LMFDB - Embedded newform 630.2.u.a.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(109,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("630.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.u (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.289
Dual form			630.2.u.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(-2.23205 + 0.133975i) q^{10} +(1.50000 + 2.59808i) q^{11} +5.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-2.00000 - 1.00000i) q^{20} +3.00000i q^{22} +(6.06218 + 3.50000i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(2.59808 + 0.500000i) q^{28} -4.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +2.00000 q^{34} +(-0.767949 + 5.86603i) q^{35} +(-0.866025 - 0.500000i) q^{37} +(-4.33013 + 2.50000i) q^{38} +(-1.23205 - 1.86603i) q^{40} -3.00000 q^{41} -2.00000i q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-6.06218 - 3.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(4.00000 - 3.00000i) q^{50} +(-4.33013 + 2.50000i) q^{52} +(7.79423 - 4.50000i) q^{53} +(-6.00000 - 3.00000i) q^{55} +(2.00000 + 1.73205i) q^{56} +(-3.46410 - 2.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} +2.00000i q^{62} -1.00000 q^{64} +(-6.16025 - 9.33013i) q^{65} +(1.73205 - 1.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(-3.59808 + 4.69615i) q^{70} +6.00000 q^{71} +(13.8564 - 8.00000i) q^{73} +(-0.500000 - 0.866025i) q^{74} -5.00000 q^{76} +(7.79423 + 1.50000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.133975 - 2.23205i) q^{80} +(-2.59808 - 1.50000i) q^{82} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(10.0000 + 8.66025i) q^{91} +7.00000i q^{92} +(-3.50000 - 6.06218i) q^{94} +(-0.669873 - 11.1603i) q^{95} -12.0000i q^{97} +(2.59808 - 6.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{5}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^5	$ 4 q + 2 q^{4} - 4 q^{5} - 2 q^{10} + 6 q^{11} + 10 q^{14} - 2 q^{16} - 10 q^{19} - 8 q^{20} - 6 q^{25} - 10 q^{26} - 16 q^{29} + 4 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{40} - 12 q^{41} - 6 q^{44} + 14 q^{46} - 4 q^{49} + 16 q^{50} - 24 q^{55} + 8 q^{56} + 8 q^{59} - 12 q^{61} - 4 q^{64} + 10 q^{65} - 4 q^{70} + 24 q^{71} - 2 q^{74} - 20 q^{76} + 28 q^{79} - 4 q^{80} - 8 q^{85} + 4 q^{86} - 4 q^{89} + 40 q^{91} - 14 q^{94} - 20 q^{95}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^5 - 2 * q^10 + 6 * q^11 + 10 * q^14 - 2 * q^16 - 10 * q^19 - 8 * q^20 - 6 * q^25 - 10 * q^26 - 16 * q^29 + 4 * q^31 + 8 * q^34 - 10 * q^35 + 2 * q^40 - 12 * q^41 - 6 * q^44 + 14 * q^46 - 4 * q^49 + 16 * q^50 - 24 * q^55 + 8 * q^56 + 8 * q^59 - 12 * q^61 - 4 * q^64 + 10 * q^65 - 4 * q^70 + 24 * q^71 - 2 * q^74 - 20 * q^76 + 28 * q^79 - 4 * q^80 - 8 * q^85 + 4 * q^86 - 4 * q^89 + 40 * q^91 - 14 * q^94 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$6$		0			0
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.23205	+	0.133975i	−0.705836	+	0.0423665i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	0.695113	+	0.718900i	$0.255354\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$		0			0
$22$			3.00000i			0.639602i
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.973856	−	0.227167i	$-0.0729463\pi$
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.290196	+	0.956967i	$0.406280\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	−2.50000	+	4.33013i	−0.490290	+	0.849208i
$27$		0			0
$28$	2.59808	+	0.500000i	0.490990	+	0.0944911i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	2.00000			0.342997
$35$	−0.767949	+	5.86603i	−0.129807	+	0.991539i
$36$		0			0
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	0.427121	−	0.904194i	$-0.359528\pi$
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	−0.569495	+	0.821995i	$0.692861\pi$
$38$	−4.33013	+	2.50000i	−0.702439	+	0.405554i
$39$		0			0
$40$	−1.23205	−	1.86603i	−0.194804	−	0.295045i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	−6.06218	−	3.50000i	−0.884260	−	0.510527i	−0.0121990	−	0.999926i	$-0.503883\pi$
$47$	−6.06218	−	3.50000i	−0.884260	−	0.510527i	−0.872060	+	0.489398i	$0.837217\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$	−4.33013	+	2.50000i	−0.600481	+	0.346688i
$53$	7.79423	−	4.50000i	1.07062	−	0.618123i	0.142269	−	0.989828i	$-0.454560\pi$
$53$	7.79423	−	4.50000i	1.07062	−	0.618123i	0.928351	+	0.371706i	$0.121227\pi$
$54$		0			0
$55$	−6.00000	−	3.00000i	−0.809040	−	0.404520i
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$	−3.46410	−	2.00000i	−0.454859	−	0.262613i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$			2.00000i			0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.16025	−	9.33013i	−0.764085	−	1.15726i
$66$		0			0
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	1.73205	+	1.00000i	0.210042	+	0.121268i
$69$		0			0
$70$	−3.59808	+	4.69615i	−0.430052	+	0.561298i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	13.8564	−	8.00000i	1.62177	−	0.936329i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	13.8564	−	8.00000i	1.62177	−	0.936329i	0.986447	−	0.164083i	$-0.0524664\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	−5.00000			−0.573539
$77$	7.79423	+	1.50000i	0.888235	+	0.170941i
$78$		0			0
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$	−0.133975	−	2.23205i	−0.0149788	−	0.249551i
$81$		0			0
$82$	−2.59808	−	1.50000i	−0.286910	−	0.165647i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$	−2.00000	+	4.00000i	−0.216930	+	0.433861i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$		0			0
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	10.0000	+	8.66025i	1.04828	+	0.907841i
$92$			7.00000i			0.729800i
$93$		0			0
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$	−0.669873	−	11.1603i	−0.0687275	−	1.14502i
$96$		0			0
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$	2.59808	−	6.50000i	0.262445	−	0.656599i
$99$		0			0
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−6.92820	−	4.00000i	−0.682656	−	0.394132i	0.118199	−	0.992990i	$-0.462288\pi$
$103$	−6.92820	−	4.00000i	−0.682656	−	0.394132i	−0.800855	+	0.598858i	$0.795621\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	9.00000			0.874157
$107$	−13.8564	−	8.00000i	−1.33955	−	0.773389i	−0.352809	−	0.935695i	$-0.614773\pi$
$107$	−13.8564	−	8.00000i	−1.33955	−	0.773389i	−0.986740	+	0.162306i	$0.948107\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−3.69615	−	5.59808i	−0.352414	−	0.533756i
$111$		0			0
$112$	0.866025	+	2.50000i	0.0818317	+	0.236228i
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	−15.6244	+	0.937822i	−1.45698	+	0.0874524i
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$		0			0
$118$			4.00000i			0.368230i
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−5.19615	+	3.00000i	−0.470438	+	0.271607i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$			7.00000i			0.621150i	0.950549	+	0.310575i	$0.100522\pi$
$127$			7.00000i			0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.669873	−	11.1603i	−0.0587517	−	0.978819i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	4.33013	+	12.5000i	0.375470	+	1.08389i
$134$	2.00000			0.172774
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	6.92820	−	4.00000i	0.591916	−	0.341743i	−0.173939	−	0.984757i	$-0.555649\pi$
$137$	6.92820	−	4.00000i	0.591916	−	0.341743i	0.765855	+	0.643013i	$0.222316\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$	−5.46410	+	2.26795i	−0.461801	+	0.191677i
$141$		0			0
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$	−12.9904	+	7.50000i	−1.08631	+	0.627182i
$144$		0			0
$145$	7.46410	−	4.92820i	0.619860	−	0.409265i
$146$	16.0000			1.32417
$147$		0			0
$148$		−	1.00000i		−	0.0821995i
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	0.961888	−	0.273442i	$-0.0881622\pi$
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	−0.717752	+	0.696299i	$0.754829\pi$
$152$	−4.33013	−	2.50000i	−0.351220	−	0.202777i
$153$		0			0
$154$	6.00000	+	5.19615i	0.483494	+	0.418718i
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$		0			0
$157$	−7.79423	+	4.50000i	−0.622047	+	0.359139i	−0.777666	−	0.628678i	$-0.783596\pi$
$157$	−7.79423	+	4.50000i	−0.622047	+	0.359139i	0.155618	+	0.987817i	$0.450263\pi$
$158$	12.1244	−	7.00000i	0.964562	−	0.556890i
$159$		0			0
$160$	1.00000	−	2.00000i	0.0790569	−	0.158114i
$161$	17.5000	−	6.06218i	1.37919	−	0.477767i
$162$		0			0
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	0.0343508	−	0.999410i	$-0.489064\pi$
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	−0.848339	+	0.529454i	$0.822397\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$		−	15.0000i		−	1.16073i	−0.814355	−	0.580367i	$-0.802909\pi$
$167$		−	15.0000i		−	1.16073i	0.814355	−	0.580367i	$-0.197091\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−3.73205	+	2.46410i	−0.286235	+	0.188988i
$171$		0			0
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	−7.79423	−	4.50000i	−0.592584	−	0.342129i	0.173534	−	0.984828i	$-0.444481\pi$
$173$	−7.79423	−	4.50000i	−0.592584	−	0.342129i	−0.766119	+	0.642699i	$0.777815\pi$
$174$		0			0
$175$	−5.79423	−	11.8923i	−0.438003	−	0.898974i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	−1.73205	+	1.00000i	−0.129823	+	0.0749532i
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	0.514035	−	0.857769i	$-0.328150\pi$
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	−0.999867	+	0.0162823i	$0.994817\pi$
$180$		0			0
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$	4.33013	+	12.5000i	0.320970	+	0.926562i
$183$		0			0
$184$	−3.50000	+	6.06218i	−0.258023	+	0.446910i
$185$	2.23205	−	0.133975i	0.164104	−	0.00985001i
$186$		0			0
$187$	5.19615	+	3.00000i	0.379980	+	0.219382i
$188$		−	7.00000i		−	0.510527i
$189$		0			0
$190$	5.00000	−	10.0000i	0.362738	−	0.725476i
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$		0			0
$193$	8.66025	−	5.00000i	0.623379	−	0.359908i	−0.154805	−	0.987945i	$-0.549475\pi$
$193$	8.66025	−	5.00000i	0.623379	−	0.359908i	0.778183	+	0.628037i	$0.216141\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$			5.00000i			0.356235i	0.984009	+	0.178118i	$0.0570008\pi$
$197$			5.00000i			0.356235i	−0.984009	+	0.178118i	$0.942999\pi$
$198$		0			0
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	0.985873	+	0.167497i	$0.0535685\pi$
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	−0.347879	+	0.937539i	$0.613098\pi$
$200$	4.59808	+	1.96410i	0.325133	+	0.138883i
$201$		0			0
$202$		0			0
$203$	−6.92820	+	8.00000i	−0.486265	+	0.561490i
$204$		0			0
$205$	5.59808	−	3.69615i	0.390987	−	0.258150i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$	−4.33013	−	2.50000i	−0.300240	−	0.173344i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	7.79423	+	4.50000i	0.535310	+	0.309061i
$213$		0			0
$214$	−8.00000	−	13.8564i	−0.546869	−	0.947204i
$215$	2.46410	+	3.73205i	0.168050	+	0.254524i
$216$		0			0
$217$	5.19615	+	1.00000i	0.352738	+	0.0678844i
$218$			2.00000i			0.135457i
$219$		0			0
$220$	−0.401924	−	6.69615i	−0.0270977	−	0.451455i
$221$	5.00000	+	8.66025i	0.336336	+	0.582552i
$222$		0			0
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	−7.00000	+	12.1244i	−0.465633	+	0.806500i
$227$	5.19615	−	3.00000i	0.344881	−	0.199117i	−0.317547	−	0.948242i	$-0.602859\pi$
$227$	5.19615	−	3.00000i	0.344881	−	0.199117i	0.662428	+	0.749125i	$0.269526\pi$
$228$		0			0
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	−0.470787	−	0.882247i	$-0.656030\pi$
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	0.999442	−	0.0334101i	$-0.0106368\pi$
$230$	−14.0000	−	7.00000i	−0.923133	−	0.461566i
$231$		0			0
$232$		−	4.00000i		−	0.262613i
$233$	6.92820	+	4.00000i	0.453882	+	0.262049i	0.709468	−	0.704737i	$-0.248935\pi$
$233$	6.92820	+	4.00000i	0.453882	+	0.262049i	−0.255586	+	0.966786i	$0.582269\pi$
$234$		0			0
$235$	15.6244	−	0.937822i	1.01922	−	0.0611768i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$		0			0
$238$	3.46410	−	4.00000i	0.224544	−	0.259281i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	0.973779	−	0.227498i	$-0.0730544\pi$
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	−0.683908	+	0.729568i	$0.739721\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$		0			0
$244$	−6.00000			−0.384111
$245$	10.4019	+	11.6962i	0.664555	+	0.747240i
$246$		0			0
$247$	−21.6506	−	12.5000i	−1.37760	−	0.795356i
$248$	−1.73205	+	1.00000i	−0.109985	+	0.0635001i
$249$		0			0
$250$	−3.76795	+	10.5263i	−0.238306	+	0.665740i
$251$	−5.00000			−0.315597			−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000			−0.315597			−0.157799	+	0.987471i	$0.550440\pi$
$252$		0			0
$253$			21.0000i			1.32026i
$254$	−3.50000	+	6.06218i	−0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.19615	−	3.00000i	−0.324127	−	0.187135i	0.329104	−	0.944294i	$-0.393253\pi$
$257$	−5.19615	−	3.00000i	−0.324127	−	0.187135i	−0.653231	+	0.757159i	$0.726587\pi$
$258$		0			0
$259$	−2.50000	+	0.866025i	−0.155342	+	0.0538122i
$260$	5.00000	−	10.0000i	0.310087	−	0.620174i
$261$		0			0
$262$	−0.866025	+	0.500000i	−0.0535032	+	0.0308901i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$	−9.00000	+	18.0000i	−0.552866	+	1.10573i
$266$	−2.50000	+	12.9904i	−0.153285	+	0.796491i
$267$		0			0
$268$	1.73205	+	1.00000i	0.105802	+	0.0610847i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$		0			0
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	0.228380	+	0.973572i	$0.426657\pi$
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	−0.957328	+	0.289003i	$0.906676\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	8.00000			0.483298
$275$	14.8923	−	1.79423i	0.898040	−	0.108196i
$276$		0			0
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	−13.8564	−	8.00000i	−0.831052	−	0.479808i
$279$		0			0
$280$	−5.86603	−	0.767949i	−0.350562	−	0.0458937i
$281$	−9.00000			−0.536895			−0.268447	−	0.963294i	$-0.586511\pi$
$281$	−9.00000			−0.536895			−0.268447	+	0.963294i	$0.586511\pi$
$282$		0			0
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	−0.815017	−	0.579437i	$-0.803272\pi$
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	0.0942988	+	0.995544i	$0.469939\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	−15.0000			−0.886969
$287$	−5.19615	+	6.00000i	−0.306719	+	0.354169i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$	8.92820	−	0.535898i	0.524282	−	0.0314690i
$291$		0			0
$292$	13.8564	+	8.00000i	0.810885	+	0.468165i
$293$		−	9.00000i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$		0			0
$295$	−8.00000	−	4.00000i	−0.465778	−	0.232889i
$296$	0.500000	−	0.866025i	0.0290619	−	0.0503367i
$297$		0			0
$298$	15.5885	−	9.00000i	0.903015	−	0.521356i
$299$	−17.5000	+	30.3109i	−1.01205	+	1.75292i
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$			6.00000i			0.345261i
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	−0.803848	−	13.3923i	−0.0460282	−	0.766841i
$306$		0			0
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$	2.59808	+	7.50000i	0.148039	+	0.427352i
$309$		0			0
$310$	−2.46410	−	3.73205i	−0.139952	−	0.211966i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$		0			0
$313$	−19.0526	−	11.0000i	−1.07691	−	0.621757i	−0.146852	−	0.989158i	$-0.546914\pi$
$313$	−19.0526	−	11.0000i	−1.07691	−	0.621757i	−0.930062	+	0.367402i	$0.880247\pi$
$314$	−9.00000			−0.507899
$315$		0			0
$316$	14.0000			0.787562
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	0.450570	−	0.892741i	$-0.351221\pi$
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	−0.547852	+	0.836576i	$0.684554\pi$
$318$		0			0
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	1.86603	−	1.23205i	0.104314	−	0.0688737i
$321$		0			0
$322$	18.1865	+	3.50000i	1.01350	+	0.195047i
$323$			10.0000i			0.556415i
$324$		0			0
$325$	22.9904	+	9.82051i	1.27528	+	0.544744i
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$		0			0
$328$		−	3.00000i		−	0.165647i
$329$	−17.5000	+	6.06218i	−0.964806	+	0.334219i
$330$		0			0
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	−0.926516	−	0.376254i	$-0.877212\pi$
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	0.789104	+	0.614260i	$0.210545\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$		0			0
$334$	7.50000	−	12.9904i	0.410382	−	0.710802i
$335$	−2.00000	+	4.00000i	−0.109272	+	0.218543i
$336$		0			0
$337$			10.0000i			0.544735i	0.962193	+	0.272367i	$0.0878066\pi$
$337$			10.0000i			0.544735i	−0.962193	+	0.272367i	$0.912193\pi$
$338$	−10.3923	−	6.00000i	−0.565267	−	0.326357i
$339$		0			0
$340$	−4.46410	+	0.267949i	−0.242100	+	0.0145316i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	2.00000			0.107833
$345$		0			0
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$		0			0
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$	0.928203	−	13.1962i	0.0496145	−	0.705364i
$351$		0			0
$352$	−2.59808	−	1.50000i	−0.138478	−	0.0799503i
$353$	20.7846	−	12.0000i	1.10625	−	0.638696i	0.168397	−	0.985719i	$-0.446141\pi$
$353$	20.7846	−	12.0000i	1.10625	−	0.638696i	0.937856	+	0.347024i	$0.112808\pi$
$354$		0			0
$355$	−11.1962	+	7.39230i	−0.594230	+	0.392343i
$356$	−2.00000			−0.106000
$357$		0			0
$358$		−	13.0000i		−	0.687071i
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	−0.996157	−	0.0875892i	$-0.972084\pi$
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	0.573933	+	0.818902i	$0.305417\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	22.5167	+	13.0000i	1.18345	+	0.683265i
$363$		0			0
$364$	−2.50000	+	12.9904i	−0.131036	+	0.680881i
$365$	−16.0000	+	32.0000i	−0.837478	+	1.67496i
$366$		0			0
$367$	11.2583	−	6.50000i	0.587680	−	0.339297i	−0.176500	−	0.984301i	$-0.556477\pi$
$367$	11.2583	−	6.50000i	0.587680	−	0.339297i	0.764180	+	0.645003i	$0.223144\pi$
$368$	−6.06218	+	3.50000i	−0.316013	+	0.182450i
$369$		0			0
$370$	2.00000	+	1.00000i	0.103975	+	0.0519875i
$371$	4.50000	−	23.3827i	0.233628	−	1.21397i
$372$		0			0
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.952703	−	0.303902i	$-0.0982894\pi$
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.213165	+	0.977016i	$0.431623\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$		0			0
$376$	3.50000	−	6.06218i	0.180499	−	0.312633i
$377$		−	20.0000i		−	1.03005i
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	9.33013	−	6.16025i	0.478625	−	0.316014i
$381$		0			0
$382$	−17.3205	+	10.0000i	−0.886194	+	0.511645i
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.0427020	−	0.999088i	$-0.513597\pi$
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.886586	+	0.462563i	$0.846930\pi$
$384$		0			0
$385$	−16.3923	+	6.80385i	−0.835429	+	0.346756i
$386$	10.0000			0.508987
$387$		0			0
$388$	10.3923	−	6.00000i	0.527589	−	0.304604i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$	6.92820	−	1.00000i	0.349927	−	0.0505076i
$393$		0			0
$394$	−2.50000	+	4.33013i	−0.125948	+	0.218149i
$395$	1.87564	+	31.2487i	0.0943739	+	1.57229i
$396$		0			0
$397$	12.1244	+	7.00000i	0.608504	+	0.351320i	0.772380	−	0.635161i	$-0.219066\pi$
$397$	12.1244	+	7.00000i	0.608504	+	0.351320i	−0.163876	+	0.986481i	$0.552400\pi$
$398$			18.0000i			0.902258i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$		0			0
$403$	−8.66025	+	5.00000i	−0.431398	+	0.249068i
$404$		0			0
$405$		0			0
$406$	−10.0000	+	3.46410i	−0.496292	+	0.171920i
$407$		−	3.00000i		−	0.148704i
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	6.69615	−	0.401924i	0.330699	−	0.0198496i
$411$		0			0
$412$		−	8.00000i		−	0.394132i
$413$	10.3923	+	2.00000i	0.511372	+	0.0984136i
$414$		0			0
$415$	7.39230	+	11.1962i	0.362874	+	0.549598i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$		0			0
$418$	−12.9904	−	7.50000i	−0.635380	−	0.366837i
$419$	35.0000			1.70986			0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000			1.70986			0.854931	+	0.518742i	$0.173599\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	−7.79423	−	4.50000i	−0.379417	−	0.219057i
$423$		0			0
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−1.19615	−	9.92820i	−0.0580219	−	0.481589i
$426$		0			0
$427$	5.19615	+	15.0000i	0.251459	+	0.725901i
$428$		−	16.0000i		−	0.773389i
$429$		0			0
$430$	0.267949	+	4.46410i	0.0129217	+	0.215278i
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$		0			0
$433$		−	28.0000i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$433$		−	28.0000i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$434$	4.00000	+	3.46410i	0.192006	+	0.166282i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−30.3109	+	17.5000i	−1.44997	+	0.837139i
$438$		0			0
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$	3.00000	−	6.00000i	0.143019	−	0.286039i
$441$		0			0
$442$			10.0000i			0.475651i
$443$	−25.9808	−	15.0000i	−1.23438	−	0.712672i	−0.266443	−	0.963851i	$-0.585848\pi$
$443$	−25.9808	−	15.0000i	−1.23438	−	0.712672i	−0.967941	+	0.251179i	$0.919182\pi$
$444$		0			0
$445$	−0.267949	−	4.46410i	−0.0127020	−	0.211619i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	−1.73205	+	2.00000i	−0.0818317	+	0.0944911i
$449$	5.00000			0.235965			0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000			0.235965			0.117982	+	0.993016i	$0.462357\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−12.1244	+	7.00000i	−0.570282	+	0.329252i
$453$		0			0
$454$	6.00000			0.281594
$455$	−29.3301	−	3.83975i	−1.37502	−	0.180010i
$456$		0			0
$457$	8.66025	+	5.00000i	0.405110	+	0.233890i	0.688686	−	0.725059i	$-0.258188\pi$
$457$	8.66025	+	5.00000i	0.405110	+	0.233890i	−0.283577	+	0.958950i	$0.591521\pi$
$458$	13.8564	−	8.00000i	0.647467	−	0.373815i
$459$		0			0
$460$	−8.62436	−	13.0622i	−0.402113	−	0.609027i
$461$	32.0000			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$462$		0			0
$463$			17.0000i			0.790057i	0.918669	+	0.395029i	$0.129265\pi$
$463$			17.0000i			0.790057i	−0.918669	+	0.395029i	$0.870735\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$		0			0
$466$	4.00000	+	6.92820i	0.185296	+	0.320943i
$467$	29.4449	+	17.0000i	1.36255	+	0.786666i	0.989962	−	0.141332i	$-0.0451386\pi$
$467$	29.4449	+	17.0000i	1.36255	+	0.786666i	0.372584	+	0.927999i	$0.378472\pi$
$468$		0			0
$469$	1.00000	−	5.19615i	0.0461757	−	0.239936i
$470$	14.0000	+	7.00000i	0.645772	+	0.322886i
$471$		0			0
$472$	−3.46410	+	2.00000i	−0.159448	+	0.0920575i
$473$	5.19615	−	3.00000i	0.238919	−	0.137940i
$474$		0			0
$475$	15.0000	+	20.0000i	0.688247	+	0.917663i
$476$	5.00000	−	1.73205i	0.229175	−	0.0793884i
$477$		0			0
$478$	17.3205	+	10.0000i	0.792222	+	0.457389i
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	−0.903859	−	0.427830i	$-0.859278\pi$
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	0.0814184	−	0.996680i	$-0.474055\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$			9.00000i			0.409939i
$483$		0			0
$484$	2.00000			0.0909091
$485$	14.7846	+	22.3923i	0.671335	+	1.01678i
$486$		0			0
$487$	−27.7128	+	16.0000i	−1.25579	+	0.725029i	−0.972253	−	0.233933i	$-0.924840\pi$
$487$	−27.7128	+	16.0000i	−1.25579	+	0.725029i	−0.283535	+	0.958962i	$0.591507\pi$
$488$	−5.19615	−	3.00000i	−0.235219	−	0.135804i
$489$		0			0
$490$	3.16025	+	15.3301i	0.142766	+	0.692545i
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$		0			0
$493$	−6.92820	+	4.00000i	−0.312031	+	0.180151i
$494$	−12.5000	−	21.6506i	−0.562402	−	0.974108i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	10.3923	−	12.0000i	0.466159	−	0.538274i
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−8.52628	+	7.23205i	−0.381307	+	0.323427i
$501$		0			0
$502$	−4.33013	−	2.50000i	−0.193263	−	0.111580i
$503$			40.0000i			1.78351i	0.452517	+	0.891756i	$0.350526\pi$
$503$			40.0000i			1.78351i	−0.452517	+	0.891756i	$0.649474\pi$
$504$		0			0
$505$		0			0
$506$	−10.5000	+	18.1865i	−0.466782	+	0.808490i
$507$		0			0
$508$	−6.06218	+	3.50000i	−0.268966	+	0.155287i
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	−0.192599	−	0.981278i	$-0.561692\pi$
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	0.946111	−	0.323843i	$-0.104975\pi$
$510$		0			0
$511$	8.00000	−	41.5692i	0.353899	−	1.83891i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	17.8564	−	1.07180i	0.786847	−	0.0472290i
$516$		0			0
$517$		−	21.0000i		−	0.923579i
$518$	−2.59808	−	0.500000i	−0.114153	−	0.0219687i
$519$		0			0
$520$	9.33013	−	6.16025i	0.409153	−	0.270145i
$521$	−13.5000	−	23.3827i	−0.591446	−	1.02441i	−0.994038	−	0.109035i	$-0.965224\pi$
$521$	−13.5000	−	23.3827i	−0.591446	−	1.02441i	0.402592	−	0.915379i	$-0.368109\pi$
$522$		0			0
$523$	13.8564	+	8.00000i	0.605898	+	0.349816i	0.771358	−	0.636401i	$-0.219578\pi$
$523$	13.8564	+	8.00000i	0.605898	+	0.349816i	−0.165460	+	0.986216i	$0.552911\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$		0			0
$527$	3.46410	+	2.00000i	0.150899	+	0.0871214i
$528$		0			0
$529$	13.0000	+	22.5167i	0.565217	+	0.978985i
$530$	−16.7942	+	11.0885i	−0.729495	+	0.481652i
$531$		0			0
$532$	−8.66025	+	10.0000i	−0.375470	+	0.433555i
$533$		−	15.0000i		−	0.649722i
$534$		0			0
$535$	35.7128	−	2.14359i	1.54400	−	0.0926756i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$		0			0
$538$			10.0000i			0.431131i
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$	−20.7846	+	12.0000i	−0.892775	+	0.515444i
$543$		0			0
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−4.00000	−	2.00000i	−0.171341	−	0.0856706i
$546$		0			0
$547$		−	26.0000i		−	1.11168i	−0.831289	−	0.555840i	$-0.812397\pi$
$547$		−	26.0000i		−	1.11168i	0.831289	−	0.555840i	$-0.187603\pi$
$548$	6.92820	+	4.00000i	0.295958	+	0.170872i
$549$		0			0
$550$	13.7942	+	5.89230i	0.588188	+	0.251249i
$551$	10.0000	−	17.3205i	0.426014	−	0.737878i
$552$		0			0
$553$	−12.1244	−	35.0000i	−0.515580	−	1.48835i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−19.9186	+	11.5000i	−0.843978	+	0.487271i	−0.858614	−	0.512622i	$-0.828674\pi$
$557$	−19.9186	+	11.5000i	−0.843978	+	0.487271i	0.0146368	+	0.999893i	$0.495341\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$	−4.69615	−	3.59808i	−0.198449	−	0.152046i
$561$		0			0
$562$	−7.79423	−	4.50000i	−0.328780	−	0.189821i
$563$	1.73205	−	1.00000i	0.0729972	−	0.0421450i	−0.463057	−	0.886328i	$-0.653248\pi$
$563$	1.73205	−	1.00000i	0.0729972	−	0.0421450i	0.536054	+	0.844183i	$0.319914\pi$
$564$		0			0
$565$	−17.2487	−	26.1244i	−0.725659	−	1.09906i
$566$	−14.0000			−0.588464
$567$		0			0
$568$			6.00000i			0.251754i
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	−12.9904	−	7.50000i	−0.543155	−	0.313591i
$573$		0			0
$574$	−7.50000	+	2.59808i	−0.313044	+	0.108442i
$575$	28.0000	−	21.0000i	1.16768	−	0.875761i
$576$		0			0
$577$	−3.46410	+	2.00000i	−0.144212	+	0.0832611i	−0.570370	−	0.821388i	$-0.693200\pi$
$577$	−3.46410	+	2.00000i	−0.144212	+	0.0832611i	0.426158	+	0.904649i	$0.359867\pi$
$578$	−11.2583	+	6.50000i	−0.468285	+	0.270364i
$579$		0			0
$580$	8.00000	+	4.00000i	0.332182	+	0.166091i
$581$	−12.0000	−	10.3923i	−0.497844	−	0.431145i
$582$		0			0
$583$	23.3827	+	13.5000i	0.968412	+	0.559113i
$584$	8.00000	+	13.8564i	0.331042	+	0.573382i
$585$		0			0
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$		−	34.0000i		−	1.40333i	−0.712507	−	0.701665i	$-0.752440\pi$
$587$		−	34.0000i		−	1.40333i	0.712507	−	0.701665i	$-0.247560\pi$
$588$		0			0
$589$	−10.0000			−0.412043
$590$	−4.92820	−	7.46410i	−0.202891	−	0.307292i
$591$		0			0
$592$	0.866025	−	0.500000i	0.0355934	−	0.0205499i
$593$	5.19615	+	3.00000i	0.213380	+	0.123195i	0.602881	−	0.797831i	$-0.294019\pi$
$593$	5.19615	+	3.00000i	0.213380	+	0.123195i	−0.389501	+	0.921026i	$0.627353\pi$
$594$		0			0
$595$	4.53590	+	10.9282i	0.185954	+	0.448013i
$596$	18.0000			0.737309
$597$		0			0
$598$	−30.3109	+	17.5000i	−1.23950	+	0.715628i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−1.73205	−	5.00000i	−0.0705931	−	0.203785i
$603$		0			0
$604$	−3.00000	+	5.19615i	−0.122068	+	0.211428i
$605$	0.267949	+	4.46410i	0.0108937	+	0.181492i
$606$		0			0
$607$	11.2583	+	6.50000i	0.456962	+	0.263827i	0.710766	−	0.703429i	$-0.248349\pi$
$607$	11.2583	+	6.50000i	0.456962	+	0.263827i	−0.253804	+	0.967256i	$0.581682\pi$
$608$		−	5.00000i		−	0.202777i
$609$		0			0
$610$	6.00000	−	12.0000i	0.242933	−	0.485866i
$611$	17.5000	−	30.3109i	0.707974	−	1.22625i
$612$		0			0
$613$	12.9904	−	7.50000i	0.524677	−	0.302922i	−0.214169	−	0.976797i	$-0.568704\pi$
$613$	12.9904	−	7.50000i	0.524677	−	0.302922i	0.738846	+	0.673874i	$0.235371\pi$
$614$	11.0000	−	19.0526i	0.443924	−	0.768899i
$615$		0			0
$616$	−1.50000	+	7.79423i	−0.0604367	+	0.314038i
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$		0			0
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	−0.267949	−	4.46410i	−0.0107611	−	0.179283i
$621$		0			0
$622$			6.00000i			0.240578i
$623$	1.73205	+	5.00000i	0.0693932	+	0.200321i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−11.0000	−	19.0526i	−0.439648	−	0.761493i
$627$		0			0
$628$	−7.79423	−	4.50000i	−0.311024	−	0.179570i
$629$	−2.00000			−0.0797452
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	12.1244	+	7.00000i	0.482281	+	0.278445i
$633$		0			0
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−8.62436	−	13.0622i	−0.342247	−	0.518357i
$636$		0			0
$637$	34.6410	−	5.00000i	1.37253	−	0.198107i
$638$		−	12.0000i		−	0.475085i
$639$		0			0
$640$	2.23205	−	0.133975i	0.0882296	−	0.00529581i
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	0.812421	−	0.583071i	$-0.198149\pi$
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	−0.911165	+	0.412042i	$0.864816\pi$
$642$		0			0
$643$			14.0000i			0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$	14.0000	+	12.1244i	0.551677	+	0.477767i
$645$		0			0
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.0358667	−	0.999357i	$-0.488581\pi$
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.883402	+	0.468617i	$0.155247\pi$
$648$		0			0
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$	15.0000	+	20.0000i	0.588348	+	0.784465i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$	−2.59808	−	1.50000i	−0.101671	−	0.0586995i	0.448303	−	0.893882i	$-0.352029\pi$
$653$	−2.59808	−	1.50000i	−0.101671	−	0.0586995i	−0.549973	+	0.835182i	$0.685362\pi$
$654$		0			0
$655$	−0.133975	−	2.23205i	−0.00523482	−	0.0872134i
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$		0			0
$658$	−18.1865	−	3.50000i	−0.708985	−	0.136444i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−8.00000	−	13.8564i	−0.311164	−	0.538952i	0.667451	−	0.744654i	$-0.267385\pi$
$661$	−8.00000	−	13.8564i	−0.311164	−	0.538952i	−0.978615	+	0.205702i	$0.934052\pi$
$662$	−4.33013	+	2.50000i	−0.168295	+	0.0971653i
$663$		0			0
$664$	6.00000			0.232845
$665$	−23.4808	−	17.9904i	−0.910545	−	0.697637i
$666$		0			0
$667$	−24.2487	−	14.0000i	−0.938914	−	0.542082i
$668$	12.9904	−	7.50000i	0.502613	−	0.290184i
$669$		0			0
$670$	−3.73205	+	2.46410i	−0.144182	+	0.0951966i
$671$	−18.0000			−0.694882
$672$		0			0
$673$		−	32.0000i		−	1.23351i	−0.787155	−	0.616755i	$-0.788447\pi$
$673$		−	32.0000i		−	1.23351i	0.787155	−	0.616755i	$-0.211553\pi$
$674$	−5.00000	+	8.66025i	−0.192593	+	0.333581i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−14.7224	−	8.50000i	−0.565829	−	0.326682i	0.189653	−	0.981851i	$-0.439264\pi$
$677$	−14.7224	−	8.50000i	−0.565829	−	0.326682i	−0.755482	+	0.655170i	$0.772597\pi$
$678$		0			0
$679$	−24.0000	−	20.7846i	−0.921035	−	0.797640i
$680$	−4.00000	−	2.00000i	−0.153393	−	0.0766965i
$681$		0			0
$682$	−5.19615	+	3.00000i	−0.198971	+	0.114876i
$683$	−38.1051	+	22.0000i	−1.45805	+	0.841807i	−0.998916	−	0.0465592i	$-0.985174\pi$
$683$	−38.1051	+	22.0000i	−1.45805	+	0.841807i	−0.459136	+	0.888366i	$0.651841\pi$
$684$		0			0
$685$	−8.00000	+	16.0000i	−0.305664	+	0.611329i
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$		0			0
$688$	1.73205	+	1.00000i	0.0660338	+	0.0381246i
$689$	22.5000	+	38.9711i	0.857182	+	1.48468i
$690$		0			0
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	−0.0555386	−	0.998457i	$-0.517688\pi$
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	0.892458	−	0.451130i	$-0.148979\pi$
$692$		−	9.00000i		−	0.342129i
$693$		0			0
$694$	12.0000			0.455514
$695$	29.8564	−	19.7128i	1.13252	−	0.747750i
$696$		0			0
$697$	−5.19615	+	3.00000i	−0.196818	+	0.113633i
$698$	10.3923	+	6.00000i	0.393355	+	0.227103i
$699$		0			0
$700$	7.40192	−	10.9641i	0.279766	−	0.414404i
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$		0			0
$703$	4.33013	−	2.50000i	0.163314	−	0.0942893i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$		0			0
$709$	6.00000	−	10.3923i	0.225335	−	0.390291i	−0.731085	−	0.682286i	$-0.760986\pi$
$709$	6.00000	−	10.3923i	0.225335	−	0.390291i	0.956420	+	0.291995i	$0.0943191\pi$
$710$	−13.3923	+	0.803848i	−0.502604	+	0.0301679i
$711$		0			0
$712$	−1.73205	−	1.00000i	−0.0649113	−	0.0374766i
$713$			14.0000i			0.524304i
$714$		0			0
$715$	15.0000	−	30.0000i	0.560968	−	1.12194i
$716$	6.50000	−	11.2583i	0.242916	−	0.420744i
$717$		0			0
$718$	−13.8564	+	8.00000i	−0.517116	+	0.298557i
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	−0.999848	−	0.0174426i	$-0.994448\pi$
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	0.515030	+	0.857172i	$0.327781\pi$
$720$		0			0
$721$	−20.0000	+	6.92820i	−0.744839	+	0.258020i
$722$		−	6.00000i		−	0.223297i
$723$		0			0
$724$	13.0000	+	22.5167i	0.483141	+	0.836825i
$725$	−7.85641	+	18.3923i	−0.291780	+	0.683073i
$726$		0			0
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$	−8.66025	+	10.0000i	−0.320970	+	0.370625i
$729$		0			0
$730$	−29.8564	+	19.7128i	−1.10504	+	0.729604i
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$		0			0
$733$	35.5070	+	20.5000i	1.31148	+	0.757185i	0.982342	−	0.187096i	$-0.0599076\pi$
$733$	35.5070	+	20.5000i	1.31148	+	0.757185i	0.329141	+	0.944281i	$0.393241\pi$
$734$	13.0000			0.479839
$735$		0			0
$736$	−7.00000			−0.258023
$737$	5.19615	+	3.00000i	0.191403	+	0.110506i
$738$		0			0
$739$	−14.5000	−	25.1147i	−0.533391	−	0.923861i	−0.999239	−	0.0389959i	$-0.987584\pi$
$739$	−14.5000	−	25.1147i	−0.533391	−	0.923861i	0.465848	−	0.884865i	$-0.345749\pi$
$740$	1.23205	+	1.86603i	0.0452911	+	0.0685965i
$741$		0			0
$742$	15.5885	−	18.0000i	0.572270	−	0.660801i
$743$		−	21.0000i		−	0.770415i	−0.922830	−	0.385208i	$-0.874130\pi$
$743$		−	21.0000i		−	0.770415i	0.922830	−	0.385208i	$-0.125870\pi$
$744$		0			0
$745$	2.41154	+	40.1769i	0.0883521	+	1.47197i
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$		0			0
$748$			6.00000i			0.219382i
$749$	−40.0000	+	13.8564i	−1.46157	+	0.506302i
$750$		0			0
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	6.06218	−	3.50000i	0.221065	−	0.127632i
$753$		0			0
$754$	10.0000	−	17.3205i	0.364179	−	0.630776i
$755$	−12.0000	−	6.00000i	−0.436725	−	0.218362i
$756$		0			0
$757$			42.0000i			1.52652i	0.646094	+	0.763258i	$0.276401\pi$
$757$			42.0000i			1.52652i	−0.646094	+	0.763258i	$0.723599\pi$
$758$	25.1147	+	14.5000i	0.912208	+	0.526664i
$759$		0			0
$760$	11.1603	−	0.669873i	0.404825	−	0.0242988i
$761$	0.500000	−	0.866025i	0.0181250	−	0.0313934i	−0.856821	−	0.515615i	$-0.827564\pi$
$761$	0.500000	−	0.866025i	0.0181250	−	0.0313934i	0.874946	+	0.484221i	$0.160897\pi$
$762$		0			0
$763$	5.19615	+	1.00000i	0.188113	+	0.0362024i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$	−17.3205	+	10.0000i	−0.625407	+	0.361079i
$768$		0			0
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$	−17.5981	−	2.30385i	−0.634191	−	0.0830249i
$771$		0			0
$772$	8.66025	+	5.00000i	0.311689	+	0.179954i
$773$	38.9711	−	22.5000i	1.40169	−	0.809269i	0.407128	−	0.913371i	$-0.366530\pi$
$773$	38.9711	−	22.5000i	1.40169	−	0.809269i	0.994567	+	0.104102i	$0.0331970\pi$
$774$		0			0
$775$	9.92820	−	1.19615i	0.356632	−	0.0429671i
$776$	12.0000			0.430775
$777$		0			0
$778$			6.00000i			0.215110i
$779$	7.50000	−	12.9904i	0.268715	−	0.465429i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	12.1244	+	7.00000i	0.433566	+	0.250319i
$783$		0			0
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$	9.00000	−	18.0000i	0.321224	−	0.642448i
$786$		0			0
$787$	15.5885	−	9.00000i	0.555668	−	0.320815i	−0.195737	−	0.980656i	$-0.562710\pi$
$787$	15.5885	−	9.00000i	0.555668	−	0.320815i	0.751405	+	0.659841i	$0.229376\pi$
$788$	−4.33013	+	2.50000i	−0.154254	+	0.0890588i
$789$		0			0
$790$	−14.0000	+	28.0000i	−0.498098	+	0.996195i
$791$	28.0000	+	24.2487i	0.995565	+	0.862185i
$792$		0			0
$793$	−25.9808	−	15.0000i	−0.922604	−	0.532666i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	−9.00000	+	15.5885i	−0.318997	+	0.552518i
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$	−14.0000			−0.495284
$800$	0.598076	+	4.96410i	0.0211452	+	0.175507i
$801$		0			0
$802$	−12.9904	+	7.50000i	−0.458706	+	0.264834i
$803$	41.5692	+	24.0000i	1.46695	+	0.846942i
$804$		0			0
$805$	−25.1865	+	32.8731i	−0.887709	+	1.15862i
$806$	−10.0000			−0.352235
$807$		0			0
$808$		0			0
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	0.906621	−	0.421945i	$-0.138653\pi$
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	−0.818726	+	0.574184i	$0.805319\pi$
$810$		0			0
$811$	−33.0000			−1.15879			−0.579393	−	0.815048i	$-0.696710\pi$
$811$	−33.0000			−1.15879			−0.579393	+	0.815048i	$0.696710\pi$
$812$	−10.3923	−	2.00000i	−0.364698	−	0.0701862i
$813$		0			0
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$	26.7846	−	1.60770i	0.938224	−	0.0563151i
$816$		0			0
$817$	8.66025	+	5.00000i	0.302984	+	0.174928i
$818$		−	14.0000i		−	0.489499i
$819$		0			0
$820$	6.00000	+	3.00000i	0.209529	+	0.104765i
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$		0			0
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	−0.0919029	−	0.995768i	$-0.529295\pi$
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	0.816409	+	0.577474i	$0.195962\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$		0			0
$826$	8.00000	+	6.92820i	0.278356	+	0.241063i
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$		0			0
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	0.546971	−	0.837151i	$-0.315781\pi$
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	−0.998480	+	0.0551154i	$0.982447\pi$
$830$	0.803848	+	13.3923i	0.0279020	+	0.464854i
$831$		0			0
$832$		−	5.00000i		−	0.173344i
$833$	−8.66025	−	11.0000i	−0.300060	−	0.381127i
$834$		0			0
$835$	18.4808	+	27.9904i	0.639553	+	0.968647i
$836$	−7.50000	−	12.9904i	−0.259393	−	0.449282i
$837$		0			0
$838$	30.3109	+	17.5000i	1.04707	+	0.604527i
$839$	−34.0000			−1.17381			−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000			−1.17381			−0.586905	+	0.809656i	$0.699654\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−17.3205	−	10.0000i	−0.596904	−	0.344623i
$843$		0			0
$844$	−4.50000	−	7.79423i	−0.154896	−	0.268288i
$845$	22.3923	−	14.7846i	0.770319	−	0.508606i
$846$		0			0
$847$	−1.73205	−	5.00000i	−0.0595140	−	0.171802i
$848$			9.00000i			0.309061i
$849$		0			0
$850$	3.92820	−	9.19615i	0.134736	−	0.315425i
$851$	−3.50000	−	6.06218i	−0.119978	−	0.207809i
$852$		0			0
$853$			43.0000i			1.47229i	0.676823	+	0.736146i	$0.263356\pi$
$853$			43.0000i			1.47229i	−0.676823	+	0.736146i	$0.736644\pi$
$854$	−3.00000	+	15.5885i	−0.102658	+	0.533426i
$855$		0			0
$856$	8.00000	−	13.8564i	0.273434	−	0.473602i
$857$	−6.92820	+	4.00000i	−0.236663	+	0.136637i	−0.613642	−	0.789584i	$-0.710296\pi$
$857$	−6.92820	+	4.00000i	−0.236663	+	0.136637i	0.376979	+	0.926222i	$0.376963\pi$
$858$		0			0
$859$	−6.00000	+	10.3923i	−0.204717	+	0.354581i	−0.950043	−	0.312120i	$-0.898961\pi$
$859$	−6.00000	+	10.3923i	−0.204717	+	0.354581i	0.745325	+	0.666701i	$0.232294\pi$
$860$	−2.00000	+	4.00000i	−0.0681994	+	0.136399i
$861$		0			0
$862$			2.00000i			0.0681203i
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	0.653298	−	0.757101i	$-0.273385\pi$
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	−0.329020	+	0.944323i	$0.606718\pi$
$864$		0			0
$865$	20.0885	−	1.20577i	0.683028	−	0.0409975i
$866$	14.0000	−	24.2487i	0.475739	−	0.824005i
$867$		0			0
$868$	1.73205	+	5.00000i	0.0587896	+	0.169711i
$869$	42.0000			1.42475
$870$		0			0
$871$	5.00000	+	8.66025i	0.169419	+	0.293442i
$872$	−1.73205	+	1.00000i	−0.0586546	+	0.0338643i
$873$		0			0
$874$	−35.0000			−1.18389
$875$	25.4641	+	15.0526i	0.860844	+	0.508869i
$876$		0			0
$877$	−26.8468	−	15.5000i	−0.906552	−	0.523398i	−0.0272316	−	0.999629i	$-0.508669\pi$
$877$	−26.8468	−	15.5000i	−0.906552	−	0.523398i	−0.879320	+	0.476231i	$0.842002\pi$
$878$	−24.2487	+	14.0000i	−0.818354	+	0.472477i
$879$		0			0
$880$	5.59808	−	3.69615i	0.188711	−	0.124597i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$	−5.00000	+	8.66025i	−0.168168	+	0.291276i
$885$		0			0
$886$	−15.0000	−	25.9808i	−0.503935	−	0.872841i
$887$	31.1769	+	18.0000i	1.04682	+	0.604381i	0.921757	−	0.387768i	$-0.126754\pi$
$887$	31.1769	+	18.0000i	1.04682	+	0.604381i	0.125061	+	0.992149i	$0.460087\pi$
$888$		0			0
$889$	14.0000	+	12.1244i	0.469545	+	0.406638i
$890$	2.00000	−	4.00000i	0.0670402	−	0.134080i
$891$		0			0
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$	30.3109	−	17.5000i	1.01432	−	0.585615i
$894$		0			0
$895$	26.0000	+	13.0000i	0.869084	+	0.434542i
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$		0			0
$898$	4.33013	+	2.50000i	0.144498	+	0.0834261i
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		−	9.00000i		−	0.299667i
$903$		0			0
$904$	−14.0000			−0.465633
$905$	−48.5167	+	32.0333i	−1.61275	+	1.06482i
$906$		0			0
$907$	−34.6410	+	20.0000i	−1.15024	+	0.664089i	−0.948945	−	0.315442i	$-0.897847\pi$
$907$	−34.6410	+	20.0000i	−1.15024	+	0.664089i	−0.201291	+	0.979531i	$0.564514\pi$
$908$	5.19615	+	3.00000i	0.172440	+	0.0995585i
$909$		0			0
$910$	−23.4808	−	17.9904i	−0.778380	−	0.596375i
$911$	−2.00000			−0.0662630			−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000			−0.0662630			−0.0331315	+	0.999451i	$0.510548\pi$
$912$		0			0
$913$	15.5885	−	9.00000i	0.515903	−	0.297857i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	16.0000			0.528655
$917$	0.866025	+	2.50000i	0.0285987	+	0.0825573i
$918$		0			0
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	−0.652616	−	0.757689i	$-0.726329\pi$
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	0.982486	+	0.186338i	$0.0596619\pi$
$920$	−0.937822	−	15.6244i	−0.0309191	−	0.515120i
$921$		0			0
$922$	27.7128	+	16.0000i	0.912673	+	0.526932i
$923$			30.0000i			0.987462i
$924$		0			0
$925$	−4.00000	+	3.00000i	−0.131519	+	0.0986394i
$926$	−8.50000	+	14.7224i	−0.279327	+	0.483809i
$927$		0			0
$928$	3.46410	−	2.00000i	0.113715	−	0.0656532i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	32.5000	+	12.9904i	1.06514	+	0.425743i
$932$			8.00000i			0.262049i
$933$		0			0
$934$	17.0000	+	29.4449i	0.556257	+	0.963465i
$935$	−13.3923	+	0.803848i	−0.437975	+	0.0262886i
$936$		0			0
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$	3.46410	−	4.00000i	0.113107	−	0.130605i
$939$		0			0
$940$	8.62436	+	13.0622i	0.281295	+	0.426041i
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	0.542380	−	0.840133i	$-0.317523\pi$
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	−0.998767	+	0.0496480i	$0.984190\pi$
$942$		0			0
$943$	−18.1865	−	10.5000i	−0.592235	−	0.341927i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	6.00000			0.195077
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$		0			0
$949$	40.0000	+	69.2820i	1.29845	+	2.24899i
$950$	2.99038	+	24.8205i	0.0970208	+	0.805284i
$951$		0			0
$952$	5.19615	+	1.00000i	0.168408	+	0.0324102i
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	−2.67949	−	44.6410i	−0.0867063	−	1.44455i
$956$	10.0000	+	17.3205i	0.323423	+	0.560185i
$957$		0			0
$958$		−	36.0000i		−	1.16311i
$959$	4.00000	−	20.7846i	0.129167	−	0.671170i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	4.33013	−	2.50000i	0.139609	−	0.0806032i
$963$		0			0
$964$	−4.50000	+	7.79423i	−0.144935	+	0.251035i
$965$	−10.0000	+	20.0000i	−0.321911	+	0.643823i
$966$		0			0
$967$			32.0000i			1.02905i	0.857475	+	0.514525i	$0.172032\pi$
$967$			32.0000i			1.02905i	−0.857475	+	0.514525i	$0.827968\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$		0			0
$970$	1.60770	+	26.7846i	0.0516200	+	0.860002i
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	0.469897	+	0.882721i	$0.344291\pi$
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	−0.999408	+	0.0344175i	$0.989042\pi$
$972$		0			0
$973$	−27.7128	+	32.0000i	−0.888432	+	1.02587i
$974$	−32.0000			−1.02535
$975$		0			0
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	−46.7654	+	27.0000i	−1.49616	+	0.863807i	−0.999990	−	0.00442082i	$-0.998593\pi$
$977$	−46.7654	+	27.0000i	−1.49616	+	0.863807i	−0.496167	+	0.868227i	$0.665259\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$	−4.92820	+	14.8564i	−0.157426	+	0.474570i
$981$		0			0
$982$	−20.7846	−	12.0000i	−0.663264	−	0.382935i
$983$	−25.1147	+	14.5000i	−0.801036	+	0.462478i	−0.843833	−	0.536606i	$-0.819706\pi$
$983$	−25.1147	+	14.5000i	−0.801036	+	0.462478i	0.0427975	+	0.999084i	$0.486373\pi$
$984$		0			0
$985$	−6.16025	−	9.33013i	−0.196282	−	0.297283i
$986$	−8.00000			−0.254772
$987$		0			0
$988$		−	25.0000i		−	0.795356i
$989$	7.00000	−	12.1244i	0.222587	−	0.385532i
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	−1.73205	−	1.00000i	−0.0549927	−	0.0317500i
$993$		0			0
$994$	15.0000	−	5.19615i	0.475771	−	0.164812i
$995$	−36.0000	−	18.0000i	−1.14128	−	0.570638i
$996$		0			0
$997$	−32.9090	+	19.0000i	−1.04224	+	0.601736i	−0.920466	−	0.390822i	$-0.872191\pi$
$997$	−32.9090	+	19.0000i	−1.04224	+	0.601736i	−0.121771	+	0.992558i	$0.538857\pi$
$998$	3.46410	−	2.00000i	0.109654	−	0.0633089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.u.a.289.2		4
3.2	odd	2		70.2.i.b.9.1	✓	4
5.4	even	2	inner	630.2.u.a.289.1		4
7.4	even	3	inner	630.2.u.a.109.1		4
12.11	even	2		560.2.bw.d.289.2		4
15.2	even	4		350.2.e.j.51.1		2
15.8	even	4		350.2.e.c.51.1		2
15.14	odd	2		70.2.i.b.9.2	yes	4
21.2	odd	6		490.2.c.a.99.2		2
21.5	even	6		490.2.c.d.99.2		2
21.11	odd	6		70.2.i.b.39.2	yes	4
21.17	even	6		490.2.i.a.459.2		4
21.20	even	2		490.2.i.a.79.1		4
35.4	even	6	inner	630.2.u.a.109.2		4
60.59	even	2		560.2.bw.d.289.1		4
84.11	even	6		560.2.bw.d.529.1		4
105.2	even	12		2450.2.a.k.1.1		1
105.23	even	12		2450.2.a.ba.1.1		1
105.32	even	12		350.2.e.j.151.1		2
105.44	odd	6		490.2.c.a.99.1		2
105.47	odd	12		2450.2.a.j.1.1		1
105.53	even	12		350.2.e.c.151.1		2
105.59	even	6		490.2.i.a.459.1		4
105.68	odd	12		2450.2.a.bb.1.1		1
105.74	odd	6		70.2.i.b.39.1	yes	4
105.89	even	6		490.2.c.d.99.1		2
105.104	even	2		490.2.i.a.79.2		4
420.179	even	6		560.2.bw.d.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.b.9.1	✓	4	3.2	odd	2
70.2.i.b.9.2	yes	4	15.14	odd	2
70.2.i.b.39.1	yes	4	105.74	odd	6
70.2.i.b.39.2	yes	4	21.11	odd	6
350.2.e.c.51.1		2	15.8	even	4
350.2.e.c.151.1		2	105.53	even	12
350.2.e.j.51.1		2	15.2	even	4
350.2.e.j.151.1		2	105.32	even	12
490.2.c.a.99.1		2	105.44	odd	6
490.2.c.a.99.2		2	21.2	odd	6
490.2.c.d.99.1		2	105.89	even	6
490.2.c.d.99.2		2	21.5	even	6
490.2.i.a.79.1		4	21.20	even	2
490.2.i.a.79.2		4	105.104	even	2
490.2.i.a.459.1		4	105.59	even	6
490.2.i.a.459.2		4	21.17	even	6
560.2.bw.d.289.1		4	60.59	even	2
560.2.bw.d.289.2		4	12.11	even	2
560.2.bw.d.529.1		4	84.11	even	6
560.2.bw.d.529.2		4	420.179	even	6
630.2.u.a.109.1		4	7.4	even	3	inner
630.2.u.a.109.2		4	35.4	even	6	inner
630.2.u.a.289.1		4	5.4	even	2	inner
630.2.u.a.289.2		4	1.1	even	1	trivial
2450.2.a.j.1.1		1	105.47	odd	12
2450.2.a.k.1.1		1	105.2	even	12
2450.2.a.ba.1.1		1	105.23	even	12
2450.2.a.bb.1.1		1	105.68	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(-2.23205 + 0.133975i) q^{10} +(1.50000 + 2.59808i) q^{11} +5.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-2.00000 - 1.00000i) q^{20} +3.00000i q^{22} +(6.06218 + 3.50000i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(2.59808 + 0.500000i) q^{28} -4.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +2.00000 q^{34} +(-0.767949 + 5.86603i) q^{35} +(-0.866025 - 0.500000i) q^{37} +(-4.33013 + 2.50000i) q^{38} +(-1.23205 - 1.86603i) q^{40} -3.00000 q^{41} -2.00000i q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-6.06218 - 3.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(4.00000 - 3.00000i) q^{50} +(-4.33013 + 2.50000i) q^{52} +(7.79423 - 4.50000i) q^{53} +(-6.00000 - 3.00000i) q^{55} +(2.00000 + 1.73205i) q^{56} +(-3.46410 - 2.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} +2.00000i q^{62} -1.00000 q^{64} +(-6.16025 - 9.33013i) q^{65} +(1.73205 - 1.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(-3.59808 + 4.69615i) q^{70} +6.00000 q^{71} +(13.8564 - 8.00000i) q^{73} +(-0.500000 - 0.866025i) q^{74} -5.00000 q^{76} +(7.79423 + 1.50000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.133975 - 2.23205i) q^{80} +(-2.59808 - 1.50000i) q^{82} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(10.0000 + 8.66025i) q^{91} +7.00000i q^{92} +(-3.50000 - 6.06218i) q^{94} +(-0.669873 - 11.1603i) q^{95} -12.0000i q^{97} +(2.59808 - 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{5}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^5	\( 4 q + 2 q^{4} - 4 q^{5} - 2 q^{10} + 6 q^{11} + 10 q^{14} - 2 q^{16} - 10 q^{19} - 8 q^{20} - 6 q^{25} - 10 q^{26} - 16 q^{29} + 4 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{40} - 12 q^{41} - 6 q^{44} + 14 q^{46} - 4 q^{49} + 16 q^{50} - 24 q^{55} + 8 q^{56} + 8 q^{59} - 12 q^{61} - 4 q^{64} + 10 q^{65} - 4 q^{70} + 24 q^{71} - 2 q^{74} - 20 q^{76} + 28 q^{79} - 4 q^{80} - 8 q^{85} + 4 q^{86} - 4 q^{89} + 40 q^{91} - 14 q^{94} - 20 q^{95}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^5 - 2 * q^10 + 6 * q^11 + 10 * q^14 - 2 * q^16 - 10 * q^19 - 8 * q^20 - 6 * q^25 - 10 * q^26 - 16 * q^29 + 4 * q^31 + 8 * q^34 - 10 * q^35 + 2 * q^40 - 12 * q^41 - 6 * q^44 + 14 * q^46 - 4 * q^49 + 16 * q^50 - 24 * q^55 + 8 * q^56 + 8 * q^59 - 12 * q^61 - 4 * q^64 + 10 * q^65 - 4 * q^70 + 24 * q^71 - 2 * q^74 - 20 * q^76 + 28 * q^79 - 4 * q^80 - 8 * q^85 + 4 * q^86 - 4 * q^89 + 40 * q^91 - 14 * q^94 - 20 * q^95

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