LMFDB - Embedded newform 210.2.g.b.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(169,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("210.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.g (of order $2$, degree $1$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	210.169
Dual form			210.2.g.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} +2.00000 q^{11} +1.00000i q^{12} -6.00000i q^{13} +1.00000 q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} -1.00000i q^{18} +6.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -1.00000 q^{21} +2.00000i q^{22} +8.00000i q^{23} -1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +6.00000 q^{26} +1.00000i q^{27} +1.00000i q^{28} -6.00000 q^{29} +(1.00000 - 2.00000i) q^{30} -2.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} -4.00000 q^{34} +(-2.00000 - 1.00000i) q^{35} +1.00000 q^{36} +4.00000i q^{37} +6.00000i q^{38} -6.00000 q^{39} +(-2.00000 - 1.00000i) q^{40} +2.00000 q^{41} -1.00000i q^{42} -4.00000i q^{43} -2.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} -8.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +4.00000 q^{51} +6.00000i q^{52} -6.00000i q^{53} -1.00000 q^{54} +(2.00000 - 4.00000i) q^{55} -1.00000 q^{56} -6.00000i q^{57} -6.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -10.0000 q^{61} -2.00000i q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-12.0000 - 6.00000i) q^{65} +2.00000 q^{66} +8.00000i q^{67} -4.00000i q^{68} +8.00000 q^{69} +(1.00000 - 2.00000i) q^{70} -6.00000 q^{71} +1.00000i q^{72} +14.0000i q^{73} -4.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -6.00000 q^{76} -2.00000i q^{77} -6.00000i q^{78} +12.0000 q^{79} +(1.00000 - 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} +8.00000i q^{83} +1.00000 q^{84} +(8.00000 + 4.00000i) q^{85} +4.00000 q^{86} +6.00000i q^{87} -2.00000i q^{88} +10.0000 q^{89} +(-2.00000 - 1.00000i) q^{90} -6.00000 q^{91} -8.00000i q^{92} +2.00000i q^{93} -8.00000 q^{94} +(6.00000 - 12.0000i) q^{95} +1.00000 q^{96} -10.0000i q^{97} -1.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{14} - 4 q^{15} + 2 q^{16} + 12 q^{19} - 2 q^{20} - 2 q^{21} - 2 q^{24} - 6 q^{25} + 12 q^{26} - 12 q^{29} + 2 q^{30} - 4 q^{31} - 8 q^{34} - 4 q^{35} + 2 q^{36} - 12 q^{39} - 4 q^{40} + 4 q^{41} - 4 q^{44} - 2 q^{45} - 16 q^{46} - 2 q^{49} + 8 q^{50} + 8 q^{51} - 2 q^{54} + 4 q^{55} - 2 q^{56} + 16 q^{59} + 4 q^{60} - 20 q^{61} - 2 q^{64} - 24 q^{65} + 4 q^{66} + 16 q^{69} + 2 q^{70} - 12 q^{71} - 8 q^{74} - 8 q^{75} - 12 q^{76} + 24 q^{79} + 2 q^{80} + 2 q^{81} + 2 q^{84} + 16 q^{85} + 8 q^{86} + 20 q^{89} - 4 q^{90} - 12 q^{91} - 16 q^{94} + 12 q^{95} + 2 q^{96} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^14 - 4 * q^15 + 2 * q^16 + 12 * q^19 - 2 * q^20 - 2 * q^21 - 2 * q^24 - 6 * q^25 + 12 * q^26 - 12 * q^29 + 2 * q^30 - 4 * q^31 - 8 * q^34 - 4 * q^35 + 2 * q^36 - 12 * q^39 - 4 * q^40 + 4 * q^41 - 4 * q^44 - 2 * q^45 - 16 * q^46 - 2 * q^49 + 8 * q^50 + 8 * q^51 - 2 * q^54 + 4 * q^55 - 2 * q^56 + 16 * q^59 + 4 * q^60 - 20 * q^61 - 2 * q^64 - 24 * q^65 + 4 * q^66 + 16 * q^69 + 2 * q^70 - 12 * q^71 - 8 * q^74 - 8 * q^75 - 12 * q^76 + 24 * q^79 + 2 * q^80 + 2 * q^81 + 2 * q^84 + 16 * q^85 + 8 * q^86 + 20 * q^89 - 4 * q^90 - 12 * q^91 - 16 * q^94 + 12 * q^95 + 2 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	1.00000			0.408248
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$			1.00000i			0.288675i
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	1.00000			0.267261
$15$	−2.00000	−	1.00000i	−0.516398	−	0.258199i
$16$	1.00000			0.250000
$17$			4.00000i			0.970143i	0.874475	+	0.485071i	$0.161206\pi$
$17$			4.00000i			0.970143i	−0.874475	+	0.485071i	$0.838794\pi$
$18$		−	1.00000i		−	0.235702i
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$	−1.00000			−0.218218
$22$			2.00000i			0.426401i
$23$			8.00000i			1.66812i	0.551677	+	0.834058i	$0.313988\pi$
$23$			8.00000i			1.66812i	−0.551677	+	0.834058i	$0.686012\pi$
$24$	−1.00000			−0.204124
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	6.00000			1.17670
$27$			1.00000i			0.192450i
$28$			1.00000i			0.188982i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	1.00000	−	2.00000i	0.182574	−	0.365148i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$			1.00000i			0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	−4.00000			−0.685994
$35$	−2.00000	−	1.00000i	−0.338062	−	0.169031i
$36$	1.00000			0.166667
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$			6.00000i			0.973329i
$39$	−6.00000			−0.960769
$40$	−2.00000	−	1.00000i	−0.316228	−	0.158114i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		−	1.00000i		−	0.154303i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	−2.00000			−0.301511
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$	−8.00000			−1.17954
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000			−0.142857
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	4.00000			0.560112
$52$			6.00000i			0.832050i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−1.00000			−0.136083
$55$	2.00000	−	4.00000i	0.269680	−	0.539360i
$56$	−1.00000			−0.133631
$57$		−	6.00000i		−	0.794719i
$58$		−	6.00000i		−	0.787839i
$59$	8.00000			1.04151			0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$	2.00000	+	1.00000i	0.258199	+	0.129099i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$		−	2.00000i		−	0.254000i
$63$			1.00000i			0.125988i
$64$	−1.00000			−0.125000
$65$	−12.0000	−	6.00000i	−1.48842	−	0.744208i
$66$	2.00000			0.246183
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		−	4.00000i		−	0.485071i
$69$	8.00000			0.963087
$70$	1.00000	−	2.00000i	0.119523	−	0.239046i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$			1.00000i			0.117851i
$73$			14.0000i			1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$			14.0000i			1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$	−4.00000			−0.464991
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	−6.00000			−0.688247
$77$		−	2.00000i		−	0.227921i
$78$		−	6.00000i		−	0.679366i
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$	1.00000	−	2.00000i	0.111803	−	0.223607i
$81$	1.00000			0.111111
$82$			2.00000i			0.220863i
$83$			8.00000i			0.878114i	0.898459	+	0.439057i	$0.144687\pi$
$83$			8.00000i			0.878114i	−0.898459	+	0.439057i	$0.855313\pi$
$84$	1.00000			0.109109
$85$	8.00000	+	4.00000i	0.867722	+	0.433861i
$86$	4.00000			0.431331
$87$			6.00000i			0.643268i
$88$		−	2.00000i		−	0.213201i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−2.00000	−	1.00000i	−0.210819	−	0.105409i
$91$	−6.00000			−0.628971
$92$		−	8.00000i		−	0.834058i
$93$			2.00000i			0.207390i
$94$	−8.00000			−0.825137
$95$	6.00000	−	12.0000i	0.615587	−	1.23117i
$96$	1.00000			0.102062
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$		−	1.00000i		−	0.101015i
$99$	−2.00000			−0.201008
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$			4.00000i			0.396059i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	−6.00000			−0.588348
$105$	−1.00000	+	2.00000i	−0.0975900	+	0.195180i
$106$	6.00000			0.582772
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	4.00000	+	2.00000i	0.381385	+	0.190693i
$111$	4.00000			0.379663
$112$		−	1.00000i		−	0.0944911i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	6.00000			0.561951
$115$	16.0000	+	8.00000i	1.49201	+	0.746004i
$116$	6.00000			0.557086
$117$			6.00000i			0.554700i
$118$			8.00000i			0.736460i
$119$	4.00000			0.366679
$120$	−1.00000	+	2.00000i	−0.0912871	+	0.182574i
$121$	−7.00000			−0.636364
$122$		−	10.0000i		−	0.905357i
$123$		−	2.00000i		−	0.180334i
$124$	2.00000			0.179605
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	−1.00000			−0.0890871
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.00000			−0.352180
$130$	6.00000	−	12.0000i	0.526235	−	1.05247i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$			2.00000i			0.174078i
$133$		−	6.00000i		−	0.520266i
$134$	−8.00000			−0.691095
$135$	2.00000	+	1.00000i	0.172133	+	0.0860663i
$136$	4.00000			0.342997
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$			8.00000i			0.681005i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	2.00000	+	1.00000i	0.169031	+	0.0845154i
$141$	8.00000			0.673722
$142$		−	6.00000i		−	0.503509i
$143$		−	12.0000i		−	1.00349i
$144$	−1.00000			−0.0833333
$145$	−6.00000	+	12.0000i	−0.498273	+	0.996546i
$146$	−14.0000			−1.15865
$147$			1.00000i			0.0824786i
$148$		−	4.00000i		−	0.328798i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	−3.00000	−	4.00000i	−0.244949	−	0.326599i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	6.00000i		−	0.486664i
$153$		−	4.00000i		−	0.323381i
$154$	2.00000			0.161165
$155$	−2.00000	+	4.00000i	−0.160644	+	0.321288i
$156$	6.00000			0.480384
$157$		−	22.0000i		−	1.75579i	−0.478852	−	0.877896i	$-0.658947\pi$
$157$		−	22.0000i		−	1.75579i	0.478852	−	0.877896i	$-0.341053\pi$
$158$			12.0000i			0.954669i
$159$	−6.00000			−0.475831
$160$	2.00000	+	1.00000i	0.158114	+	0.0790569i
$161$	8.00000			0.630488
$162$			1.00000i			0.0785674i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	−2.00000			−0.156174
$165$	−4.00000	−	2.00000i	−0.311400	−	0.155700i
$166$	−8.00000			−0.620920
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$			1.00000i			0.0771517i
$169$	−23.0000			−1.76923
$170$	−4.00000	+	8.00000i	−0.306786	+	0.613572i
$171$	−6.00000			−0.458831
$172$			4.00000i			0.304997i
$173$		−	8.00000i		−	0.608229i	−0.952636	−	0.304114i	$-0.901639\pi$
$173$		−	8.00000i		−	0.608229i	0.952636	−	0.304114i	$-0.0983605\pi$
$174$	−6.00000			−0.454859
$175$	−4.00000	+	3.00000i	−0.302372	+	0.226779i
$176$	2.00000			0.150756
$177$		−	8.00000i		−	0.601317i
$178$			10.0000i			0.749532i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	1.00000	−	2.00000i	0.0745356	−	0.149071i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		−	6.00000i		−	0.444750i
$183$			10.0000i			0.739221i
$184$	8.00000			0.589768
$185$	8.00000	+	4.00000i	0.588172	+	0.294086i
$186$	−2.00000			−0.146647
$187$			8.00000i			0.585018i
$188$		−	8.00000i		−	0.583460i
$189$	1.00000			0.0727393
$190$	12.0000	+	6.00000i	0.870572	+	0.435286i
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$			1.00000i			0.0721688i
$193$			8.00000i			0.575853i	0.957653	+	0.287926i	$0.0929658\pi$
$193$			8.00000i			0.575853i	−0.957653	+	0.287926i	$0.907034\pi$
$194$	10.0000			0.717958
$195$	−6.00000	+	12.0000i	−0.429669	+	0.859338i
$196$	1.00000			0.0714286
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$		−	2.00000i		−	0.142134i
$199$	−6.00000			−0.425329			−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000			−0.425329			−0.212664	+	0.977125i	$0.568214\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$	8.00000			0.564276
$202$			10.0000i			0.703598i
$203$			6.00000i			0.421117i
$204$	−4.00000			−0.280056
$205$	2.00000	−	4.00000i	0.139686	−	0.279372i
$206$	8.00000			0.557386
$207$		−	8.00000i		−	0.556038i
$208$		−	6.00000i		−	0.416025i
$209$	12.0000			0.830057
$210$	−2.00000	−	1.00000i	−0.138013	−	0.0690066i
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$			6.00000i			0.412082i
$213$			6.00000i			0.411113i
$214$	−12.0000			−0.820303
$215$	−8.00000	−	4.00000i	−0.545595	−	0.272798i
$216$	1.00000			0.0680414
$217$			2.00000i			0.135769i
$218$			14.0000i			0.948200i
$219$	14.0000			0.946032
$220$	−2.00000	+	4.00000i	−0.134840	+	0.269680i
$221$	24.0000			1.61441
$222$			4.00000i			0.268462i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	1.00000			0.0668153
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$	6.00000			0.399114
$227$		−	8.00000i		−	0.530979i	−0.964114	−	0.265489i	$-0.914466\pi$
$227$		−	8.00000i		−	0.530979i	0.964114	−	0.265489i	$-0.0855335\pi$
$228$			6.00000i			0.397360i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	−8.00000	+	16.0000i	−0.527504	+	1.05501i
$231$	−2.00000			−0.131590
$232$			6.00000i			0.393919i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	−6.00000			−0.392232
$235$	16.0000	+	8.00000i	1.04372	+	0.521862i
$236$	−8.00000			−0.520756
$237$		−	12.0000i		−	0.779484i
$238$			4.00000i			0.259281i
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	−2.00000	−	1.00000i	−0.129099	−	0.0645497i
$241$	−26.0000			−1.67481			−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000			−1.67481			−0.837404	+	0.546585i	$0.815928\pi$
$242$		−	7.00000i		−	0.449977i
$243$		−	1.00000i		−	0.0641500i
$244$	10.0000			0.640184
$245$	−1.00000	+	2.00000i	−0.0638877	+	0.127775i
$246$	2.00000			0.127515
$247$		−	36.0000i		−	2.29063i
$248$			2.00000i			0.127000i
$249$	8.00000			0.506979
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		−	1.00000i		−	0.0629941i
$253$			16.0000i			1.00591i
$254$	−4.00000			−0.250982
$255$	4.00000	−	8.00000i	0.250490	−	0.500979i
$256$	1.00000			0.0625000
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		−	4.00000i		−	0.249029i
$259$	4.00000			0.248548
$260$	12.0000	+	6.00000i	0.744208	+	0.372104i
$261$	6.00000			0.371391
$262$		−	12.0000i		−	0.741362i
$263$		−	16.0000i		−	0.986602i	−0.869859	−	0.493301i	$-0.835790\pi$
$263$		−	16.0000i		−	0.986602i	0.869859	−	0.493301i	$-0.164210\pi$
$264$	−2.00000			−0.123091
$265$	−12.0000	−	6.00000i	−0.737154	−	0.368577i
$266$	6.00000			0.367884
$267$		−	10.0000i		−	0.611990i
$268$		−	8.00000i		−	0.488678i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$	−1.00000	+	2.00000i	−0.0608581	+	0.121716i
$271$	10.0000			0.607457			0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000			0.607457			0.303728	+	0.952759i	$0.401768\pi$
$272$			4.00000i			0.242536i
$273$			6.00000i			0.363137i
$274$	6.00000			0.362473
$275$	−6.00000	−	8.00000i	−0.361814	−	0.482418i
$276$	−8.00000			−0.481543
$277$			28.0000i			1.68236i	0.540758	+	0.841178i	$0.318138\pi$
$277$			28.0000i			1.68236i	−0.540758	+	0.841178i	$0.681862\pi$
$278$			14.0000i			0.839664i
$279$	2.00000			0.119737
$280$	−1.00000	+	2.00000i	−0.0597614	+	0.119523i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$			8.00000i			0.476393i
$283$		−	20.0000i		−	1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$		−	20.0000i		−	1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	6.00000			0.356034
$285$	−12.0000	−	6.00000i	−0.710819	−	0.355409i
$286$	12.0000			0.709575
$287$		−	2.00000i		−	0.118056i
$288$		−	1.00000i		−	0.0589256i
$289$	1.00000			0.0588235
$290$	−12.0000	−	6.00000i	−0.704664	−	0.352332i
$291$	−10.0000			−0.586210
$292$		−	14.0000i		−	0.819288i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−1.00000			−0.0583212
$295$	8.00000	−	16.0000i	0.465778	−	0.931556i
$296$	4.00000			0.232495
$297$			2.00000i			0.116052i
$298$		−	10.0000i		−	0.579284i
$299$	48.0000			2.77591
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$	−4.00000			−0.230556
$302$		−	8.00000i		−	0.460348i
$303$		−	10.0000i		−	0.574485i
$304$	6.00000			0.344124
$305$	−10.0000	+	20.0000i	−0.572598	+	1.14520i
$306$	4.00000			0.228665
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$			2.00000i			0.113961i
$309$	−8.00000			−0.455104
$310$	−4.00000	−	2.00000i	−0.227185	−	0.113592i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$			6.00000i			0.339683i
$313$			2.00000i			0.113047i	0.998401	+	0.0565233i	$0.0180015\pi$
$313$			2.00000i			0.113047i	−0.998401	+	0.0565233i	$0.981998\pi$
$314$	22.0000			1.24153
$315$	2.00000	+	1.00000i	0.112687	+	0.0563436i
$316$	−12.0000			−0.675053
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$		−	6.00000i		−	0.336463i
$319$	−12.0000			−0.671871
$320$	−1.00000	+	2.00000i	−0.0559017	+	0.111803i
$321$	12.0000			0.669775
$322$			8.00000i			0.445823i
$323$			24.0000i			1.33540i
$324$	−1.00000			−0.0555556
$325$	−24.0000	+	18.0000i	−1.33128	+	0.998460i
$326$	−4.00000			−0.221540
$327$		−	14.0000i		−	0.774202i
$328$		−	2.00000i		−	0.110432i
$329$	8.00000			0.441054
$330$	2.00000	−	4.00000i	0.110096	−	0.220193i
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$		−	8.00000i		−	0.439057i
$333$		−	4.00000i		−	0.219199i
$334$	12.0000			0.656611
$335$	16.0000	+	8.00000i	0.874173	+	0.437087i
$336$	−1.00000			−0.0545545
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$		−	23.0000i		−	1.25104i
$339$	−6.00000			−0.325875
$340$	−8.00000	−	4.00000i	−0.433861	−	0.216930i
$341$	−4.00000			−0.216612
$342$		−	6.00000i		−	0.324443i
$343$			1.00000i			0.0539949i
$344$	−4.00000			−0.215666
$345$	8.00000	−	16.0000i	0.430706	−	0.861411i
$346$	8.00000			0.430083
$347$			36.0000i			1.93258i	0.257454	+	0.966291i	$0.417117\pi$
$347$			36.0000i			1.93258i	−0.257454	+	0.966291i	$0.582883\pi$
$348$		−	6.00000i		−	0.321634i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	−3.00000	−	4.00000i	−0.160357	−	0.213809i
$351$	6.00000			0.320256
$352$			2.00000i			0.106600i
$353$		−	20.0000i		−	1.06449i	−0.846590	−	0.532246i	$-0.821348\pi$
$353$		−	20.0000i		−	1.06449i	0.846590	−	0.532246i	$-0.178652\pi$
$354$	8.00000			0.425195
$355$	−6.00000	+	12.0000i	−0.318447	+	0.636894i
$356$	−10.0000			−0.529999
$357$		−	4.00000i		−	0.211702i
$358$		−	10.0000i		−	0.528516i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$	2.00000	+	1.00000i	0.105409	+	0.0527046i
$361$	17.0000			0.894737
$362$			2.00000i			0.105118i
$363$			7.00000i			0.367405i
$364$	6.00000			0.314485
$365$	28.0000	+	14.0000i	1.46559	+	0.732793i
$366$	−10.0000			−0.522708
$367$		−	32.0000i		−	1.67039i	−0.549957	−	0.835193i	$-0.685356\pi$
$367$		−	32.0000i		−	1.67039i	0.549957	−	0.835193i	$-0.314644\pi$
$368$			8.00000i			0.417029i
$369$	−2.00000			−0.104116
$370$	−4.00000	+	8.00000i	−0.207950	+	0.415900i
$371$	−6.00000			−0.311504
$372$		−	2.00000i		−	0.103695i
$373$			24.0000i			1.24267i	0.783544	+	0.621336i	$0.213410\pi$
$373$			24.0000i			1.24267i	−0.783544	+	0.621336i	$0.786590\pi$
$374$	−8.00000			−0.413670
$375$	2.00000	+	11.0000i	0.103280	+	0.568038i
$376$	8.00000			0.412568
$377$			36.0000i			1.85409i
$378$			1.00000i			0.0514344i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−6.00000	+	12.0000i	−0.307794	+	0.615587i
$381$	4.00000			0.204926
$382$		−	18.0000i		−	0.920960i
$383$		−	20.0000i		−	1.02195i	−0.859595	−	0.510976i	$-0.829284\pi$
$383$		−	20.0000i		−	1.02195i	0.859595	−	0.510976i	$-0.170716\pi$
$384$	−1.00000			−0.0510310
$385$	−4.00000	−	2.00000i	−0.203859	−	0.101929i
$386$	−8.00000			−0.407189
$387$			4.00000i			0.203331i
$388$			10.0000i			0.507673i
$389$	−2.00000			−0.101404			−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000			−0.101404			−0.0507020	+	0.998714i	$0.516146\pi$
$390$	−12.0000	−	6.00000i	−0.607644	−	0.303822i
$391$	−32.0000			−1.61831
$392$			1.00000i			0.0505076i
$393$			12.0000i			0.605320i
$394$	−2.00000			−0.100759
$395$	12.0000	−	24.0000i	0.603786	−	1.20757i
$396$	2.00000			0.100504
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$		−	6.00000i		−	0.300753i
$399$	−6.00000			−0.300376
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−14.0000			−0.699127			−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000			−0.699127			−0.349563	+	0.936913i	$0.613670\pi$
$402$			8.00000i			0.399004i
$403$			12.0000i			0.597763i
$404$	−10.0000			−0.497519
$405$	1.00000	−	2.00000i	0.0496904	−	0.0993808i
$406$	−6.00000			−0.297775
$407$			8.00000i			0.396545i
$408$		−	4.00000i		−	0.198030i
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$	4.00000	+	2.00000i	0.197546	+	0.0987730i
$411$	−6.00000			−0.295958
$412$			8.00000i			0.394132i
$413$		−	8.00000i		−	0.393654i
$414$	8.00000			0.393179
$415$	16.0000	+	8.00000i	0.785409	+	0.392705i
$416$	6.00000			0.294174
$417$		−	14.0000i		−	0.685583i
$418$			12.0000i			0.586939i
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$	1.00000	−	2.00000i	0.0487950	−	0.0975900i
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$		−	8.00000i		−	0.388973i
$424$	−6.00000			−0.291386
$425$	16.0000	−	12.0000i	0.776114	−	0.582086i
$426$	−6.00000			−0.290701
$427$			10.0000i			0.483934i
$428$		−	12.0000i		−	0.580042i
$429$	−12.0000			−0.579365
$430$	4.00000	−	8.00000i	0.192897	−	0.385794i
$431$	2.00000			0.0963366			0.0481683	−	0.998839i	$-0.484662\pi$
$431$	2.00000			0.0963366			0.0481683	+	0.998839i	$0.484662\pi$
$432$			1.00000i			0.0481125i
$433$			26.0000i			1.24948i	0.780833	+	0.624740i	$0.214795\pi$
$433$			26.0000i			1.24948i	−0.780833	+	0.624740i	$0.785205\pi$
$434$	−2.00000			−0.0960031
$435$	12.0000	+	6.00000i	0.575356	+	0.287678i
$436$	−14.0000			−0.670478
$437$			48.0000i			2.29615i
$438$			14.0000i			0.668946i
$439$	18.0000			0.859093			0.429547	−	0.903045i	$-0.358673\pi$
$439$	18.0000			0.859093			0.429547	+	0.903045i	$0.358673\pi$
$440$	−4.00000	−	2.00000i	−0.190693	−	0.0953463i
$441$	1.00000			0.0476190
$442$			24.0000i			1.14156i
$443$			12.0000i			0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$443$			12.0000i			0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$444$	−4.00000			−0.189832
$445$	10.0000	−	20.0000i	0.474045	−	0.948091i
$446$	−8.00000			−0.378811
$447$			10.0000i			0.472984i
$448$			1.00000i			0.0472456i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	4.00000			0.188353
$452$			6.00000i			0.282216i
$453$			8.00000i			0.375873i
$454$	8.00000			0.375459
$455$	−6.00000	+	12.0000i	−0.281284	+	0.562569i
$456$	−6.00000			−0.280976
$457$			28.0000i			1.30978i	0.755722	+	0.654892i	$0.227286\pi$
$457$			28.0000i			1.30978i	−0.755722	+	0.654892i	$0.772714\pi$
$458$		−	14.0000i		−	0.654177i
$459$	−4.00000			−0.186704
$460$	−16.0000	−	8.00000i	−0.746004	−	0.373002i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		−	2.00000i		−	0.0930484i
$463$		−	36.0000i		−	1.67306i	−0.547920	−	0.836531i	$-0.684580\pi$
$463$		−	36.0000i		−	1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$464$	−6.00000			−0.278543
$465$	4.00000	+	2.00000i	0.185496	+	0.0927478i
$466$	−10.0000			−0.463241
$467$		−	24.0000i		−	1.11059i	−0.831654	−	0.555294i	$-0.812606\pi$
$467$		−	24.0000i		−	1.11059i	0.831654	−	0.555294i	$-0.187394\pi$
$468$		−	6.00000i		−	0.277350i
$469$	8.00000			0.369406
$470$	−8.00000	+	16.0000i	−0.369012	+	0.738025i
$471$	−22.0000			−1.01371
$472$		−	8.00000i		−	0.368230i
$473$		−	8.00000i		−	0.367840i
$474$	12.0000			0.551178
$475$	−18.0000	−	24.0000i	−0.825897	−	1.10120i
$476$	−4.00000			−0.183340
$477$			6.00000i			0.274721i
$478$		−	26.0000i		−	1.18921i
$479$	−8.00000			−0.365529			−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000			−0.365529			−0.182765	+	0.983157i	$0.558505\pi$
$480$	1.00000	−	2.00000i	0.0456435	−	0.0912871i
$481$	24.0000			1.09431
$482$		−	26.0000i		−	1.18427i
$483$		−	8.00000i		−	0.364013i
$484$	7.00000			0.318182
$485$	−20.0000	−	10.0000i	−0.908153	−	0.454077i
$486$	1.00000			0.0453609
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$			10.0000i			0.452679i
$489$	4.00000			0.180886
$490$	−2.00000	−	1.00000i	−0.0903508	−	0.0451754i
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$			2.00000i			0.0901670i
$493$		−	24.0000i		−	1.08091i
$494$	36.0000			1.61972
$495$	−2.00000	+	4.00000i	−0.0898933	+	0.179787i
$496$	−2.00000			−0.0898027
$497$			6.00000i			0.269137i
$498$			8.00000i			0.358489i
$499$	12.0000			0.537194			0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000			0.537194			0.268597	+	0.963253i	$0.413440\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$	−12.0000			−0.536120
$502$		0			0
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$	1.00000			0.0445435
$505$	10.0000	−	20.0000i	0.444994	−	0.889988i
$506$	−16.0000			−0.711287
$507$			23.0000i			1.02147i
$508$		−	4.00000i		−	0.177471i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	8.00000	+	4.00000i	0.354246	+	0.177123i
$511$	14.0000			0.619324
$512$			1.00000i			0.0441942i
$513$			6.00000i			0.264906i
$514$		0			0
$515$	−16.0000	−	8.00000i	−0.705044	−	0.352522i
$516$	4.00000			0.176090
$517$			16.0000i			0.703679i
$518$			4.00000i			0.175750i
$519$	−8.00000			−0.351161
$520$	−6.00000	+	12.0000i	−0.263117	+	0.526235i
$521$	−26.0000			−1.13908			−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000			−1.13908			−0.569540	+	0.821963i	$0.692879\pi$
$522$			6.00000i			0.262613i
$523$			28.0000i			1.22435i	0.790721	+	0.612177i	$0.209706\pi$
$523$			28.0000i			1.22435i	−0.790721	+	0.612177i	$0.790294\pi$
$524$	12.0000			0.524222
$525$	3.00000	+	4.00000i	0.130931	+	0.174574i
$526$	16.0000			0.697633
$527$		−	8.00000i		−	0.348485i
$528$		−	2.00000i		−	0.0870388i
$529$	−41.0000			−1.78261
$530$	6.00000	−	12.0000i	0.260623	−	0.521247i
$531$	−8.00000			−0.347170
$532$			6.00000i			0.260133i
$533$		−	12.0000i		−	0.519778i
$534$	10.0000			0.432742
$535$	24.0000	+	12.0000i	1.03761	+	0.518805i
$536$	8.00000			0.345547
$537$			10.0000i			0.431532i
$538$		−	18.0000i		−	0.776035i
$539$	−2.00000			−0.0861461
$540$	−2.00000	−	1.00000i	−0.0860663	−	0.0430331i
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$			10.0000i			0.429537i
$543$		−	2.00000i		−	0.0858282i
$544$	−4.00000			−0.171499
$545$	14.0000	−	28.0000i	0.599694	−	1.19939i
$546$	−6.00000			−0.256776
$547$			40.0000i			1.71028i	0.518400	+	0.855138i	$0.326528\pi$
$547$			40.0000i			1.71028i	−0.518400	+	0.855138i	$0.673472\pi$
$548$			6.00000i			0.256307i
$549$	10.0000			0.426790
$550$	8.00000	−	6.00000i	0.341121	−	0.255841i
$551$	−36.0000			−1.53365
$552$		−	8.00000i		−	0.340503i
$553$		−	12.0000i		−	0.510292i
$554$	−28.0000			−1.18961
$555$	4.00000	−	8.00000i	0.169791	−	0.339581i
$556$	−14.0000			−0.593732
$557$		−	42.0000i		−	1.77960i	−0.456354	−	0.889799i	$-0.650845\pi$
$557$		−	42.0000i		−	1.77960i	0.456354	−	0.889799i	$-0.349155\pi$
$558$			2.00000i			0.0846668i
$559$	−24.0000			−1.01509
$560$	−2.00000	−	1.00000i	−0.0845154	−	0.0422577i
$561$	8.00000			0.337760
$562$			30.0000i			1.26547i
$563$			4.00000i			0.168580i	0.996441	+	0.0842900i	$0.0268622\pi$
$563$			4.00000i			0.168580i	−0.996441	+	0.0842900i	$0.973138\pi$
$564$	−8.00000			−0.336861
$565$	−12.0000	−	6.00000i	−0.504844	−	0.252422i
$566$	20.0000			0.840663
$567$		−	1.00000i		−	0.0419961i
$568$			6.00000i			0.251754i
$569$	46.0000			1.92842			0.964210	−	0.265139i	$-0.0854179\pi$
$569$	46.0000			1.92842			0.964210	+	0.265139i	$0.0854179\pi$
$570$	6.00000	−	12.0000i	0.251312	−	0.502625i
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$			12.0000i			0.501745i
$573$			18.0000i			0.751961i
$574$	2.00000			0.0834784
$575$	32.0000	−	24.0000i	1.33449	−	1.00087i
$576$	1.00000			0.0416667
$577$		−	26.0000i		−	1.08239i	−0.840896	−	0.541197i	$-0.817971\pi$
$577$		−	26.0000i		−	1.08239i	0.840896	−	0.541197i	$-0.182029\pi$
$578$			1.00000i			0.0415945i
$579$	8.00000			0.332469
$580$	6.00000	−	12.0000i	0.249136	−	0.498273i
$581$	8.00000			0.331896
$582$		−	10.0000i		−	0.414513i
$583$		−	12.0000i		−	0.496989i
$584$	14.0000			0.579324
$585$	12.0000	+	6.00000i	0.496139	+	0.248069i
$586$		0			0
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		−	1.00000i		−	0.0412393i
$589$	−12.0000			−0.494451
$590$	16.0000	+	8.00000i	0.658710	+	0.329355i
$591$	2.00000			0.0822690
$592$			4.00000i			0.164399i
$593$		−	12.0000i		−	0.492781i	−0.969171	−	0.246390i	$-0.920755\pi$
$593$		−	12.0000i		−	0.492781i	0.969171	−	0.246390i	$-0.0792446\pi$
$594$	−2.00000			−0.0820610
$595$	4.00000	−	8.00000i	0.163984	−	0.327968i
$596$	10.0000			0.409616
$597$			6.00000i			0.245564i
$598$			48.0000i			1.96287i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	3.00000	+	4.00000i	0.122474	+	0.163299i
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$		−	4.00000i		−	0.163028i
$603$		−	8.00000i		−	0.325785i
$604$	8.00000			0.325515
$605$	−7.00000	+	14.0000i	−0.284590	+	0.569181i
$606$	10.0000			0.406222
$607$			8.00000i			0.324710i	0.986732	+	0.162355i	$0.0519090\pi$
$607$			8.00000i			0.324710i	−0.986732	+	0.162355i	$0.948091\pi$
$608$			6.00000i			0.243332i
$609$	6.00000			0.243132
$610$	−20.0000	−	10.0000i	−0.809776	−	0.404888i
$611$	48.0000			1.94187
$612$			4.00000i			0.161690i
$613$		−	28.0000i		−	1.13091i	−0.824779	−	0.565455i	$-0.808701\pi$
$613$		−	28.0000i		−	1.13091i	0.824779	−	0.565455i	$-0.191299\pi$
$614$	12.0000			0.484281
$615$	−4.00000	−	2.00000i	−0.161296	−	0.0806478i
$616$	−2.00000			−0.0805823
$617$		−	26.0000i		−	1.04672i	−0.852111	−	0.523360i	$-0.824678\pi$
$617$		−	26.0000i		−	1.04672i	0.852111	−	0.523360i	$-0.175322\pi$
$618$		−	8.00000i		−	0.321807i
$619$	22.0000			0.884255			0.442127	−	0.896952i	$-0.354224\pi$
$619$	22.0000			0.884255			0.442127	+	0.896952i	$0.354224\pi$
$620$	2.00000	−	4.00000i	0.0803219	−	0.160644i
$621$	−8.00000			−0.321029
$622$			24.0000i			0.962312i
$623$		−	10.0000i		−	0.400642i
$624$	−6.00000			−0.240192
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−2.00000			−0.0799361
$627$		−	12.0000i		−	0.479234i
$628$			22.0000i			0.877896i
$629$	−16.0000			−0.637962
$630$	−1.00000	+	2.00000i	−0.0398410	+	0.0796819i
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$		−	12.0000i		−	0.477334i
$633$		0			0
$634$	2.00000			0.0794301
$635$	8.00000	+	4.00000i	0.317470	+	0.158735i
$636$	6.00000			0.237915
$637$			6.00000i			0.237729i
$638$		−	12.0000i		−	0.475085i
$639$	6.00000			0.237356
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	14.0000			0.552967			0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000			0.552967			0.276483	+	0.961019i	$0.410831\pi$
$642$			12.0000i			0.473602i
$643$		−	12.0000i		−	0.473234i	−0.971603	−	0.236617i	$-0.923961\pi$
$643$		−	12.0000i		−	0.473234i	0.971603	−	0.236617i	$-0.0760386\pi$
$644$	−8.00000			−0.315244
$645$	−4.00000	+	8.00000i	−0.157500	+	0.315000i
$646$	−24.0000			−0.944267
$647$			36.0000i			1.41531i	0.706560	+	0.707653i	$0.250246\pi$
$647$			36.0000i			1.41531i	−0.706560	+	0.707653i	$0.749754\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	16.0000			0.628055
$650$	−18.0000	−	24.0000i	−0.706018	−	0.941357i
$651$	2.00000			0.0783862
$652$		−	4.00000i		−	0.156652i
$653$		−	34.0000i		−	1.33052i	−0.746611	−	0.665261i	$-0.768320\pi$
$653$		−	34.0000i		−	1.33052i	0.746611	−	0.665261i	$-0.231680\pi$
$654$	14.0000			0.547443
$655$	−12.0000	+	24.0000i	−0.468879	+	0.937758i
$656$	2.00000			0.0780869
$657$		−	14.0000i		−	0.546192i
$658$			8.00000i			0.311872i
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$	4.00000	+	2.00000i	0.155700	+	0.0778499i
$661$	38.0000			1.47803			0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000			1.47803			0.739014	+	0.673690i	$0.235292\pi$
$662$		−	8.00000i		−	0.310929i
$663$		−	24.0000i		−	0.932083i
$664$	8.00000			0.310460
$665$	−12.0000	−	6.00000i	−0.465340	−	0.232670i
$666$	4.00000			0.154997
$667$		−	48.0000i		−	1.85857i
$668$			12.0000i			0.464294i
$669$	8.00000			0.309298
$670$	−8.00000	+	16.0000i	−0.309067	+	0.618134i
$671$	−20.0000			−0.772091
$672$		−	1.00000i		−	0.0385758i
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$	8.00000			0.308148
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	23.0000			0.884615
$677$			40.0000i			1.53732i	0.639655	+	0.768662i	$0.279077\pi$
$677$			40.0000i			1.53732i	−0.639655	+	0.768662i	$0.720923\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−10.0000			−0.383765
$680$	4.00000	−	8.00000i	0.153393	−	0.306786i
$681$	−8.00000			−0.306561
$682$		−	4.00000i		−	0.153168i
$683$		−	4.00000i		−	0.153056i	−0.997067	−	0.0765279i	$-0.975617\pi$
$683$		−	4.00000i		−	0.153056i	0.997067	−	0.0765279i	$-0.0243834\pi$
$684$	6.00000			0.229416
$685$	−12.0000	−	6.00000i	−0.458496	−	0.229248i
$686$	−1.00000			−0.0381802
$687$			14.0000i			0.534133i
$688$		−	4.00000i		−	0.152499i
$689$	−36.0000			−1.37149
$690$	16.0000	+	8.00000i	0.609110	+	0.304555i
$691$	−2.00000			−0.0760836			−0.0380418	−	0.999276i	$-0.512112\pi$
$691$	−2.00000			−0.0760836			−0.0380418	+	0.999276i	$0.512112\pi$
$692$			8.00000i			0.304114i
$693$			2.00000i			0.0759737i
$694$	−36.0000			−1.36654
$695$	14.0000	−	28.0000i	0.531050	−	1.06210i
$696$	6.00000			0.227429
$697$			8.00000i			0.303022i
$698$			26.0000i			0.984115i
$699$	10.0000			0.378235
$700$	4.00000	−	3.00000i	0.151186	−	0.113389i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$			6.00000i			0.226455i
$703$			24.0000i			0.905177i
$704$	−2.00000			−0.0753778
$705$	8.00000	−	16.0000i	0.301297	−	0.602595i
$706$	20.0000			0.752710
$707$		−	10.0000i		−	0.376089i
$708$			8.00000i			0.300658i
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	−12.0000	−	6.00000i	−0.450352	−	0.225176i
$711$	−12.0000			−0.450035
$712$		−	10.0000i		−	0.374766i
$713$		−	16.0000i		−	0.599205i
$714$	4.00000			0.149696
$715$	−24.0000	−	12.0000i	−0.897549	−	0.448775i
$716$	10.0000			0.373718
$717$			26.0000i			0.970988i
$718$		−	6.00000i		−	0.223918i
$719$	4.00000			0.149175			0.0745874	−	0.997214i	$-0.476236\pi$
$719$	4.00000			0.149175			0.0745874	+	0.997214i	$0.476236\pi$
$720$	−1.00000	+	2.00000i	−0.0372678	+	0.0745356i
$721$	−8.00000			−0.297936
$722$			17.0000i			0.632674i
$723$			26.0000i			0.966950i
$724$	−2.00000			−0.0743294
$725$	18.0000	+	24.0000i	0.668503	+	0.891338i
$726$	−7.00000			−0.259794
$727$			24.0000i			0.890111i	0.895503	+	0.445055i	$0.146816\pi$
$727$			24.0000i			0.890111i	−0.895503	+	0.445055i	$0.853184\pi$
$728$			6.00000i			0.222375i
$729$	−1.00000			−0.0370370
$730$	−14.0000	+	28.0000i	−0.518163	+	1.03633i
$731$	16.0000			0.591781
$732$		−	10.0000i		−	0.369611i
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$	32.0000			1.18114
$735$	2.00000	+	1.00000i	0.0737711	+	0.0368856i
$736$	−8.00000			−0.294884
$737$			16.0000i			0.589368i
$738$		−	2.00000i		−	0.0736210i
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	−8.00000	−	4.00000i	−0.294086	−	0.147043i
$741$	−36.0000			−1.32249
$742$		−	6.00000i		−	0.220267i
$743$			48.0000i			1.76095i	0.474093	+	0.880475i	$0.342776\pi$
$743$			48.0000i			1.76095i	−0.474093	+	0.880475i	$0.657224\pi$
$744$	2.00000			0.0733236
$745$	−10.0000	+	20.0000i	−0.366372	+	0.732743i
$746$	−24.0000			−0.878702
$747$		−	8.00000i		−	0.292705i
$748$		−	8.00000i		−	0.292509i
$749$	12.0000			0.438470
$750$	−11.0000	+	2.00000i	−0.401663	+	0.0730297i
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$			8.00000i			0.291730i
$753$		0			0
$754$	−36.0000			−1.31104
$755$	−8.00000	+	16.0000i	−0.291150	+	0.582300i
$756$	−1.00000			−0.0363696
$757$		−	32.0000i		−	1.16306i	−0.813525	−	0.581530i	$-0.802454\pi$
$757$		−	32.0000i		−	1.16306i	0.813525	−	0.581530i	$-0.197546\pi$
$758$		−	20.0000i		−	0.726433i
$759$	16.0000			0.580763
$760$	−12.0000	−	6.00000i	−0.435286	−	0.217643i
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$			4.00000i			0.144905i
$763$		−	14.0000i		−	0.506834i
$764$	18.0000			0.651217
$765$	−8.00000	−	4.00000i	−0.289241	−	0.144620i
$766$	20.0000			0.722629
$767$		−	48.0000i		−	1.73318i
$768$		−	1.00000i		−	0.0360844i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$	2.00000	−	4.00000i	0.0720750	−	0.144150i
$771$		0			0
$772$		−	8.00000i		−	0.287926i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	−4.00000			−0.143777
$775$	6.00000	+	8.00000i	0.215526	+	0.287368i
$776$	−10.0000			−0.358979
$777$		−	4.00000i		−	0.143499i
$778$		−	2.00000i		−	0.0717035i
$779$	12.0000			0.429945
$780$	6.00000	−	12.0000i	0.214834	−	0.429669i
$781$	−12.0000			−0.429394
$782$		−	32.0000i		−	1.14432i
$783$		−	6.00000i		−	0.214423i
$784$	−1.00000			−0.0357143
$785$	−44.0000	−	22.0000i	−1.57043	−	0.785214i
$786$	−12.0000			−0.428026
$787$			28.0000i			0.998092i	0.866575	+	0.499046i	$0.166316\pi$
$787$			28.0000i			0.998092i	−0.866575	+	0.499046i	$0.833684\pi$
$788$		−	2.00000i		−	0.0712470i
$789$	−16.0000			−0.569615
$790$	24.0000	+	12.0000i	0.853882	+	0.426941i
$791$	−6.00000			−0.213335
$792$			2.00000i			0.0710669i
$793$			60.0000i			2.13066i
$794$	2.00000			0.0709773
$795$	−6.00000	+	12.0000i	−0.212798	+	0.425596i
$796$	6.00000			0.212664
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		−	6.00000i		−	0.212398i
$799$	−32.0000			−1.13208
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$	−10.0000			−0.353333
$802$		−	14.0000i		−	0.494357i
$803$			28.0000i			0.988099i
$804$	−8.00000			−0.282138
$805$	8.00000	−	16.0000i	0.281963	−	0.563926i
$806$	−12.0000			−0.422682
$807$			18.0000i			0.633630i
$808$		−	10.0000i		−	0.351799i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$	2.00000	+	1.00000i	0.0702728	+	0.0351364i
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$		−	6.00000i		−	0.210559i
$813$		−	10.0000i		−	0.350715i
$814$	−8.00000			−0.280400
$815$	8.00000	+	4.00000i	0.280228	+	0.140114i
$816$	4.00000			0.140028
$817$		−	24.0000i		−	0.839654i
$818$		−	26.0000i		−	0.909069i
$819$	6.00000			0.209657
$820$	−2.00000	+	4.00000i	−0.0698430	+	0.139686i
$821$	22.0000			0.767805			0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000			0.767805			0.383903	+	0.923374i	$0.374580\pi$
$822$		−	6.00000i		−	0.209274i
$823$		−	12.0000i		−	0.418294i	−0.977884	−	0.209147i	$-0.932931\pi$
$823$		−	12.0000i		−	0.418294i	0.977884	−	0.209147i	$-0.0670687\pi$
$824$	−8.00000			−0.278693
$825$	−8.00000	+	6.00000i	−0.278524	+	0.208893i
$826$	8.00000			0.278356
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$			8.00000i			0.278019i
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$	−8.00000	+	16.0000i	−0.277684	+	0.555368i
$831$	28.0000			0.971309
$832$			6.00000i			0.208013i
$833$		−	4.00000i		−	0.138592i
$834$	14.0000			0.484780
$835$	−24.0000	−	12.0000i	−0.830554	−	0.415277i
$836$	−12.0000			−0.415029
$837$		−	2.00000i		−	0.0691301i
$838$		−	20.0000i		−	0.690889i
$839$	20.0000			0.690477			0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000			0.690477			0.345238	+	0.938515i	$0.387798\pi$
$840$	2.00000	+	1.00000i	0.0690066	+	0.0345033i
$841$	7.00000			0.241379
$842$			34.0000i			1.17172i
$843$		−	30.0000i		−	1.03325i
$844$		0			0
$845$	−23.0000	+	46.0000i	−0.791224	+	1.58245i
$846$	8.00000			0.275046
$847$			7.00000i			0.240523i
$848$		−	6.00000i		−	0.206041i
$849$	−20.0000			−0.686398
$850$	12.0000	+	16.0000i	0.411597	+	0.548795i
$851$	−32.0000			−1.09695
$852$		−	6.00000i		−	0.205557i
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$	−10.0000			−0.342193
$855$	−6.00000	+	12.0000i	−0.205196	+	0.410391i
$856$	12.0000			0.410152
$857$			24.0000i			0.819824i	0.912125	+	0.409912i	$0.134441\pi$
$857$			24.0000i			0.819824i	−0.912125	+	0.409912i	$0.865559\pi$
$858$		−	12.0000i		−	0.409673i
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	8.00000	+	4.00000i	0.272798	+	0.136399i
$861$	−2.00000			−0.0681598
$862$			2.00000i			0.0681203i
$863$			48.0000i			1.63394i	0.576681	+	0.816970i	$0.304348\pi$
$863$			48.0000i			1.63394i	−0.576681	+	0.816970i	$0.695652\pi$
$864$	−1.00000			−0.0340207
$865$	−16.0000	−	8.00000i	−0.544016	−	0.272008i
$866$	−26.0000			−0.883516
$867$		−	1.00000i		−	0.0339618i
$868$		−	2.00000i		−	0.0678844i
$869$	24.0000			0.814144
$870$	−6.00000	+	12.0000i	−0.203419	+	0.406838i
$871$	48.0000			1.62642
$872$		−	14.0000i		−	0.474100i
$873$			10.0000i			0.338449i
$874$	−48.0000			−1.62362
$875$	2.00000	+	11.0000i	0.0676123	+	0.371868i
$876$	−14.0000			−0.473016
$877$		−	28.0000i		−	0.945493i	−0.881199	−	0.472746i	$-0.843263\pi$
$877$		−	28.0000i		−	0.945493i	0.881199	−	0.472746i	$-0.156737\pi$
$878$			18.0000i			0.607471i
$879$		0			0
$880$	2.00000	−	4.00000i	0.0674200	−	0.134840i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$			1.00000i			0.0336718i
$883$		−	24.0000i		−	0.807664i	−0.914833	−	0.403832i	$-0.867678\pi$
$883$		−	24.0000i		−	0.807664i	0.914833	−	0.403832i	$-0.132322\pi$
$884$	−24.0000			−0.807207
$885$	−16.0000	−	8.00000i	−0.537834	−	0.268917i
$886$	−12.0000			−0.403148
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		−	4.00000i		−	0.134231i
$889$	4.00000			0.134156
$890$	20.0000	+	10.0000i	0.670402	+	0.335201i
$891$	2.00000			0.0670025
$892$		−	8.00000i		−	0.267860i
$893$			48.0000i			1.60626i
$894$	−10.0000			−0.334450
$895$	−10.0000	+	20.0000i	−0.334263	+	0.668526i
$896$	−1.00000			−0.0334077
$897$		−	48.0000i		−	1.60267i
$898$			6.00000i			0.200223i
$899$	12.0000			0.400222
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$	24.0000			0.799556
$902$			4.00000i			0.133185i
$903$			4.00000i			0.133112i
$904$	−6.00000			−0.199557
$905$	2.00000	−	4.00000i	0.0664822	−	0.132964i
$906$	−8.00000			−0.265782
$907$			24.0000i			0.796907i	0.917189	+	0.398453i	$0.130453\pi$
$907$			24.0000i			0.796907i	−0.917189	+	0.398453i	$0.869547\pi$
$908$			8.00000i			0.265489i
$909$	−10.0000			−0.331679
$910$	−12.0000	−	6.00000i	−0.397796	−	0.198898i
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		−	6.00000i		−	0.198680i
$913$			16.0000i			0.529523i
$914$	−28.0000			−0.926158
$915$	20.0000	+	10.0000i	0.661180	+	0.330590i
$916$	14.0000			0.462573
$917$			12.0000i			0.396275i
$918$		−	4.00000i		−	0.132020i
$919$	−60.0000			−1.97922			−0.989609	−	0.143787i	$-0.954072\pi$
$919$	−60.0000			−1.97922			−0.989609	+	0.143787i	$0.954072\pi$
$920$	8.00000	−	16.0000i	0.263752	−	0.527504i
$921$	−12.0000			−0.395413
$922$		−	18.0000i		−	0.592798i
$923$			36.0000i			1.18495i
$924$	2.00000			0.0657952
$925$	16.0000	−	12.0000i	0.526077	−	0.394558i
$926$	36.0000			1.18303
$927$			8.00000i			0.262754i
$928$		−	6.00000i		−	0.196960i
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$	−2.00000	+	4.00000i	−0.0655826	+	0.131165i
$931$	−6.00000			−0.196642
$932$		−	10.0000i		−	0.327561i
$933$		−	24.0000i		−	0.785725i
$934$	24.0000			0.785304
$935$	16.0000	+	8.00000i	0.523256	+	0.261628i
$936$	6.00000			0.196116
$937$			26.0000i			0.849383i	0.905338	+	0.424691i	$0.139617\pi$
$937$			26.0000i			0.849383i	−0.905338	+	0.424691i	$0.860383\pi$
$938$			8.00000i			0.261209i
$939$	2.00000			0.0652675
$940$	−16.0000	−	8.00000i	−0.521862	−	0.260931i
$941$	−10.0000			−0.325991			−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000			−0.325991			−0.162995	+	0.986627i	$0.552116\pi$
$942$		−	22.0000i		−	0.716799i
$943$			16.0000i			0.521032i
$944$	8.00000			0.260378
$945$	1.00000	−	2.00000i	0.0325300	−	0.0650600i
$946$	8.00000			0.260102
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$			12.0000i			0.389742i
$949$	84.0000			2.72676
$950$	24.0000	−	18.0000i	0.778663	−	0.583997i
$951$	−2.00000			−0.0648544
$952$		−	4.00000i		−	0.129641i
$953$			10.0000i			0.323932i	0.986796	+	0.161966i	$0.0517835\pi$
$953$			10.0000i			0.323932i	−0.986796	+	0.161966i	$0.948217\pi$
$954$	−6.00000			−0.194257
$955$	−18.0000	+	36.0000i	−0.582466	+	1.16493i
$956$	26.0000			0.840900
$957$			12.0000i			0.387905i
$958$		−	8.00000i		−	0.258468i
$959$	−6.00000			−0.193750
$960$	2.00000	+	1.00000i	0.0645497	+	0.0322749i
$961$	−27.0000			−0.870968
$962$			24.0000i			0.773791i
$963$		−	12.0000i		−	0.386695i
$964$	26.0000			0.837404
$965$	16.0000	+	8.00000i	0.515058	+	0.257529i
$966$	8.00000			0.257396
$967$			56.0000i			1.80084i	0.435023	+	0.900419i	$0.356740\pi$
$967$			56.0000i			1.80084i	−0.435023	+	0.900419i	$0.643260\pi$
$968$			7.00000i			0.224989i
$969$	24.0000			0.770991
$970$	10.0000	−	20.0000i	0.321081	−	0.642161i
$971$	−24.0000			−0.770197			−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000			−0.770197			−0.385098	+	0.922876i	$0.625832\pi$
$972$			1.00000i			0.0320750i
$973$		−	14.0000i		−	0.448819i
$974$	−12.0000			−0.384505
$975$	18.0000	+	24.0000i	0.576461	+	0.768615i
$976$	−10.0000			−0.320092
$977$		−	18.0000i		−	0.575871i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$		−	18.0000i		−	0.575871i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$			4.00000i			0.127906i
$979$	20.0000			0.639203
$980$	1.00000	−	2.00000i	0.0319438	−	0.0638877i
$981$	−14.0000			−0.446986
$982$		−	30.0000i		−	0.957338i
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$	−2.00000			−0.0637577
$985$	4.00000	+	2.00000i	0.127451	+	0.0637253i
$986$	24.0000			0.764316
$987$		−	8.00000i		−	0.254643i
$988$			36.0000i			1.14531i
$989$	32.0000			1.01754
$990$	−4.00000	−	2.00000i	−0.127128	−	0.0635642i
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$		−	2.00000i		−	0.0635001i
$993$			8.00000i			0.253872i
$994$	−6.00000			−0.190308
$995$	−6.00000	+	12.0000i	−0.190213	+	0.380426i
$996$	−8.00000			−0.253490
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$			12.0000i			0.379853i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.g.b.169.2	yes	2
3.2	odd	2		630.2.g.c.379.1		2
4.3	odd	2		1680.2.t.e.1009.2		2
5.2	odd	4		1050.2.a.d.1.1		1
5.3	odd	4		1050.2.a.p.1.1		1
5.4	even	2	inner	210.2.g.b.169.1	✓	2
7.2	even	3		1470.2.n.b.949.2		4
7.3	odd	6		1470.2.n.f.79.1		4
7.4	even	3		1470.2.n.b.79.1		4
7.5	odd	6		1470.2.n.f.949.2		4
7.6	odd	2		1470.2.g.b.589.2		2
12.11	even	2		5040.2.t.h.1009.2		2
15.2	even	4		3150.2.a.bk.1.1		1
15.8	even	4		3150.2.a.d.1.1		1
15.14	odd	2		630.2.g.c.379.2		2
20.3	even	4		8400.2.a.w.1.1		1
20.7	even	4		8400.2.a.bp.1.1		1
20.19	odd	2		1680.2.t.e.1009.1		2
35.4	even	6		1470.2.n.b.79.2		4
35.9	even	6		1470.2.n.b.949.1		4
35.13	even	4		7350.2.a.bz.1.1		1
35.19	odd	6		1470.2.n.f.949.1		4
35.24	odd	6		1470.2.n.f.79.2		4
35.27	even	4		7350.2.a.bk.1.1		1
35.34	odd	2		1470.2.g.b.589.1		2
60.59	even	2		5040.2.t.h.1009.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.g.b.169.1	✓	2	5.4	even	2	inner
210.2.g.b.169.2	yes	2	1.1	even	1	trivial
630.2.g.c.379.1		2	3.2	odd	2
630.2.g.c.379.2		2	15.14	odd	2
1050.2.a.d.1.1		1	5.2	odd	4
1050.2.a.p.1.1		1	5.3	odd	4
1470.2.g.b.589.1		2	35.34	odd	2
1470.2.g.b.589.2		2	7.6	odd	2
1470.2.n.b.79.1		4	7.4	even	3
1470.2.n.b.79.2		4	35.4	even	6
1470.2.n.b.949.1		4	35.9	even	6
1470.2.n.b.949.2		4	7.2	even	3
1470.2.n.f.79.1		4	7.3	odd	6
1470.2.n.f.79.2		4	35.24	odd	6
1470.2.n.f.949.1		4	35.19	odd	6
1470.2.n.f.949.2		4	7.5	odd	6
1680.2.t.e.1009.1		2	20.19	odd	2
1680.2.t.e.1009.2		2	4.3	odd	2
3150.2.a.d.1.1		1	15.8	even	4
3150.2.a.bk.1.1		1	15.2	even	4
5040.2.t.h.1009.1		2	60.59	even	2
5040.2.t.h.1009.2		2	12.11	even	2
7350.2.a.bk.1.1		1	35.27	even	4
7350.2.a.bz.1.1		1	35.13	even	4
8400.2.a.w.1.1		1	20.3	even	4
8400.2.a.bp.1.1		1	20.7	even	4

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} +2.00000 q^{11} +1.00000i q^{12} -6.00000i q^{13} +1.00000 q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} -1.00000i q^{18} +6.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -1.00000 q^{21} +2.00000i q^{22} +8.00000i q^{23} -1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +6.00000 q^{26} +1.00000i q^{27} +1.00000i q^{28} -6.00000 q^{29} +(1.00000 - 2.00000i) q^{30} -2.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} -4.00000 q^{34} +(-2.00000 - 1.00000i) q^{35} +1.00000 q^{36} +4.00000i q^{37} +6.00000i q^{38} -6.00000 q^{39} +(-2.00000 - 1.00000i) q^{40} +2.00000 q^{41} -1.00000i q^{42} -4.00000i q^{43} -2.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} -8.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +4.00000 q^{51} +6.00000i q^{52} -6.00000i q^{53} -1.00000 q^{54} +(2.00000 - 4.00000i) q^{55} -1.00000 q^{56} -6.00000i q^{57} -6.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -10.0000 q^{61} -2.00000i q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-12.0000 - 6.00000i) q^{65} +2.00000 q^{66} +8.00000i q^{67} -4.00000i q^{68} +8.00000 q^{69} +(1.00000 - 2.00000i) q^{70} -6.00000 q^{71} +1.00000i q^{72} +14.0000i q^{73} -4.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -6.00000 q^{76} -2.00000i q^{77} -6.00000i q^{78} +12.0000 q^{79} +(1.00000 - 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} +8.00000i q^{83} +1.00000 q^{84} +(8.00000 + 4.00000i) q^{85} +4.00000 q^{86} +6.00000i q^{87} -2.00000i q^{88} +10.0000 q^{89} +(-2.00000 - 1.00000i) q^{90} -6.00000 q^{91} -8.00000i q^{92} +2.00000i q^{93} -8.00000 q^{94} +(6.00000 - 12.0000i) q^{95} +1.00000 q^{96} -10.0000i q^{97} -1.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{14} - 4 q^{15} + 2 q^{16} + 12 q^{19} - 2 q^{20} - 2 q^{21} - 2 q^{24} - 6 q^{25} + 12 q^{26} - 12 q^{29} + 2 q^{30} - 4 q^{31} - 8 q^{34} - 4 q^{35} + 2 q^{36} - 12 q^{39} - 4 q^{40} + 4 q^{41} - 4 q^{44} - 2 q^{45} - 16 q^{46} - 2 q^{49} + 8 q^{50} + 8 q^{51} - 2 q^{54} + 4 q^{55} - 2 q^{56} + 16 q^{59} + 4 q^{60} - 20 q^{61} - 2 q^{64} - 24 q^{65} + 4 q^{66} + 16 q^{69} + 2 q^{70} - 12 q^{71} - 8 q^{74} - 8 q^{75} - 12 q^{76} + 24 q^{79} + 2 q^{80} + 2 q^{81} + 2 q^{84} + 16 q^{85} + 8 q^{86} + 20 q^{89} - 4 q^{90} - 12 q^{91} - 16 q^{94} + 12 q^{95} + 2 q^{96} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^14 - 4 * q^15 + 2 * q^16 + 12 * q^19 - 2 * q^20 - 2 * q^21 - 2 * q^24 - 6 * q^25 + 12 * q^26 - 12 * q^29 + 2 * q^30 - 4 * q^31 - 8 * q^34 - 4 * q^35 + 2 * q^36 - 12 * q^39 - 4 * q^40 + 4 * q^41 - 4 * q^44 - 2 * q^45 - 16 * q^46 - 2 * q^49 + 8 * q^50 + 8 * q^51 - 2 * q^54 + 4 * q^55 - 2 * q^56 + 16 * q^59 + 4 * q^60 - 20 * q^61 - 2 * q^64 - 24 * q^65 + 4 * q^66 + 16 * q^69 + 2 * q^70 - 12 * q^71 - 8 * q^74 - 8 * q^75 - 12 * q^76 + 24 * q^79 + 2 * q^80 + 2 * q^81 + 2 * q^84 + 16 * q^85 + 8 * q^86 + 20 * q^89 - 4 * q^90 - 12 * q^91 - 16 * q^94 + 12 * q^95 + 2 * q^96 - 4 * q^99

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