i	$0.440022\pi$
$60$		0			0
$61$	−6.45364	+	11.1780i	−0.826304	+	1.43120i	0.0746146	+	0.997212i	$0.476227\pi$
$61$	−6.45364	+	11.1780i	−0.826304	+	1.43120i	−0.900919	+	0.433988i	$0.857106\pi$
$62$		0			0
$63$	1.69781	−	0.980228i	0.213903	−	0.123497i
$64$		0			0
$65$	−4.08877	−	2.19099i	−0.507149	−	0.271759i
$66$		0			0
$67$	−2.07379	+	1.19730i	−0.253354	+	0.146274i	−0.621299	−	0.783574i	$-0.713395\pi$
$67$	−2.07379	+	1.19730i	−0.253354	+	0.146274i	0.367945	+	0.929847i	$0.380061\pi$
$68$		0			0
$69$	−3.48954	+	6.04406i	−0.420091	+	0.727619i
$70$		0			0
$71$	13.0926	+	7.55904i	1.55381	+	0.897093i	0.997826	+	0.0658992i	$0.0209916\pi$
$71$	13.0926	+	7.55904i	1.55381	+	0.897093i	0.555984	+	0.831193i	$0.312342\pi$
$72$		0			0
$73$			2.62301i			0.307000i	0.988149	+	0.153500i	$0.0490545\pi$
$73$			2.62301i			0.307000i	−0.988149	+	0.153500i	$0.950945\pi$
$74$		0			0
$75$	1.67237	+	2.89663i	0.193108	+	0.334474i
$76$		0			0
$77$	10.8119			1.23213
$78$		0			0
$79$	−6.15661			−0.692673			−0.346336	−	0.938110i	$-0.612574\pi$
$79$	−6.15661			−0.692673			−0.346336	+	0.938110i	$0.612574\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			5.59406i			0.614028i	0.951705	+	0.307014i	$0.0993299\pi$
$83$			5.59406i			0.614028i	−0.951705	+	0.307014i	$0.900670\pi$
$84$		0			0
$85$	2.03060	+	1.17237i	0.220250	+	0.127161i
$86$		0			0
$87$	−1.11420	+	1.92986i	−0.119455	+	0.206902i
$88$		0			0
$89$	13.0163	−	7.51498i	1.37973	−	0.796586i	0.387601	−	0.921827i	$-0.373304\pi$
$89$	13.0163	−	7.51498i	1.37973	−	0.796586i	0.992126	+	0.125241i	$0.0399705\pi$
$90$		0			0
$91$	6.00651	−	3.72638i	0.629653	−	0.390631i
$92$		0			0
$93$	−3.84990	+	2.22274i	−0.399216	+	0.230487i
$94$		0			0
$95$	5.20297	−	9.01181i	0.533813	−	0.924592i
$96$		0			0
$97$	−12.0783	−	6.97341i	−1.22637	−	0.708043i	−0.260098	−	0.965582i	$-0.583755\pi$
$97$	−12.0783	−	6.97341i	−1.22637	−	0.708043i	−0.966268	+	0.257539i	$0.917088\pi$
$98$		0			0
$99$		−	5.51498i		−	0.554276i
$100$		0			0
$101$	2.62918	+	4.55387i	0.261613	+	0.453127i	0.966671	−	0.256023i	$-0.0824122\pi$
$101$	2.62918	+	4.55387i	0.261613	+	0.453127i	−0.705058	+	0.709150i	$0.749079\pi$
$102$		0			0
$103$	7.39561			0.728711			0.364356	−	0.931260i	$-0.381289\pi$
$103$	7.39561			0.728711			0.364356	+	0.931260i	$0.381289\pi$
$104$		0			0
$105$	2.52227			0.246148
$106$		0			0
$107$	3.88515	+	6.72928i	0.375592	+	0.650544i	0.990415	−	0.138121i	$-0.0441062\pi$
$107$	3.88515	+	6.72928i	0.375592	+	0.650544i	−0.614824	+	0.788665i	$0.710773\pi$
$108$		0			0
$109$		−	12.4455i		−	1.19206i	−0.802962	−	0.596030i	$-0.796744\pi$
$109$		−	12.4455i		−	1.19206i	0.802962	−	0.596030i	$-0.203256\pi$
$110$		0			0
$111$	−2.42621	−	1.40077i	−0.230286	−	0.132956i
$112$		0			0
$113$	−2.08877	+	3.61785i	−0.196495	+	0.340338i	−0.947389	−	0.320083i	$-0.896289\pi$
$113$	−2.08877	+	3.61785i	−0.196495	+	0.340338i	0.750895	+	0.660422i	$0.229622\pi$
$114$		0			0
$115$	−7.77611	+	4.48954i	−0.725126	+	0.418652i
$116$		0			0
$117$	−1.90077	−	3.06383i	−0.175727	−	0.283251i
$118$		0			0
$119$	−3.09420	+	1.78644i	−0.283645	+	0.163762i
$120$		0			0
$121$	9.70748	−	16.8139i	0.882499	−	1.52853i
$122$		0			0
$123$	−3.96940	−	2.29173i	−0.357909	−	0.206639i
$124$		0			0
$125$			10.7361i			0.960265i
$126$		0			0
$127$	2.09923	+	3.63597i	0.186276	+	0.322640i	0.944006	−	0.329929i	$-0.107025\pi$
$127$	2.09923	+	3.63597i	0.186276	+	0.322640i	−0.757730	+	0.652569i	$0.773691\pi$
$128$		0			0
$129$	5.39561			0.475057
$130$		0			0
$131$	−11.5013			−1.00488			−0.502439	−	0.864613i	$-0.667564\pi$
$131$	−11.5013			−1.00488			−0.502439	+	0.864613i	$0.667564\pi$
$132$		0			0
$133$	7.92820	+	13.7321i	0.687462	+	1.19072i
$134$		0			0
$135$		−	1.28657i		−	0.110730i
$136$		0			0
$137$	7.58613	+	4.37985i	0.648127	+	0.374196i	0.787738	−	0.616010i	$-0.211252\pi$
$137$	7.58613	+	4.37985i	0.648127	+	0.374196i	−0.139612	+	0.990206i	$0.544585\pi$
$138$		0			0
$139$	7.48424	−	12.9631i	0.634805	−	1.09951i	−0.351751	−	0.936093i	$-0.614414\pi$
$139$	7.48424	−	12.9631i	0.634805	−	1.09951i	0.986556	−	0.163421i	$-0.0522529\pi$
$140$		0			0
$141$	4.38050	−	2.52908i	0.368905	−	0.212987i
$142$		0			0
$143$	−0.629827	−	19.8746i	−0.0526688	−	1.66199i
$144$		0			0
$145$	−2.48290	+	1.43350i	−0.206193	+	0.119046i
$146$		0			0
$147$	1.57830	−	2.73370i	0.130176	−	0.225472i
$148$		0			0
$149$	6.73822	+	3.89031i	0.552016	+	0.318707i	0.749935	−	0.661512i	$-0.230085\pi$
$149$	6.73822	+	3.89031i	0.552016	+	0.318707i	−0.197918	+	0.980218i	$0.563418\pi$
$150$		0			0
$151$			5.51498i			0.448802i	0.974497	+	0.224401i	$0.0720426\pi$
$151$			5.51498i			0.448802i	−0.974497	+	0.224401i	$0.927957\pi$
$152$		0			0
$153$	0.911235	+	1.57830i	0.0736690	+	0.127598i
$154$		0			0
$155$	−5.71942			−0.459395
$156$		0			0
$157$	20.5104			1.63691			0.818453	−	0.574573i	$-0.194832\pi$
$157$	20.5104			1.63691			0.818453	+	0.574573i	$0.194832\pi$
$158$		0			0
$159$	−1.22324	−	2.11872i	−0.0970095	−	0.168025i
$160$		0			0
$161$		−	13.6822i		−	1.07831i
$162$		0			0
$163$	15.8695	+	9.16228i	1.24300	+	0.717645i	0.969703	−	0.244286i	$-0.0785535\pi$
$163$	15.8695	+	9.16228i	1.24300	+	0.717645i	0.273294	+	0.961931i	$0.411887\pi$
$164$		0			0
$165$	3.54770	−	6.14480i	0.276188	−	0.478372i
$166$		0			0
$167$	7.08083	−	4.08812i	0.547931	−	0.316348i	−0.200356	−	0.979723i	$-0.564210\pi$
$167$	7.08083	−	4.08812i	0.547931	−	0.316348i	0.748287	+	0.663375i	$0.230877\pi$
$168$		0			0
$169$	−7.19980	−	10.8242i	−0.553831	−	0.832629i
$170$		0			0
$171$	7.00452	−	4.04406i	0.535649	−	0.309257i
$172$		0			0
$173$	4.28657	−	7.42456i	0.325902	−	0.564479i	−0.655793	−	0.754941i	$-0.727665\pi$
$173$	4.28657	−	7.42456i	0.325902	−	0.564479i	0.981694	+	0.190462i	$0.0609987\pi$
$174$		0			0
$175$	−5.67871	−	3.27860i	−0.429270	−	0.247839i
$176$		0			0
$177$			10.0372i			0.754445i
$178$		0			0
$179$	1.86552	+	3.23118i	0.139436	+	0.241510i	0.927283	−	0.374361i	$-0.122138\pi$
$179$	1.86552	+	3.23118i	0.139436	+	0.241510i	−0.787847	+	0.615870i	$0.788804\pi$
$180$		0			0
$181$	5.24933			0.390179			0.195090	−	0.980785i	$-0.437500\pi$
$181$	5.24933			0.390179			0.195090	+	0.980785i	$0.437500\pi$
$182$		0			0
$183$	−12.9073			−0.954134
$184$		0			0
$185$	−1.80219	−	3.12149i	−0.132500	−	0.229497i
$186$		0			0
$187$			10.0509i			0.734993i
$188$		0			0
$189$	1.69781	+	0.980228i	0.123497	+	0.0713011i
$190$		0			0
$191$	−2.77159	+	4.80054i	−0.200546	+	0.347355i	−0.948704	−	0.316165i	$-0.897605\pi$
$191$	−2.77159	+	4.80054i	−0.200546	+	0.347355i	0.748159	+	0.663520i	$0.230938\pi$
$192$		0			0
$193$	−8.82381	+	5.09443i	−0.635152	+	0.366705i	−0.782745	−	0.622343i	$-0.786181\pi$
$193$	−8.82381	+	5.09443i	−0.635152	+	0.366705i	0.147593	+	0.989048i	$0.452848\pi$
$194$		0			0
$195$	−0.146930	−	4.63647i	−0.0105219	−	0.332024i
$196$		0			0
$197$	−22.3923	+	12.9282i	−1.59539	+	0.921096i	−0.603025	+	0.797722i	$0.706038\pi$
$197$	−22.3923	+	12.9282i	−1.59539	+	0.921096i	−0.992360	+	0.123374i	$0.960628\pi$
$198$		0			0
$199$	−6.27095	+	10.8616i	−0.444536	+	0.769958i	−0.998020	−	0.0629014i	$-0.979965\pi$
$199$	−6.27095	+	10.8616i	−0.444536	+	0.769958i	0.553484	+	0.832860i	$0.313298\pi$
$200$		0			0
$201$	−2.07379	−	1.19730i	−0.146274	−	0.0844512i
$202$		0			0
$203$		−	4.36869i		−	0.306622i
$204$		0			0
$205$	−2.94848	−	5.10691i	−0.205931	−	0.356682i
$206$		0			0
$207$	−6.97908			−0.485079
$208$		0			0
$209$	44.6058			3.08545
$210$		0			0
$211$	−6.20496	−	10.7473i	−0.427167	−	0.739875i	0.569453	−	0.822024i	$-0.307155\pi$
$211$	−6.20496	−	10.7473i	−0.427167	−	0.739875i	−0.996620	+	0.0821488i	$0.973822\pi$
$212$		0			0
$213$			15.1181i			1.03587i
$214$		0			0
$215$	6.01181	+	3.47092i	0.410002	+	0.236715i
$216$		0			0
$217$	4.35759	−	7.54756i	0.295812	−	0.512362i
$218$		0			0
$219$	−2.27159	+	1.31151i	−0.153500	+	0.0886233i
$220$		0			0
$221$	3.46410	+	5.58374i	0.233021	+	0.375603i
$222$		0			0
$223$	−16.6134	+	9.59176i	−1.11252	+	0.642312i	−0.939480	−	0.342603i	$-0.888691\pi$
$223$	−16.6134	+	9.59176i	−1.11252	+	0.642312i	−0.173037	+	0.984915i	$0.555358\pi$
$224$		0			0
$225$	−1.67237	+	2.89663i	−0.111491	+	0.193108i
$226$		0			0
$227$	−9.16443	−	5.29109i	−0.608265	−	0.351182i	0.164021	−	0.986457i	$-0.447553\pi$
$227$	−9.16443	−	5.29109i	−0.608265	−	0.351182i	−0.772286	+	0.635275i	$0.780887\pi$
$228$		0			0
$229$		−	19.4595i		−	1.28592i	−0.765900	−	0.642960i	$-0.777706\pi$
$229$		−	19.4595i		−	1.28592i	0.765900	−	0.642960i	$-0.222294\pi$
$230$		0			0
$231$	5.40594	+	9.36336i	0.355685	+	0.616064i
$232$		0			0
$233$	−27.4243			−1.79662			−0.898312	−	0.439358i	$-0.855206\pi$
$233$	−27.4243			−1.79662			−0.898312	+	0.439358i	$0.855206\pi$
$234$		0			0
$235$	6.50769			0.424515
$236$		0			0
$237$	−3.07830	−	5.33178i	−0.199957	−	0.346336i
$238$		0			0
$239$			2.76100i			0.178594i	0.996005	+	0.0892971i	$0.0284621\pi$
$239$			2.76100i			0.178594i	−0.996005	+	0.0892971i	$0.971538\pi$
$240$		0			0
$241$	5.34990	+	3.08877i	0.344617	+	0.198965i	0.662312	−	0.749228i	$-0.269575\pi$
$241$	5.34990	+	3.08877i	0.344617	+	0.198965i	−0.317695	+	0.948193i	$0.602909\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	3.51710	−	2.03060i	0.224699	−	0.129730i
$246$		0			0
$247$	24.7806	−	15.3737i	1.57675	−	0.978204i
$248$		0			0
$249$	−4.84460	+	2.79703i	−0.307014	+	0.177255i
$250$		0			0
$251$	7.05816	−	12.2251i	0.445507	−	0.771641i	−0.552580	−	0.833460i	$-0.686357\pi$
$251$	7.05816	−	12.2251i	0.445507	−	0.771641i	0.998087	+	0.0618184i	$0.0196900\pi$
$252$		0			0
$253$	−33.3328	−	19.2447i	−2.09562	−	1.20991i
$254$		0			0
$255$			2.34474i			0.146833i
$256$		0			0
$257$	−5.81123	−	10.0653i	−0.362494	−	0.627859i	0.625876	−	0.779922i	$-0.284741\pi$
$257$	−5.81123	−	10.0653i	−0.362494	−	0.627859i	−0.988371	+	0.152064i	$0.951408\pi$
$258$		0			0
$259$	5.49231			0.341276
$260$		0			0
$261$	−2.22841			−0.137935
$262$		0			0
$263$	−4.31201	−	7.46862i	−0.265890	−	0.460535i	0.701907	−	0.712269i	$-0.252332\pi$
$263$	−4.31201	−	7.46862i	−0.265890	−	0.460535i	−0.967796	+	0.251734i	$0.918999\pi$
$264$		0			0
$265$		−	3.14758i		−	0.193354i
$266$		0			0
$267$	13.0163	+	7.51498i	0.796586	+	0.459909i
$268$		0			0
$269$	−12.6240	+	21.8654i	−0.769700	+	1.33316i	0.168026	+	0.985783i	$0.446261\pi$
$269$	−12.6240	+	21.8654i	−0.769700	+	1.33316i	−0.937726	+	0.347377i	$0.887073\pi$
$270$		0			0
$271$	−2.59632	+	1.49898i	−0.157715	+	0.0910568i	−0.576780	−	0.816899i	$-0.695691\pi$
$271$	−2.59632	+	1.49898i	−0.157715	+	0.0910568i	0.419065	+	0.907956i	$0.362358\pi$
$272$		0			0
$273$	6.23040	+	3.33860i	0.377081	+	0.202061i
$274$		0			0
$275$	−15.9748	+	9.22307i	−0.963318	+	0.556172i
$276$		0			0
$277$	−12.4562	+	21.5747i	−0.748418	+	1.29630i	0.200162	+	0.979763i	$0.435853\pi$
$277$	−12.4562	+	21.5747i	−0.748418	+	1.29630i	−0.948581	+	0.316536i	$0.897480\pi$
$278$		0			0
$279$	−3.84990	−	2.22274i	−0.230487	−	0.133072i
$280$		0			0
$281$			8.38198i			0.500027i	0.968242	+	0.250013i	$0.0804351\pi$
$281$			8.38198i			0.500027i	−0.968242	+	0.250013i	$0.919565\pi$
$282$		0			0
$283$	12.9053	+	22.3526i	0.767140	+	1.32873i	0.939108	+	0.343623i	$0.111654\pi$
$283$	12.9053	+	22.3526i	0.767140	+	1.32873i	−0.171968	+	0.985103i	$0.555013\pi$
$284$		0			0
$285$	10.4059			0.616394
$286$		0			0
$287$	8.98569			0.530409
$288$		0			0
$289$	6.83930	+	11.8460i	0.402312	+	0.696825i
$290$		0			0
$291$		−	13.9468i		−	0.817577i
$292$		0			0
$293$	−11.0441	−	6.37634i	−0.645206	−	0.372510i	0.141411	−	0.989951i	$-0.454836\pi$
$293$	−11.0441	−	6.37634i	−0.645206	−	0.372510i	−0.786617	+	0.617441i	$0.788169\pi$
$294$		0			0
$295$	−6.45681	+	11.1835i	−0.375930	+	0.651130i
$296$		0			0
$297$	4.77611	−	2.75749i	0.277138	−	0.160006i
$298$		0			0
$299$	−25.1508	+	0.797032i	−1.45451	+	0.0460935i
$300$		0			0
$301$	−9.16070	+	5.28893i	−0.528014	+	0.304849i
$302$		0			0
$303$	−2.62918	+	4.55387i	−0.151042	+	0.261613i
$304$		0			0
$305$	−14.3813	−	8.30307i	−0.823473	−	0.475432i
$306$		0			0
$307$		−	16.6307i		−	0.949167i	−0.880210	−	0.474583i	$-0.842599\pi$
$307$		−	16.6307i		−	0.949167i	0.880210	−	0.474583i	$-0.157401\pi$
$308$		0			0
$309$	3.69781	+	6.40479i	0.210361	+	0.364356i
$310$		0			0
$311$	19.3940			1.09974			0.549868	−	0.835252i	$-0.314678\pi$
$311$	19.3940			1.09974			0.549868	+	0.835252i	$0.314678\pi$
$312$		0			0
$313$	−26.5091			−1.49838			−0.749191	−	0.662354i	$-0.769557\pi$
$313$	−26.5091			−1.49838			−0.749191	+	0.662354i	$0.769557\pi$
$314$		0			0
$315$	1.26113	+	2.18435i	0.0710568	+	0.123074i
$316$		0			0
$317$		−	8.13569i		−	0.456946i	−0.973550	−	0.228473i	$-0.926627\pi$
$317$		−	8.13569i		−	0.456946i	0.973550	−	0.228473i	$-0.0733732\pi$
$318$		0			0
$319$	−10.6431	−	6.14480i	−0.595900	−	0.344043i
$320$		0			0
$321$	−3.88515	+	6.72928i	−0.216848	+	0.375592i
$322$		0			0
$323$	−12.7655	+	7.37017i	−0.710292	+	0.410087i
$324$		0			0
$325$	−5.69598	+	10.6297i	−0.315956	+	0.589629i
$326$		0			0
$327$	10.7781	−	6.22274i	0.596030	−	0.344118i
$328$		0			0
$329$	−4.95816	+	8.58778i	−0.273352	+	0.473460i
$330$		0			0
$331$	27.7008	+	15.9930i	1.52257	+	0.879057i	0.999644	+	0.0266797i	$0.00849342\pi$
$331$	27.7008	+	15.9930i	1.52257	+	0.879057i	0.522927	+	0.852377i	$0.324840\pi$
$332$		0			0
$333$		−	2.80155i		−	0.153524i
$334$		0			0
$335$	−1.54041	−	2.66808i	−0.0841618	−	0.145773i
$336$		0			0
$337$	8.14628			0.443756			0.221878	−	0.975074i	$-0.428781\pi$
$337$	8.14628			0.443756			0.221878	+	0.975074i	$0.428781\pi$
$338$		0			0
$339$	−4.17753			−0.226892
$340$		0			0
$341$	−12.2584	−	21.2321i	−0.663827	−	1.14978i
$342$		0			0
$343$			19.9116i			1.07512i
$344$		0			0
$345$	−7.77611	−	4.48954i	−0.418652	−	0.241709i
$346$		0			0
$347$	−15.8746	+	27.4955i	−0.852191	+	1.47604i	0.0270362	+	0.999634i	$0.491393\pi$
$347$	−15.8746	+	27.4955i	−0.852191	+	1.47604i	−0.879227	+	0.476403i	$0.841940\pi$
$348$		0			0
$349$	9.86953	−	5.69817i	0.528304	−	0.305016i	−0.212022	−	0.977265i	$-0.568005\pi$
$349$	9.86953	−	5.69817i	0.528304	−	0.305016i	0.740325	+	0.672249i	$0.234671\pi$
$350$		0			0
$351$	1.70297	−	3.17803i	0.0908977	−	0.169631i
$352$		0			0
$353$	−19.8797	+	11.4776i	−1.05809	+	0.610889i	−0.924903	−	0.380202i	$-0.875854\pi$
$353$	−19.8797	+	11.4776i	−1.05809	+	0.610889i	−0.133187	+	0.991091i	$0.542521\pi$
$354$		0			0
$355$	−9.72523	+	16.8446i	−0.516162	+	0.894019i
$356$		0			0
$357$	−3.09420	−	1.78644i	−0.163762	−	0.0945482i
$358$		0			0
$359$		−	8.77558i		−	0.463157i	−0.972816	−	0.231579i	$-0.925611\pi$
$359$		−	8.77558i		−	0.463157i	0.972816	−	0.231579i	$-0.0743891\pi$
$360$		0			0
$361$	23.2088	+	40.1989i	1.22152	+	2.11573i
$362$		0			0
$363$	19.4150			1.01902
$364$		0			0
$365$	−3.37469			−0.176639
$366$		0			0
$367$	−16.8335	−	29.1565i	−0.878701	−	1.52196i	−0.852767	−	0.522291i	$-0.825077\pi$
$367$	−16.8335	−	29.1565i	−0.878701	−	1.52196i	−0.0259341	−	0.999664i	$-0.508256\pi$
$368$		0			0
$369$		−	4.58347i		−	0.238606i
$370$		0			0
$371$	4.15366	+	2.39811i	0.215647	+	0.124504i
$372$		0			0
$373$	−3.24616	+	5.62251i	−0.168080	+	0.291122i	−0.937745	−	0.347326i	$-0.887090\pi$
$373$	−3.24616	+	5.62251i	−0.168080	+	0.291122i	0.769665	+	0.638448i	$0.220423\pi$
$374$		0			0
$375$	−9.29773	+	5.36805i	−0.480133	+	0.277205i
$376$		0			0
$377$	−8.03060	+	0.254491i	−0.413597	+	0.0131069i
$378$		0			0
$379$	−26.4633	+	15.2786i	−1.35933	+	0.784809i	−0.989533	−	0.144304i	$-0.953906\pi$
$379$	−26.4633	+	15.2786i	−1.35933	+	0.784809i	−0.369796	+	0.929113i	$0.620572\pi$
$380$		0			0
$381$	−2.09923	+	3.63597i	−0.107547	+	0.186276i
$382$		0			0
$383$	−6.40134	−	3.69581i	−0.327093	−	0.188847i	0.327457	−	0.944866i	$-0.393808\pi$
$383$	−6.40134	−	3.69581i	−0.327093	−	0.188847i	−0.654550	+	0.756019i	$0.727142\pi$
$384$		0			0
$385$			13.9102i			0.708932i
$386$		0			0
$387$	2.69781	+	4.67274i	0.137137	+	0.237529i
$388$		0			0
$389$	24.8408			1.25948			0.629739	−	0.776807i	$-0.283162\pi$
$389$	24.8408			1.25948			0.629739	+	0.776807i	$0.283162\pi$
$390$		0			0
$391$	12.7192			0.643235
$392$		0			0
$393$	−5.75067	−	9.96046i	−0.290083	−	0.502439i
$394$		0			0
$395$		−	7.92091i		−	0.398544i
$396$		0			0
$397$	23.4127	+	13.5173i	1.17505	+	0.678416i	0.954864	−	0.297042i	$-0.0960002\pi$
$397$	23.4127	+	13.5173i	1.17505	+	0.678416i	0.220186	+	0.975458i	$0.429334\pi$
$398$		0			0
$399$	−7.92820	+	13.7321i	−0.396907	+	0.687462i
$400$		0			0
$401$	−21.4604	+	12.3902i	−1.07168	+	0.618736i	−0.928641	−	0.370981i	$-0.879022\pi$
$401$	−21.4604	+	12.3902i	−1.07168	+	0.618736i	−0.143042	+	0.989717i	$0.545688\pi$
$402$		0			0
$403$	−14.1279	−	7.57051i	−0.703760	−	0.377114i
$404$		0			0
$405$	1.11420	−	0.643285i	0.0553652	−	0.0319651i
$406$		0			0
$407$	7.72523	−	13.3805i	0.382926	−	0.663247i
$408$		0			0
$409$	13.5393	+	7.81689i	0.669473	+	0.386520i	0.795877	−	0.605458i	$-0.207010\pi$
$409$	13.5393	+	7.81689i	0.669473	+	0.386520i	−0.126404	+	0.991979i	$0.540344\pi$
$410$		0			0
$411$			8.75970i			0.432084i
$412$		0			0
$413$	−9.83879	−	17.0413i	−0.484135	−	0.838547i
$414$		0			0
$415$	−7.19716			−0.353295
$416$		0			0
$417$	14.9685			0.733010
$418$		0			0
$419$	−17.6540	−	30.5776i	−0.862453	−	1.49381i	−0.869554	−	0.493837i	$-0.835594\pi$
$419$	−17.6540	−	30.5776i	−0.862453	−	1.49381i	0.00710136	−	0.999975i	$-0.497740\pi$
$420$		0			0
$421$		−	36.6693i		−	1.78715i	−0.448912	−	0.893576i	$-0.648188\pi$
$421$		−	36.6693i		−	1.78715i	0.448912	−	0.893576i	$-0.351812\pi$
$422$		0			0
$423$	4.38050	+	2.52908i	0.212987	+	0.122968i
$424$		0			0
$425$	3.04784	−	5.27901i	0.147842	−	0.256070i
$426$		0			0
$427$	21.9141	−	12.6521i	1.06050	−	0.612277i
$428$		0			0
$429$	16.8970	−	10.4827i	0.815793	−	0.506111i
$430$		0			0
$431$	2.79243	−	1.61221i	0.134507	−	0.0776575i	−0.431237	−	0.902239i	$-0.641923\pi$
$431$	2.79243	−	1.61221i	0.134507	−	0.0776575i	0.565743	+	0.824581i	$0.308589\pi$
$432$		0			0
$433$	3.39825	−	5.88594i	0.163309	−	0.282860i	−0.772744	−	0.634718i	$-0.781116\pi$
$433$	3.39825	−	5.88594i	0.163309	−	0.282860i	0.936054	+	0.351857i	$0.114450\pi$
$434$		0			0
$435$	−2.48290	−	1.43350i	−0.119046	−	0.0687311i
$436$		0			0
$437$		−	56.4476i		−	2.70026i
$438$		0			0
$439$	4.41852	+	7.65311i	0.210885	+	0.365263i	0.951992	−	0.306124i	$-0.0990322\pi$
$439$	4.41852	+	7.65311i	0.210885	+	0.365263i	−0.741107	+	0.671387i	$0.765699\pi$
$440$		0			0
$441$	3.15661			0.150315
$442$		0			0
$443$	−9.08986			−0.431872			−0.215936	−	0.976407i	$-0.569280\pi$
$443$	−9.08986			−0.431872			−0.215936	+	0.976407i	$0.569280\pi$
$444$		0			0
$445$	9.66855	+	16.7464i	0.458333	+	0.793856i
$446$		0			0
$447$			7.78063i			0.368011i
$448$		0			0
$449$	−3.39561	−	1.96046i	−0.160249	−	0.0925197i	0.417731	−	0.908571i	$-0.362825\pi$
$449$	−3.39561	−	1.96046i	−0.160249	−	0.0925197i	−0.577980	+	0.816051i	$0.696159\pi$
$450$		0			0
$451$	12.6389	−	21.8911i	0.595141	−	1.03081i
$452$		0			0
$453$	−4.77611	+	2.75749i	−0.224401	+	0.129558i
$454$		0			0
$455$	4.79426	+	7.72780i	0.224758	+	0.362285i
$456$		0			0
$457$	21.7324	−	12.5472i	1.01660	−	0.586933i	0.103482	−	0.994631i	$-0.467002\pi$
$457$	21.7324	−	12.5472i	1.01660	−	0.586933i	0.913117	+	0.407698i	$0.133668\pi$
$458$		0			0
$459$	−0.911235	+	1.57830i	−0.0425328	+	0.0736690i
$460$		0			0
$461$	20.0799	+	11.5931i	0.935215	+	0.539947i	0.888457	−	0.458960i	$-0.151778\pi$
$461$	20.0799	+	11.5931i	0.935215	+	0.539947i	0.0467579	+	0.998906i	$0.485111\pi$
$462$		0			0
$463$			8.88866i			0.413091i	0.978437	+	0.206546i	$0.0662222\pi$
$463$			8.88866i			0.413091i	−0.978437	+	0.206546i	$0.933778\pi$
$464$		0			0
$465$	−2.85971	−	4.95317i	−0.132616	−	0.229698i
$466$		0			0
$467$	−23.1760			−1.07246			−0.536228	−	0.844073i	$-0.680151\pi$
$467$	−23.1760			−1.07246			−0.536228	+	0.844073i	$0.680151\pi$
$468$		0			0
$469$	4.69452			0.216773
$470$		0			0
$471$	10.2552	+	17.7625i	0.472534	+	0.818453i
$472$		0			0
$473$			29.7567i			1.36821i
$474$		0			0
$475$	−23.4283	−	13.5263i	−1.07496	−	0.620630i
$476$		0			0
$477$	1.22324	−	2.11872i	0.0560084	−	0.0970095i
$478$		0			0
$479$	−22.1672	+	12.7982i	−1.01285	+	0.584767i	−0.912024	−	0.410138i	$-0.865481\pi$
$479$	−22.1672	+	12.7982i	−1.01285	+	0.584767i	−0.100822	+	0.994904i	$0.532147\pi$
$480$		0			0
$481$	−0.319945	−	10.0961i	−0.0145882	−	0.460340i
$482$		0			0
$483$	11.8491	−	6.84109i	0.539153	−	0.311280i
$484$		0			0
$485$	8.97179	−	15.5396i	0.407388	−	0.705617i
$486$		0			0
$487$	−20.0151	−	11.5557i	−0.906971	−	0.523640i	−0.0275159	−	0.999621i	$-0.508760\pi$
$487$	−20.0151	−	11.5557i	−0.906971	−	0.523640i	−0.879455	+	0.475981i	$0.842093\pi$
$488$		0			0
$489$			18.3246i			0.828665i
$490$		0			0
$491$	2.42105	+	4.19338i	0.109260	+	0.189245i	0.915471	−	0.402384i	$-0.131818\pi$
$491$	2.42105	+	4.19338i	0.109260	+	0.189245i	−0.806210	+	0.591629i	$0.798485\pi$
$492$		0			0
$493$	4.06120			0.182907
$494$		0			0
$495$	7.09541			0.318915
$496$		0			0
$497$	−14.8192	−	25.6675i	−0.664730	−	1.15135i
$498$		0			0
$499$		−	40.8818i		−	1.83012i	−0.403319	−	0.915059i	$-0.632143\pi$
$499$		−	40.8818i		−	1.83012i	0.403319	−	0.915059i	$-0.367857\pi$
$500$		0			0
$501$	7.08083	+	4.08812i	0.316348	+	0.182644i
$502$		0			0
$503$	0.468618	−	0.811669i	0.0208946	−	0.0361906i	−0.855389	−	0.517986i	$-0.826682\pi$
$503$	0.468618	−	0.811669i	0.0208946	−	0.0361906i	0.876284	+	0.481796i	$0.160015\pi$
$504$		0			0
$505$	−5.85888	+	3.38263i	−0.260717	+	0.150525i
$506$		0			0
$507$	5.77412	−	11.6473i	0.256438	−	0.517275i
$508$		0			0
$509$	−19.0261	+	10.9847i	−0.843316	+	0.486889i	−0.858390	−	0.512997i	$-0.828535\pi$
$509$	−19.0261	+	10.9847i	−0.843316	+	0.486889i	0.0150738	+	0.999886i	$0.495202\pi$
$510$		0			0
$511$	2.57115	−	4.45336i	0.113741	−	0.197005i
$512$		0			0
$513$	7.00452	+	4.04406i	0.309257	+	0.178550i
$514$		0			0
$515$			9.51498i			0.419280i
$516$		0			0
$517$	13.9478	+	24.1584i	0.613425	+	1.06248i
$518$		0			0
$519$	8.57314			0.376319
$520$		0			0
$521$	22.1775			0.971615			0.485808	−	0.874066i	$-0.338526\pi$
$521$	22.1775			0.971615			0.485808	+	0.874066i	$0.338526\pi$
$522$		0			0
$523$	−7.15209	−	12.3878i	−0.312739	−	0.541680i	0.666215	−	0.745760i	$-0.267913\pi$
$523$	−7.15209	−	12.3878i	−0.312739	−	0.541680i	−0.978954	+	0.204079i	$0.934580\pi$
$524$		0			0
$525$		−	6.55721i		−	0.286180i
$526$		0			0
$527$	7.01632	+	4.05088i	0.305636	+	0.176459i
$528$		0			0
$529$	−12.8538	+	22.2634i	−0.558859	+	0.967973i
$530$		0			0
$531$	−8.69251	+	5.01862i	−0.377223	+	0.217790i
$532$		0			0
$533$	−0.523446	−	16.5176i	−0.0226729	−	0.715458i
$534$		0			0
$535$	−8.65769	+	4.99852i	−0.374305	+	0.216105i
$536$		0			0
$537$	−1.86552	+	3.23118i	−0.0805032	+	0.139436i
$538$		0			0
$539$	15.0763	+	8.70431i	0.649383	+	0.374921i
$540$		0			0
$541$		−	15.3779i		−	0.661149i	−0.943780	−	0.330575i	$-0.892757\pi$
$541$		−	15.3779i		−	0.661149i	0.943780	−	0.330575i	$-0.107243\pi$
$542$		0			0
$543$	2.62466	+	4.54605i	0.112635	+	0.195090i
$544$		0			0
$545$	16.0120			0.685878
$546$		0			0
$547$	11.1503			0.476751			0.238375	−	0.971173i	$-0.423385\pi$
$547$	11.1503			0.476751			0.238375	+	0.971173i	$0.423385\pi$
$548$		0			0
$549$	−6.45364	−	11.1780i	−0.275435	−	0.477067i
$550$		0			0
$551$		−	18.0236i		−	0.767832i
$552$		0			0
$553$	10.4527	+	6.03488i	0.444495	+	0.256629i
$554$		0			0
$555$	1.80219	−	3.12149i	0.0764989	−	0.132500i
$556$		0			0
$557$	−11.5261	+	6.65462i	−0.488378	+	0.281965i	−0.723901	−	0.689904i	$-0.757653\pi$
$557$	−11.5261	+	6.65462i	−0.488378	+	0.281965i	0.235523	+	0.971869i	$0.424320\pi$
$558$		0			0
$559$	10.2558	+	16.5312i	0.433776	+	0.699197i
$560$		0			0
$561$	−8.70431	+	5.02544i	−0.367496	+	0.212174i
$562$		0			0
$563$	3.88063	−	6.72146i	0.163549	−	0.283276i	−0.772590	−	0.634905i	$-0.781039\pi$
$563$	3.88063	−	6.72146i	0.163549	−	0.283276i	0.936139	+	0.351630i	$0.114372\pi$
$564$		0			0
$565$	−4.65462	−	2.68734i	−0.195821	−	0.113057i
$566$		0			0
$567$			1.96046i			0.0823314i
$568$		0			0
$569$	7.14932	+	12.3830i	0.299715	+	0.519122i	0.976071	−	0.217454i	$-0.0697751\pi$
$569$	7.14932	+	12.3830i	0.299715	+	0.519122i	−0.676356	+	0.736575i	$0.736442\pi$
$570$		0			0
$571$	29.6121			1.23923			0.619614	−	0.784906i	$-0.287289\pi$
$571$	29.6121			1.23923			0.619614	+	0.784906i	$0.287289\pi$
$572$		0			0
$573$	−5.54319			−0.231570
$574$		0			0
$575$	11.6716	+	20.2158i	0.486739	+	0.843056i
$576$		0			0
$577$			1.23475i			0.0514032i	0.999670	+	0.0257016i	$0.00818198\pi$
$577$			1.23475i			0.0514032i	−0.999670	+	0.0257016i	$0.991818\pi$
$578$		0			0
$579$	−8.82381	−	5.09443i	−0.366705	−	0.211717i
$580$		0			0
$581$	5.48346	−	9.49763i	0.227492	−	0.394028i
$582$		0			0
$583$	11.6847	−	6.74616i	0.483930	−	0.279397i
$584$		0			0
$585$	3.94184	−	2.44548i	0.162975	−	0.101108i
$586$		0			0
$587$	9.44796	−	5.45478i	0.389959	−	0.225143i	−0.292183	−	0.956362i	$-0.594382\pi$
$587$	9.44796	−	5.45478i	0.389959	−	0.225143i	0.682142	+	0.731219i	$0.261048\pi$
$588$		0			0
$589$	17.9778	−	31.1384i	0.740762	−	1.28304i
$590$		0			0
$591$	−22.3923	−	12.9282i	−0.921096	−	0.531795i
$592$		0			0
$593$			17.2775i			0.709503i	0.934961	+	0.354752i	$0.115435\pi$
$593$			17.2775i			0.709503i	−0.934961	+	0.354752i	$0.884565\pi$
$594$		0			0
$595$	−2.29838	−	3.98090i	−0.0942242	−	0.163201i
$596$		0			0
$597$	−12.5419			−0.513306
$598$		0			0
$599$	44.0533			1.79997			0.899984	−	0.435922i	$-0.143578\pi$
$599$	44.0533			1.79997			0.899984	+	0.435922i	$0.143578\pi$
$600$		0			0
$601$	2.17237	+	3.76265i	0.0886127	+	0.153482i	0.906925	−	0.421292i	$-0.138423\pi$
$601$	2.17237	+	3.76265i	0.0886127	+	0.153482i	−0.818312	+	0.574774i	$0.805090\pi$
$602$		0			0
$603$		−	2.39460i		−	0.0975158i
$604$		0			0
$605$	21.6322	+	12.4894i	0.879475	+	0.507765i
$606$		0			0
$607$	15.1044	−	26.1617i	0.613070	−	1.06187i	−0.377649	−	0.925949i	$-0.623268\pi$
$607$	15.1044	−	26.1617i	0.613070	−	1.06187i	0.990720	−	0.135920i	$-0.0433991\pi$
$608$		0			0
$609$	3.78340	−	2.18435i	0.153311	−	0.0885142i
$610$		0			0
$611$	16.0750	+	8.61389i	0.650326	+	0.348481i
$612$		0			0
$613$	5.74750	−	3.31832i	0.232139	−	0.134026i	−0.379419	−	0.925225i	$-0.623876\pi$
$613$	5.74750	−	3.31832i	0.232139	−	0.134026i	0.611559	+	0.791199i	$0.290543\pi$
$614$		0			0
$615$	2.94848	−	5.10691i	0.118894	−	0.205931i
$616$		0			0
$617$	21.2524	+	12.2701i	0.855589	+	0.493975i	0.862533	−	0.506001i	$-0.168877\pi$
$617$	21.2524	+	12.2701i	0.855589	+	0.493975i	−0.00694355	+	0.999976i	$0.502210\pi$
$618$		0			0
$619$			33.4563i			1.34472i	0.740224	+	0.672360i	$0.234719\pi$
$619$			33.4563i			1.34472i	−0.740224	+	0.672360i	$0.765281\pi$
$620$		0			0
$621$	−3.48954	−	6.04406i	−0.140030	−	0.242540i
$622$		0			0
$623$	−29.4656			−1.18051
$624$		0			0
$625$	2.91093			0.116437
$626$		0			0
$627$	22.3029	+	38.6297i	0.890692	+	1.54272i
$628$		0			0
$629$			5.10573i			0.203579i
$630$		0			0
$631$	12.4935	+	7.21315i	0.497360	+	0.287151i	0.727623	−	0.685978i	$-0.240625\pi$
$631$	12.4935	+	7.21315i	0.497360	+	0.287151i	−0.230263	+	0.973129i	$0.573959\pi$
$632$		0			0
$633$	6.20496	−	10.7473i	0.246625	−	0.427167i
$634$		0			0
$635$	−4.67793	+	2.70080i	−0.185638	+	0.107178i
$636$		0			0
$637$	11.3756	−	0.360494i	0.450718	−	0.0142833i
$638$		0			0
$639$	−13.0926	+	7.55904i	−0.517937	+	0.299031i
$640$		0			0
$641$	20.8112	−	36.0461i	0.821994	−	1.42374i	−0.0822011	−	0.996616i	$-0.526195\pi$
$641$	20.8112	−	36.0461i	0.821994	−	1.42374i	0.904195	−	0.427120i	$-0.140472\pi$
$642$		0			0
$643$	−10.1199	−	5.84271i	−0.399089	−	0.230414i	0.287002	−	0.957930i	$-0.407341\pi$
$643$	−10.1199	−	5.84271i	−0.399089	−	0.230414i	−0.686091	+	0.727516i	$0.740675\pi$
$644$		0			0
$645$			6.94184i			0.273334i
$646$		0			0
$647$	5.49736	+	9.52171i	0.216124	+	0.374337i	0.953620	−	0.301015i	$-0.0973253\pi$
$647$	5.49736	+	9.52171i	0.216124	+	0.374337i	−0.737496	+	0.675352i	$0.763992\pi$
$648$		0			0
$649$	−55.3552			−2.17288
$650$		0			0
$651$	8.71517			0.341574
$652$		0			0
$653$	−16.5595	−	28.6819i	−0.648024	−	1.12241i	−0.983594	−	0.180395i	$-0.942262\pi$
$653$	−16.5595	−	28.6819i	−0.648024	−	1.12241i	0.335571	−	0.942015i	$-0.391071\pi$
$654$		0			0
$655$		−	14.7973i		−	0.578178i
$656$		0			0
$657$	−2.27159	−	1.31151i	−0.0886233	−	0.0511667i
$658$		0			0
$659$	−11.0954	+	19.2178i	−0.432216	+	0.748620i	−0.997064	−	0.0765753i	$-0.975601\pi$
$659$	−11.0954	+	19.2178i	−0.432216	+	0.748620i	0.564848	+	0.825195i	$0.308935\pi$
$660$		0			0
$661$	17.1791	−	9.91838i	0.668191	−	0.385780i	−0.127200	−	0.991877i	$-0.540599\pi$
$661$	17.1791	−	9.91838i	0.668191	−	0.385780i	0.795391	+	0.606097i	$0.207266\pi$
$662$		0			0
$663$	−3.10361	+	5.79187i	−0.120534	+	0.224938i
$664$		0			0
$665$	−17.6673	+	10.2002i	−0.685107	+	0.395547i
$666$		0			0
$667$	−7.77611	+	13.4686i	−0.301092	+	0.521507i
$668$		0			0
$669$	−16.6134	−	9.59176i	−0.642312	−	0.370839i
$670$		0			0
$671$		−	71.1834i		−	2.74800i
$672$		0			0
$673$	19.4282	+	33.6506i	0.748902	+	1.29714i	0.948349	+	0.317228i	$0.102752\pi$
$673$	19.4282	+	33.6506i	0.748902	+	1.29714i	−0.199447	+	0.979909i	$0.563915\pi$
$674$		0			0
$675$	−3.34474			−0.128739
$676$		0			0
$677$	−40.8864			−1.57139			−0.785695	−	0.618614i	$-0.787695\pi$
$677$	−40.8864			−1.57139			−0.785695	+	0.618614i	$0.787695\pi$
$678$		0			0
$679$	13.6711	+	23.6790i	0.524648	+	0.908716i
$680$		0			0
$681$		−	10.5822i		−	0.405510i
$682$		0			0
$683$	38.3907	+	22.1649i	1.46898	+	0.848117i	0.999395	−	0.0347705i	$-0.0110700\pi$
$683$	38.3907	+	22.1649i	1.46898	+	0.848117i	0.469586	+	0.882887i	$0.344403\pi$
$684$		0			0
$685$	−5.63499	+	9.76009i	−0.215302	+	0.372914i
$686$		0			0
$687$	16.8524	−	9.72975i	0.642960	−	0.371213i
$688$		0			0
$689$	4.16629	−	7.77501i	0.158723	−	0.296204i
$690$		0			0
$691$	−11.0110	+	6.35722i	−0.418879	+	0.241840i	−0.694598	−	0.719398i	$-0.744418\pi$
$691$	−11.0110	+	6.35722i	−0.418879	+	0.241840i	0.275719	+	0.961238i	$0.411084\pi$
$692$		0			0
$693$	−5.40594	+	9.36336i	−0.205355	+	0.355685i
$694$		0			0
$695$	16.6779	+	9.62901i	0.632630	+	0.365249i
$696$		0			0
$697$			8.35323i			0.316401i
$698$		0			0
$699$	−13.7121	−	23.7501i	−0.518641	−	0.898312i
$700$		0			0
$701$	−13.9582			−0.527192			−0.263596	−	0.964633i	$-0.584909\pi$
$701$	−13.9582			−0.527192			−0.263596	+	0.964633i	$0.584909\pi$
$702$		0			0
$703$	22.6592			0.854610
$704$		0			0
$705$	3.25384	+	5.63582i	0.122547	+	0.212257i
$706$		0			0
$707$		−	10.3088i		−	0.387702i
$708$		0			0
$709$	−8.12455	−	4.69071i	−0.305124	−	0.176163i	0.339619	−	0.940563i	$-0.389702\pi$
$709$	−8.12455	−	4.69071i	−0.305124	−	0.176163i	−0.644742	+	0.764400i	$0.723035\pi$
$710$		0			0
$711$	3.07830	−	5.33178i	0.115445	−	0.199957i
$712$		0			0
$713$	−26.8687	+	15.5127i	−1.00624	+	0.580954i
$714$		0			0
$715$	25.5700	−	0.810317i	0.956265	−	0.0303041i
$716$		0			0
$717$	−2.39109	+	1.38050i	−0.0892971	+	0.0515557i
$718$		0			0
$719$	18.7806	−	32.5290i	0.700399	−	1.21313i	−0.267927	−	0.963439i	$-0.586339\pi$
$719$	18.7806	−	32.5290i	0.700399	−	1.21313i	0.968326	−	0.249688i	$-0.0803280\pi$
$720$		0			0
$721$	−12.5563	−	7.24939i	−0.467621	−	0.269981i
$722$		0			0
$723$			6.17753i			0.229745i
$724$		0			0
$725$	3.72671	+	6.45486i	0.138407	+	0.239727i
$726$		0			0
$727$	−25.5864			−0.948948			−0.474474	−	0.880270i	$-0.657362\pi$
$727$	−25.5864			−0.948948			−0.474474	+	0.880270i	$0.657362\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.91667	−	8.51592i	−0.181850	−	0.314973i
$732$		0			0
$733$		−	27.1633i		−	1.00330i	−0.865070	−	0.501650i	$-0.832726\pi$
$733$		−	27.1633i		−	1.00330i	0.865070	−	0.501650i	$-0.167274\pi$
$734$		0			0
$735$	3.51710	+	2.03060i	0.129730	+	0.0748998i
$736$		0			0
$737$	6.60310	−	11.4369i	0.243228	−	0.421283i
$738$		0			0
$739$	14.6673	−	8.46814i	0.539544	−	0.311506i	−0.205350	−	0.978689i	$-0.565833\pi$
$739$	14.6673	−	8.46814i	0.539544	−	0.311506i	0.744894	+	0.667183i	$0.232500\pi$
$740$		0			0
$741$	25.7043	+	13.7738i	0.944272	+	0.505994i
$742$		0			0
$743$	−16.2880	+	9.40391i	−0.597550	+	0.344996i	−0.768077	−	0.640357i	$-0.778786\pi$
$743$	−16.2880	+	9.40391i	−0.597550	+	0.344996i	0.170527	+	0.985353i	$0.445453\pi$
$744$		0			0
$745$	−5.00516	+	8.66920i	−0.183375	+	0.317615i
$746$		0			0
$747$	−4.84460	−	2.79703i	−0.177255	−	0.102338i
$748$		0			0
$749$		−	15.2333i		−	0.556614i
$750$		0			0
$751$	−1.73556	−	3.00608i	−0.0633315	−	0.109693i	0.832621	−	0.553843i	$-0.186839\pi$
$751$	−1.73556	−	3.00608i	−0.0633315	−	0.109693i	−0.895953	+	0.444150i	$0.853506\pi$
$752$		0			0
$753$	14.1163			0.514428
$754$		0			0
$755$	−7.09541			−0.258228
$756$		0			0
$757$	4.88367	+	8.45877i	0.177500	+	0.307439i	0.941024	−	0.338341i	$-0.109866\pi$
$757$	4.88367	+	8.45877i	0.177500	+	0.307439i	−0.763524	+	0.645780i	$0.776532\pi$
$758$		0			0
$759$		−	38.4895i		−	1.39708i
$760$		0			0
$761$	−10.5449	−	6.08812i	−0.382253	−	0.220694i	0.296545	−	0.955019i	$-0.404166\pi$
$761$	−10.5449	−	6.08812i	−0.382253	−	0.220694i	−0.678798	+	0.734325i	$0.737499\pi$
$762$		0			0
$763$	−12.1994	+	21.1300i	−0.441648	+	0.764957i
$764$		0			0
$765$	−2.03060	+	1.17237i	−0.0734165	+	0.0423870i
$766$		0			0
$767$	−30.7524	+	19.0785i	−1.11041	+	0.688886i
$768$		0			0
$769$	36.0938	−	20.8388i	1.30158	−	0.751466i	0.320903	−	0.947112i	$-0.396014\pi$
$769$	36.0938	−	20.8388i	1.30158	−	0.751466i	0.980675	+	0.195646i	$0.0626804\pi$
$770$		0			0
$771$	5.81123	−	10.0653i	0.209286	−	0.362494i
$772$		0			0
$773$	40.7430	+	23.5230i	1.46543	+	0.846064i	0.999254	−	0.0386307i	$-0.0122996\pi$
$773$	40.7430	+	23.5230i	1.46543	+	0.846064i	0.466172	+	0.884694i	$0.345633\pi$
$774$		0			0
$775$			14.8690i			0.534109i
$776$		0			0
$777$	2.74616	+	4.75648i	0.0985178	+	0.170638i
$778$		0			0
$779$	37.0716			1.32823
$780$		0			0
$781$	−83.3758			−2.98342
$782$		0			0
$783$	−1.11420	−	1.92986i	−0.0398184	−	0.0689674i
$784$		0			0
$785$			26.3881i			0.941830i
$786$		0			0
$787$	−3.69329	−	2.13232i	−0.131652	−	0.0760091i	0.432728	−	0.901525i	$-0.357551\pi$
$787$	−3.69329	−	2.13232i	−0.131652	−	0.0760091i	−0.564379	+	0.825516i	$0.690884\pi$
$788$		0			0
$789$	4.31201	−	7.46862i	0.153512	−	0.265890i
$790$		0			0
$791$	7.09263	−	4.09493i	0.252185	−	0.145599i
$792$		0			0
$793$	−24.5338	−	39.5457i	−0.871222	−	1.40431i
$794$		0			0
$795$	2.72588	−	1.57379i	0.0966771	−	0.0558165i
$796$		0			0
$797$	−15.7524	+	27.2840i	−0.557979	+	0.966448i	0.439686	+	0.898152i	$0.355090\pi$
$797$	−15.7524	+	27.2840i	−0.557979	+	0.966448i	−0.997665	+	0.0682966i	$0.978244\pi$
$798$		0			0
$799$	−7.98332	−	4.60917i	−0.282430	−	0.163061i
$800$		0			0
$801$			15.0300i			0.531057i
$802$		0			0
$803$	−7.23292	−	12.5278i	−0.255244	−	0.442096i
$804$		0			0
$805$	17.6031			0.620428
$806$		0			0
$807$	−25.2480			−0.888773
$808$		0			0
$809$	17.9502	+	31.0907i	0.631096	+	1.09309i	0.987328	+	0.158693i	$0.0507280\pi$
$809$	17.9502	+	31.0907i	0.631096	+	1.09309i	−0.356232	+	0.934398i	$0.615939\pi$
$810$		0			0
$811$		−	19.1515i		−	0.672502i	−0.941772	−	0.336251i	$-0.890841\pi$
$811$		−	19.1515i		−	0.672502i	0.941772	−	0.336251i	$-0.109159\pi$
$812$		0			0
$813$	−2.59632	−	1.49898i	−0.0910568	−	0.0525717i
$814$		0			0
$815$	−11.7879	+	20.4173i	−0.412913	+	0.715186i
$816$		0			0
$817$	−37.7936	+	21.8202i	−1.32223	+	0.763391i
$818$		0			0
$819$	0.223890	+	7.06498i	0.00782335	+	0.246870i
$820$		0			0
$821$	29.9765	−	17.3069i	1.04619	−	0.604016i	0.124607	−	0.992206i	$-0.460233\pi$
$821$	29.9765	−	17.3069i	1.04619	−	0.604016i	0.921579	+	0.388190i	$0.126900\pi$
$822$		0			0
$823$	−4.71012	+	8.15817i	−0.164185	+	0.284376i	−0.936365	−	0.351027i	$-0.885833\pi$
$823$	−4.71012	+	8.15817i	−0.164185	+	0.284376i	0.772181	+	0.635403i	$0.219166\pi$
$824$		0			0
$825$	−15.9748	−	9.22307i	−0.556172	−	0.321106i
$826$		0			0
$827$			9.40621i			0.327086i	0.986536	+	0.163543i	$0.0522922\pi$
$827$			9.40621i			0.327086i	−0.986536	+	0.163543i	$0.947708\pi$
$828$		0			0
$829$	−19.6808	−	34.0881i	−0.683541	−	1.18393i	−0.973893	−	0.227008i	$-0.927106\pi$
$829$	−19.6808	−	34.0881i	−0.683541	−	1.18393i	0.290352	−	0.956920i	$-0.406228\pi$
$830$		0			0
$831$	−24.9123			−0.864199
$832$		0			0
$833$	−5.75282			−0.199324
$834$		0			0
$835$	5.25965	+	9.10999i	0.182018	+	0.315264i
$836$		0			0
$837$		−	4.44548i		−	0.153658i
$838$		0			0
$839$	−26.4265	−	15.2574i	−0.912345	−	0.526742i	−0.0311597	−	0.999514i	$-0.509920\pi$
$839$	−26.4265	−	15.2574i	−0.912345	−	0.526742i	−0.881185	+	0.472772i	$0.843253\pi$
$840$		0			0
$841$	12.0171	−	20.8142i	0.414383	−	0.717732i
$842$		0			0
$843$	−7.25901	+	4.19099i	−0.250013	+	0.144345i
$844$		0			0
$845$	13.9261	−	9.26305i	0.479072	−	0.318659i
$846$		0			0
$847$	−32.9628	+	19.0311i	−1.13262	+	0.653916i
$848$		0			0
$849$	−12.9053	+	22.3526i	−0.442908	+	0.767140i
$850$		0			0
$851$	−16.9327	−	9.77611i	−0.580446	−	0.335121i
$852$		0			0
$853$		−	1.33219i		−	0.0456132i	−0.999740	−	0.0228066i	$-0.992740\pi$
$853$		−	1.33219i		−	0.0456132i	0.999740	−	0.0228066i	$-0.00726020\pi$
$854$		0			0
$855$	5.20297	+	9.01181i	0.177938	+	0.308197i
$856$		0			0
$857$	−0.771864			−0.0263664			−0.0131832	−	0.999913i	$-0.504196\pi$
$857$	−0.771864			−0.0263664			−0.0131832	+	0.999913i	$0.504196\pi$
$858$		0			0
$859$	5.09036			0.173681			0.0868404	−	0.996222i	$-0.472323\pi$
$859$	5.09036			0.173681			0.0868404	+	0.996222i	$0.472323\pi$
$860$		0			0
$861$	4.49285	+	7.78184i	0.153116	+	0.265204i
$862$		0			0
$863$			23.7264i			0.807658i	0.914835	+	0.403829i	$0.132321\pi$
$863$			23.7264i			0.807658i	−0.914835	+	0.403829i	$0.867679\pi$
$864$		0			0
$865$	9.55222	+	5.51498i	0.324785	+	0.187515i
$866$		0			0
$867$	−6.83930	+	11.8460i	−0.232275	+	0.402312i
$868$		0			0
$869$	29.4046	−	16.9768i	0.997484	−	0.575898i
$870$		0			0
$871$	−0.273471	−	8.62954i	−0.00926621	−	0.292401i
$872$		0			0
$873$	12.0783	−	6.97341i	0.408789	−	0.236014i
$874$		0			0
$875$	10.5238	−	18.2278i	0.355770	−	0.616212i
$876$		0			0
$877$	6.95326	+	4.01446i	0.234795	+	0.135559i	0.612782	−	0.790252i	$-0.290050\pi$
$877$	6.95326	+	4.01446i	0.234795	+	0.135559i	−0.377987	+	0.925811i	$0.623384\pi$
$878$		0			0
$879$		−	12.7527i		−	0.430137i
$880$		0			0
$881$	10.8727	+	18.8321i	0.366310	+	0.634468i	0.988986	−	0.148012i	$-0.0472875\pi$
$881$	10.8727	+	18.8321i	0.366310	+	0.634468i	−0.622675	+	0.782481i	$0.713954\pi$
$882$		0			0
$883$	−0.00504815			−0.000169884			−8.49419e−5	−	1.00000i	$-0.500027\pi$
$883$	−0.00504815			−0.000169884			−8.49419e−5		1.00000i	$0.500027\pi$
$884$		0			0
$885$	−12.9136			−0.434087
$886$		0			0
$887$	16.9252	+	29.3152i	0.568291	+	0.984310i	0.996735	+	0.0807412i	$0.0257287\pi$
$887$	16.9252	+	29.3152i	0.568291	+	0.984310i	−0.428444	+	0.903569i	$0.640938\pi$
$888$		0			0
$889$		−	8.23088i		−	0.276055i
$890$		0			0
$891$	4.77611	+	2.75749i	0.160006	+	0.0923793i
$892$		0			0
$893$	−20.4555	+	35.4300i	−0.684518	+	1.18562i
$894$		0			0
$895$	−4.15714	+	2.40013i	−0.138958	+	0.0802274i
$896$		0			0
$897$	−13.2656	−	21.3827i	−0.442927	−	0.713948i
$898$		0			0
$899$	−8.57914	+	4.95317i	−0.286130	+	0.165197i
$900$		0			0
$901$	−2.22932	+	3.86130i	−0.0742695	+	0.128639i
$902$		0			0
$903$	−9.16070	−	5.28893i	−0.304849	−	0.176005i
$904$		0			0
$905$			6.75363i			0.224498i
$906$		0			0
$907$	−12.6386	−	21.8907i	−0.419658	−	0.726868i	0.576247	−	0.817275i	$-0.304517\pi$
$907$	−12.6386	−	21.8907i	−0.419658	−	0.726868i	−0.995905	+	0.0904070i	$0.971183\pi$
$908$		0			0
$909$	−5.25836			−0.174409
$910$		0			0
$911$	15.5366			0.514750			0.257375	−	0.966312i	$-0.417142\pi$
$911$	15.5366			0.514750			0.257375	+	0.966312i	$0.417142\pi$
$912$		0			0
$913$	−15.4256	−	26.7179i	−0.510512	−	0.884232i
$914$		0			0
$915$		−	16.6061i		−	0.548982i
$916$		0			0
$917$	19.5270	+	11.2739i	0.644840	+	0.372298i
$918$		0			0
$919$	−25.2571	+	43.7465i	−0.833154	+	1.44306i	0.0623711	+	0.998053i	$0.480134\pi$
$919$	−25.2571	+	43.7465i	−0.833154	+	1.44306i	−0.895525	+	0.445012i	$0.853200\pi$
$920$		0			0
$921$	14.4027	−	8.31537i	0.474583	−	0.274001i
$922$		0			0
$923$	−46.3192	+	28.7360i	−1.52462	+	0.945858i
$924$		0			0
$925$	−8.11504	+	4.68522i	−0.266821	+	0.154049i
$926$		0			0
$927$	−3.69781	+	6.40479i	−0.121452	+	0.210361i
$928$		0			0
$929$	10.7214	+	6.18998i	0.351757	+	0.203087i	0.665459	−	0.746435i	$-0.268236\pi$
$929$	10.7214	+	6.18998i	0.351757	+	0.203087i	−0.313702	+	0.949521i	$0.601569\pi$
$930$		0			0
$931$			25.5310i			0.836746i
$932$		0			0
$933$	9.69702	+	16.7957i	0.317466	+	0.549868i
$934$		0			0
$935$	−12.9312			−0.422894
$936$		0			0
$937$	17.5721			0.574056			0.287028	−	0.957922i	$-0.407333\pi$
$937$	17.5721			0.574056			0.287028	+	0.957922i	$0.407333\pi$
$938$		0			0
$939$	−13.2545	−	22.9575i	−0.432546	−	0.749191i
$940$		0			0
$941$			51.8438i			1.69006i	0.534718	+	0.845030i	$0.320418\pi$
$941$			51.8438i			1.69006i	−0.534718	+	0.845030i	$0.679582\pi$
$942$		0			0
$943$	−27.7027	−	15.9942i	−0.902126	−	0.520842i
$944$		0			0
$945$	−1.26113	+	2.18435i	−0.0410247	+	0.0710568i
$946$		0			0
$947$	19.0652	−	11.0073i	0.619535	−	0.357689i	−0.157153	−	0.987574i	$-0.550232\pi$
$947$	19.0652	−	11.0073i	0.619535	−	0.357689i	0.776688	+	0.629885i	$0.216898\pi$
$948$		0			0
$949$	−8.33602	−	4.46690i	−0.270599	−	0.145002i
$950$		0			0
$951$	7.04571	−	4.06784i	0.228473	−	0.131909i
$952$		0			0
$953$	12.7716	−	22.1210i	0.413713	−	0.716571i	−0.581580	−	0.813489i	$-0.697565\pi$
$953$	12.7716	−	22.1210i	0.413713	−	0.716571i	0.995292	+	0.0969182i	$0.0308985\pi$
$954$		0			0
$955$	−6.17624	−	3.56585i	−0.199858	−	0.115388i
$956$		0			0
$957$		−	12.2896i		−	0.397267i
$958$		0			0
$959$	−8.58651	−	14.8723i	−0.277273	−	0.480251i
$960$		0			0
$961$	11.2377			0.362507
$962$		0			0
$963$	−7.77030			−0.250394
$964$		0			0
$965$	−6.55435	−	11.3525i	−0.210992	−	0.365449i
$966$		0			0
$967$		−	14.8939i		−	0.478956i	−0.970902	−	0.239478i	$-0.923024\pi$
$967$		−	14.8939i		−	0.478956i	0.970902	−	0.239478i	$-0.0769763\pi$
$968$		0			0
$969$	−12.7655	−	7.37017i	−0.410087	−	0.236764i
$970$		0			0
$971$	−4.94184	+	8.55951i	−0.158591	+	0.274688i	−0.934361	−	0.356328i	$-0.884028\pi$
$971$	−4.94184	+	8.55951i	−0.158591	+	0.274688i	0.775770	+	0.631016i	$0.217362\pi$
$972$		0			0
$973$	−25.4136	+	14.6725i	−0.814722	+	0.470380i
$974$		0			0
$975$	−12.0536	+	0.381979i	−0.386023	+	0.0122331i
$976$		0			0
$977$	43.0005	−	24.8263i	1.37571	−	0.794265i	0.384068	−	0.923305i	$-0.374523\pi$
$977$	43.0005	−	24.8263i	1.37571	−	0.794265i	0.991639	+	0.129040i	$0.0411896\pi$
$978$		0			0
$979$	−41.4449	+	71.7847i	−1.32459	+	2.29425i
$980$		0			0
$981$	10.7781	+	6.22274i	0.344118	+	0.198677i
$982$		0			0
$983$			4.41350i			0.140769i	0.997520	+	0.0703843i	$0.0224226\pi$
$983$			4.41350i			0.140769i	−0.997520	+	0.0703843i	$0.977577\pi$
$984$		0			0
$985$	−16.6330	−	28.8093i	−0.529973	−	0.917940i
$986$		0			0
$987$	−9.91631			−0.315640
$988$		0			0
$989$	37.6564			1.19740
$990$		0			0
$991$	−0.401421	−	0.695281i	−0.0127516	−	0.0220863i	0.859579	−	0.511003i	$-0.170726\pi$
$991$	−0.401421	−	0.695281i	−0.0127516	−	0.0220863i	−0.872331	+	0.488916i	$0.837392\pi$
$992$		0			0
$993$			31.9861i			1.01505i
$994$		0			0
$995$	−13.9742	−	8.06802i	−0.443012	−	0.255773i
$996$		0			0
$997$	−3.97165	+	6.87911i	−0.125784	+	0.217863i	−0.922039	−	0.387097i	$-0.873478\pi$
$997$	−3.97165	+	6.87911i	−0.125784	+	0.217863i	0.796255	+	0.604961i	$0.206811\pi$
$998$		0			0
$999$	2.42621	−	1.40077i	0.0767619	−	0.0443185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bv.g.49.3		8
3.2	odd	2		1872.2.by.m.1297.2		8
4.3	odd	2		312.2.bf.b.49.3	✓	8
12.11	even	2		936.2.bi.c.361.2		8
13.2	odd	12		8112.2.a.cq.1.4		4
13.4	even	6	inner	624.2.bv.g.433.2		8
13.11	odd	12		8112.2.a.cs.1.1		4
39.17	odd	6		1872.2.by.m.433.3		8
52.3	odd	6		4056.2.c.p.337.6		8
52.11	even	12		4056.2.a.be.1.1		4
52.15	even	12		4056.2.a.bd.1.4		4
52.23	odd	6		4056.2.c.p.337.3		8
52.43	odd	6		312.2.bf.b.121.2	yes	8
156.95	even	6		936.2.bi.c.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bf.b.49.3	✓	8	4.3	odd	2
312.2.bf.b.121.2	yes	8	52.43	odd	6
624.2.bv.g.49.3		8	1.1	even	1	trivial
624.2.bv.g.433.2		8	13.4	even	6	inner
936.2.bi.c.361.2		8	12.11	even	2
936.2.bi.c.433.3		8	156.95	even	6
1872.2.by.m.433.3		8	39.17	odd	6
1872.2.by.m.1297.2		8	3.2	odd	2
4056.2.a.bd.1.4		4	52.15	even	12
4056.2.a.be.1.1		4	52.11	even	12
4056.2.c.p.337.3		8	52.23	odd	6
4056.2.c.p.337.6		8	52.3	odd	6
8112.2.a.cq.1.4		4	13.2	odd	12
8112.2.a.cs.1.1		4	13.11	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +1.28657i q^{5} +(-1.69781 - 0.980228i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +1.28657i q^{5} +(-1.69781 - 0.980228i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-4.77611 + 2.75749i) q^{11} +(-1.70297 + 3.17803i) q^{13} +(-1.11420 + 0.643285i) q^{15} +(0.911235 - 1.57830i) q^{17} +(-7.00452 - 4.04406i) q^{19} -1.96046i q^{21} +(3.48954 + 6.04406i) q^{23} +3.34474 q^{25} -1.00000 q^{27} +(1.11420 + 1.92986i) q^{29} +4.44548i q^{31} +(-4.77611 - 2.75749i) q^{33} +(1.26113 - 2.18435i) q^{35} +(-2.42621 + 1.40077i) q^{37} +(-3.60374 + 0.114203i) q^{39} +(-3.96940 + 2.29173i) q^{41} +(2.69781 - 4.67274i) q^{43} +(-1.11420 - 0.643285i) q^{45} -5.05816i q^{47} +(-1.57830 - 2.73370i) q^{49} +1.82247 q^{51} -2.44649 q^{53} +(-3.54770 - 6.14480i) q^{55} -8.08812i q^{57} +(8.69251 + 5.01862i) q^{59} +(-6.45364 + 11.1780i) q^{61} +(1.69781 - 0.980228i) q^{63} +(-4.08877 - 2.19099i) q^{65} +(-2.07379 + 1.19730i) q^{67} +(-3.48954 + 6.04406i) q^{69} +(13.0926 + 7.55904i) q^{71} +2.62301i q^{73} +(1.67237 + 2.89663i) q^{75} +10.8119 q^{77} -6.15661 q^{79} +(-0.500000 - 0.866025i) q^{81} +5.59406i q^{83} +(2.03060 + 1.17237i) q^{85} +(-1.11420 + 1.92986i) q^{87} +(13.0163 - 7.51498i) q^{89} +(6.00651 - 3.72638i) q^{91} +(-3.84990 + 2.22274i) q^{93} +(5.20297 - 9.01181i) q^{95} +(-12.0783 - 6.97341i) q^{97} -5.51498i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51} + 4 q^{53} + 10 q^{55} + 36 q^{59} + 2 q^{61} - 28 q^{65} - 36 q^{67} - 2 q^{69} - 6 q^{71} - 2 q^{75} + 56 q^{77} + 12 q^{79} - 4 q^{81} + 24 q^{85} - 6 q^{87} - 12 q^{89} - 38 q^{91} - 6 q^{93} + 34 q^{95} - 66 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 + 12 * q^17 - 6 * q^19 + 2 * q^23 - 4 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^33 - 10 * q^35 - 24 * q^41 + 8 * q^43 - 6 * q^45 + 18 * q^49 + 24 * q^51 + 4 * q^53 + 10 * q^55 + 36 * q^59 + 2 * q^61 - 28 * q^65 - 36 * q^67 - 2 * q^69 - 6 * q^71 - 2 * q^75 + 56 * q^77 + 12 * q^79 - 4 * q^81 + 24 * q^85 - 6 * q^87 - 12 * q^89 - 38 * q^91 - 6 * q^93 + 34 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more