LMFDB - Embedded newform 1680.2.bg.l.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1680.1201
Dual form			1680.2.bg.l.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} -3.00000 q^{13} -1.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-2.50000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-1.50000 + 2.59808i) q^{39} -6.00000 q^{41} -1.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 + 3.46410i) q^{53} +6.00000 q^{55} +1.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(1.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} -4.00000 q^{69} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(0.500000 + 0.866025i) q^{75} +(12.0000 + 10.3923i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000 q^{83} -4.00000 q^{85} +(-4.00000 + 6.92820i) q^{87} +(6.00000 + 10.3923i) q^{89} +(-1.50000 + 7.79423i) q^{91} +(-0.500000 - 0.866025i) q^{93} +(0.500000 - 0.866025i) q^{95} -6.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{5} + q^{7} - q^{9}+O(q^{10}) $ 2 * q + q^3 - q^5 + q^7 - q^9	$ 2 q + q^{3} - q^{5} + q^{7} - q^{9} - 6 q^{11} - 6 q^{13} - 2 q^{15} + 4 q^{17} + q^{19} - 4 q^{21} - 4 q^{23} - q^{25} - 2 q^{27} - 16 q^{29} + q^{31} + 6 q^{33} - 5 q^{35} - 7 q^{37} - 3 q^{39} - 12 q^{41} - 2 q^{43} - q^{45} + 2 q^{47} - 13 q^{49} - 4 q^{51} - 4 q^{53} + 12 q^{55} + 2 q^{57} - 8 q^{59} + 14 q^{61} - 5 q^{63} + 3 q^{65} + 7 q^{67} - 8 q^{69} - 12 q^{71} - q^{73} + q^{75} + 24 q^{77} - q^{79} - q^{81} - 4 q^{83} - 8 q^{85} - 8 q^{87} + 12 q^{89} - 3 q^{91} - q^{93} + q^{95} - 12 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^5 + q^7 - q^9 - 6 * q^11 - 6 * q^13 - 2 * q^15 + 4 * q^17 + q^19 - 4 * q^21 - 4 * q^23 - q^25 - 2 * q^27 - 16 * q^29 + q^31 + 6 * q^33 - 5 * q^35 - 7 * q^37 - 3 * q^39 - 12 * q^41 - 2 * q^43 - q^45 + 2 * q^47 - 13 * q^49 - 4 * q^51 - 4 * q^53 + 12 * q^55 + 2 * q^57 - 8 * q^59 + 14 * q^61 - 5 * q^63 + 3 * q^65 + 7 * q^67 - 8 * q^69 - 12 * q^71 - q^73 + q^75 + 24 * q^77 - q^79 - q^81 - 4 * q^83 - 8 * q^85 - 8 * q^87 + 12 * q^89 - 3 * q^91 - q^93 + q^95 - 12 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$		0			0
$39$	−1.50000	+	2.59808i	−0.240192	+	0.416025i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$	1.00000			0.132453
$58$		0			0
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	−2.50000	+	0.866025i	−0.314970	+	0.109109i
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	−0.893801	−	0.448463i	$-0.851972\pi$
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	0.835281	+	0.549823i	$0.185305\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	12.0000	+	10.3923i	1.36753	+	1.18431i
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$		0			0
$87$	−4.00000	+	6.92820i	−0.428845	+	0.742781i
$88$		0			0
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	0.986303	+	0.164946i	$0.0527450\pi$
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	−0.350304	+	0.936636i	$0.613922\pi$
$90$		0			0
$91$	−1.50000	+	7.79423i	−0.157243	+	0.817057i
$92$		0			0
$93$	−0.500000	−	0.866025i	−0.0518476	−	0.0898027i
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	−9.50000	−	16.4545i	−0.936063	−	1.62131i	−0.772728	−	0.634738i	$-0.781108\pi$
$103$	−9.50000	−	16.4545i	−0.936063	−	1.62131i	−0.163335	−	0.986571i	$-0.552225\pi$
$104$		0			0
$105$	−0.500000	+	2.59808i	−0.0487950	+	0.253546i
$106$		0			0
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$		0			0
$109$	7.50000	−	12.9904i	0.718370	−	1.24425i	−0.243276	−	0.969957i	$-0.578222\pi$
$109$	7.50000	−	12.9904i	0.718370	−	1.24425i	0.961645	−	0.274296i	$-0.0884447\pi$
$110$		0			0
$111$	−7.00000			−0.664411
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$		0			0
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$		0			0
$119$	−8.00000	−	6.92820i	−0.733359	−	0.635107i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$		0			0
$129$	−0.500000	+	0.866025i	−0.0440225	+	0.0762493i
$130$		0			0
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	0.906399	−	0.422423i	$-0.138820\pi$
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	−0.819028	+	0.573753i	$0.805487\pi$
$132$		0			0
$133$	2.50000	−	0.866025i	0.216777	−	0.0750939i
$134$		0			0
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	−0.984757	−	0.173939i	$-0.944351\pi$
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	0.643013	+	0.765855i	$0.277684\pi$
$138$		0			0
$139$	−21.0000			−1.78120			−0.890598	−	0.454791i	$-0.849714\pi$
$139$	−21.0000			−1.78120			−0.890598	+	0.454791i	$0.849714\pi$
$140$		0			0
$141$	2.00000			0.168430
$142$		0			0
$143$	9.00000	−	15.5885i	0.752618	−	1.30357i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$		0			0
$147$	−5.50000	+	4.33013i	−0.453632	+	0.357143i
$148$		0			0
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	0.936245	−	0.351348i	$-0.114277\pi$
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	−0.772399	+	0.635138i	$0.780943\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−1.00000			−0.0803219
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$		0			0
$159$	2.00000	+	3.46410i	0.158610	+	0.274721i
$160$		0			0
$161$	−10.0000	+	3.46410i	−0.788110	+	0.273009i
$162$		0			0
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	0.529454	−	0.848339i	$-0.322397\pi$
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	−0.999410	+	0.0343508i	$0.989064\pi$
$164$		0			0
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$		0			0
$167$	10.0000			0.773823			0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000			0.773823			0.386912	+	0.922117i	$0.373542\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$		0			0
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.810745	−	0.585399i	$-0.800938\pi$
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.101598	−	0.994826i	$-0.532395\pi$
$174$		0			0
$175$	2.00000	+	1.73205i	0.151186	+	0.130931i
$176$		0			0
$177$	4.00000	+	6.92820i	0.300658	+	0.520756i
$178$		0			0
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$	−3.50000	+	6.06218i	−0.257325	+	0.445700i
$186$		0			0
$187$	12.0000	+	20.7846i	0.877527	+	1.51992i
$188$		0			0
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		0			0
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	0.988255	−	0.152813i	$-0.0488333\pi$
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	−0.626468	+	0.779447i	$0.715500\pi$
$192$		0			0
$193$	4.50000	−	7.79423i	0.323917	−	0.561041i	−0.657376	−	0.753563i	$-0.728333\pi$
$193$	4.50000	−	7.79423i	0.323917	−	0.561041i	0.981293	+	0.192522i	$0.0616668\pi$
$194$		0			0
$195$	3.00000			0.214834
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		0			0
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$		0			0
$203$	−4.00000	+	20.7846i	−0.280745	+	1.45879i
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$		0			0
$207$	−2.00000	+	3.46410i	−0.139010	+	0.240772i
$208$		0			0
$209$	−6.00000			−0.415029
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$		0			0
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$		0			0
$215$	0.500000	+	0.866025i	0.0340997	+	0.0590624i
$216$		0			0
$217$	−2.00000	−	1.73205i	−0.135769	−	0.117579i
$218$		0			0
$219$	0.500000	+	0.866025i	0.0337869	+	0.0585206i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	−0.982877	−	0.184263i	$-0.941010\pi$
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	0.651015	+	0.759065i	$0.274343\pi$
$228$		0			0
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$		0			0
$231$	15.0000	−	5.19615i	0.986928	−	0.341882i
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	1.00000	−	1.73205i	0.0652328	−	0.112987i
$236$		0			0
$237$	−1.00000			−0.0649570
$238$		0			0
$239$	−14.0000			−0.905585			−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000			−0.905585			−0.452792	+	0.891616i	$0.649572\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		0			0
$247$	−1.50000	−	2.59808i	−0.0954427	−	0.165312i
$248$		0			0
$249$	−1.00000	+	1.73205i	−0.0633724	+	0.109764i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	24.0000			1.50887
$254$		0			0
$255$	−2.00000	+	3.46410i	−0.125245	+	0.216930i
$256$		0			0
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	−17.5000	+	6.06218i	−1.08740	+	0.376685i
$260$		0			0
$261$	4.00000	+	6.92820i	0.247594	+	0.428845i
$262$		0			0
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	−0.797752	−	0.602986i	$-0.793977\pi$
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	0.921077	+	0.389380i	$0.127311\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	12.0000			0.734388
$268$		0			0
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$		0			0
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$		0			0
$273$	6.00000	+	5.19615i	0.363137	+	0.314485i
$274$		0			0
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$		0			0
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	−0.741512	−	0.670940i	$-0.765891\pi$
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	0.951807	+	0.306699i	$0.0992243\pi$
$278$		0			0
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$		0			0
$283$	−3.50000	+	6.06218i	−0.208053	+	0.360359i	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−3.50000	+	6.06218i	−0.208053	+	0.360359i	0.743048	+	0.669238i	$0.233379\pi$
$284$		0			0
$285$	−0.500000	−	0.866025i	−0.0296174	−	0.0512989i
$286$		0			0
$287$	−3.00000	+	15.5885i	−0.177084	+	0.920158i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	−3.00000	+	5.19615i	−0.175863	+	0.304604i
$292$		0			0
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$	3.00000	−	5.19615i	0.174078	−	0.301511i
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	−0.500000	+	2.59808i	−0.0288195	+	0.149751i
$302$		0			0
$303$	−5.00000	−	8.66025i	−0.287242	−	0.497519i
$304$		0			0
$305$	7.00000	−	12.1244i	0.400819	−	0.694239i
$306$		0			0
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$		0			0
$309$	−19.0000			−1.08087
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$		0			0
$315$	2.00000	+	1.73205i	0.112687	+	0.0975900i
$316$		0			0
$317$	−10.0000	−	17.3205i	−0.561656	−	0.972817i	−0.997352	−	0.0727229i	$-0.976831\pi$
$317$	−10.0000	−	17.3205i	−0.561656	−	0.972817i	0.435696	−	0.900094i	$-0.356502\pi$
$318$		0			0
$319$	24.0000	−	41.5692i	1.34374	−	2.32743i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	4.00000			0.222566
$324$		0			0
$325$	1.50000	−	2.59808i	0.0832050	−	0.144115i
$326$		0			0
$327$	−7.50000	−	12.9904i	−0.414751	−	0.718370i
$328$		0			0
$329$	5.00000	−	1.73205i	0.275659	−	0.0954911i
$330$		0			0
$331$	−4.50000	−	7.79423i	−0.247342	−	0.428410i	0.715445	−	0.698669i	$-0.246224\pi$
$331$	−4.50000	−	7.79423i	−0.247342	−	0.428410i	−0.962788	+	0.270259i	$0.912891\pi$
$332$		0			0
$333$	−3.50000	+	6.06218i	−0.191799	+	0.332205i
$334$		0			0
$335$	−7.00000			−0.382451
$336$		0			0
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$		0			0
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	2.00000	+	3.46410i	0.107676	+	0.186501i
$346$		0			0
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	3.00000			0.160128
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$	−10.0000	+	3.46410i	−0.529256	+	0.183340i
$358$		0			0
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−25.0000			−1.31216
$364$		0			0
$365$	1.00000			0.0523424
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$	−11.0000			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$380$		0			0
$381$	−2.50000	+	4.33013i	−0.128079	+	0.221839i
$382$		0			0
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	0.962818	+	0.270151i	$0.0870736\pi$
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	−0.247451	+	0.968900i	$0.579593\pi$
$384$		0			0
$385$	3.00000	−	15.5885i	0.152894	−	0.794461i
$386$		0			0
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$		0			0
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$	2.00000			0.100887
$394$		0			0
$395$	−0.500000	+	0.866025i	−0.0251577	+	0.0435745i
$396$		0			0
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.785853	+	0.618414i	$0.212224\pi$
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.142636	+	0.989775i	$0.454442\pi$
$398$		0			0
$399$	0.500000	−	2.59808i	0.0250313	−	0.130066i
$400$		0			0
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$		0			0
$403$	−1.50000	+	2.59808i	−0.0747203	+	0.129419i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	42.0000			2.08186
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	4.00000	+	6.92820i	0.197305	+	0.341743i
$412$		0			0
$413$	16.0000	+	13.8564i	0.787309	+	0.681829i
$414$		0			0
$415$	1.00000	+	1.73205i	0.0490881	+	0.0850230i
$416$		0			0
$417$	−10.5000	+	18.1865i	−0.514187	+	0.890598i
$418$		0			0
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$		0			0
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$		0			0
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$		0			0
$427$	35.0000	−	12.1244i	1.69377	−	0.586739i
$428$		0			0
$429$	−9.00000	−	15.5885i	−0.434524	−	0.752618i
$430$		0			0
$431$	−1.00000	+	1.73205i	−0.0481683	+	0.0834300i	−0.889104	−	0.457705i	$-0.848672\pi$
$431$	−1.00000	+	1.73205i	−0.0481683	+	0.0834300i	0.840936	+	0.541135i	$0.182005\pi$
$432$		0			0
$433$	−5.00000			−0.240285			−0.120142	−	0.992757i	$-0.538335\pi$
$433$	−5.00000			−0.240285			−0.120142	+	0.992757i	$0.538335\pi$
$434$		0			0
$435$	8.00000			0.383571
$436$		0			0
$437$	2.00000	−	3.46410i	0.0956730	−	0.165710i
$438$		0			0
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$		0			0
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$		0			0
$447$	4.00000			0.189194
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	18.0000	−	31.1769i	0.847587	−	1.46806i
$452$		0			0
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$		0			0
$455$	7.50000	−	2.59808i	0.351605	−	0.121800i
$456$		0			0
$457$	7.50000	+	12.9904i	0.350835	+	0.607664i	0.986396	−	0.164386i	$-0.0525644\pi$
$457$	7.50000	+	12.9904i	0.350835	+	0.607664i	−0.635561	+	0.772051i	$0.719231\pi$
$458$		0			0
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	−8.00000			−0.372597			−0.186299	−	0.982493i	$-0.559649\pi$
$461$	−8.00000			−0.372597			−0.186299	+	0.982493i	$0.559649\pi$
$462$		0			0
$463$	−3.00000			−0.139422			−0.0697109	−	0.997567i	$-0.522208\pi$
$463$	−3.00000			−0.139422			−0.0697109	+	0.997567i	$0.522208\pi$
$464$		0			0
$465$	−0.500000	+	0.866025i	−0.0231869	+	0.0401610i
$466$		0			0
$467$	11.0000	+	19.0526i	0.509019	+	0.881647i	0.999945	+	0.0104461i	$0.00332515\pi$
$467$	11.0000	+	19.0526i	0.509019	+	0.881647i	−0.490926	+	0.871201i	$0.663342\pi$
$468$		0			0
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$		0			0
$471$	5.00000	+	8.66025i	0.230388	+	0.399043i
$472$		0			0
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	−1.00000			−0.0458831
$476$		0			0
$477$	4.00000			0.183147
$478$		0			0
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		0			0
$481$	10.5000	+	18.1865i	0.478759	+	0.829235i
$482$		0			0
$483$	−2.00000	+	10.3923i	−0.0910032	+	0.472866i
$484$		0			0
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		0			0
$487$	−6.50000	+	11.2583i	−0.294543	+	0.510164i	−0.974879	−	0.222737i	$-0.928501\pi$
$487$	−6.50000	+	11.2583i	−0.294543	+	0.510164i	0.680335	+	0.732901i	$0.261834\pi$
$488$		0			0
$489$	−12.0000			−0.542659
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	−16.0000	+	27.7128i	−0.720604	+	1.24812i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$		0			0
$497$	−3.00000	+	15.5885i	−0.134568	+	0.699238i
$498$		0			0
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$		0			0
$501$	5.00000	−	8.66025i	0.223384	−	0.386912i
$502$		0			0
$503$	2.00000			0.0891756			0.0445878	−	0.999005i	$-0.485803\pi$
$503$	2.00000			0.0891756			0.0445878	+	0.999005i	$0.485803\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$		0			0
$507$	−2.00000	+	3.46410i	−0.0888231	+	0.153846i
$508$		0			0
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$		0			0
$511$	2.00000	+	1.73205i	0.0884748	+	0.0766214i
$512$		0			0
$513$	−0.500000	−	0.866025i	−0.0220755	−	0.0382360i
$514$		0			0
$515$	−9.50000	+	16.4545i	−0.418620	+	0.725071i
$516$		0			0
$517$	−12.0000			−0.527759
$518$		0			0
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−2.00000	+	3.46410i	−0.0876216	+	0.151765i	−0.906505	−	0.422194i	$-0.861260\pi$
$521$	−2.00000	+	3.46410i	−0.0876216	+	0.151765i	0.818884	+	0.573959i	$0.194593\pi$
$522$		0			0
$523$	5.50000	+	9.52628i	0.240498	+	0.416555i	0.960856	−	0.277047i	$-0.0893559\pi$
$523$	5.50000	+	9.52628i	0.240498	+	0.416555i	−0.720358	+	0.693602i	$0.756023\pi$
$524$		0			0
$525$	2.50000	−	0.866025i	0.109109	−	0.0377964i
$526$		0			0
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	8.00000			0.347170
$532$		0			0
$533$	18.0000			0.779667
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$		0			0
$537$	−9.00000	−	15.5885i	−0.388379	−	0.672692i
$538$		0			0
$539$	33.0000	−	25.9808i	1.42141	−	1.11907i
$540$		0			0
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$542$		0			0
$543$	6.50000	−	11.2583i	0.278942	−	0.483141i
$544$		0			0
$545$	−15.0000			−0.642529
$546$		0			0
$547$	−36.0000			−1.53925			−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000			−1.53925			−0.769624	+	0.638497i	$0.779557\pi$
$548$		0			0
$549$	7.00000	−	12.1244i	0.298753	−	0.517455i
$550$		0			0
$551$	−4.00000	−	6.92820i	−0.170406	−	0.295151i
$552$		0			0
$553$	−2.50000	+	0.866025i	−0.106311	+	0.0368271i
$554$		0			0
$555$	3.50000	+	6.06218i	0.148567	+	0.257325i
$556$		0			0
$557$	5.00000	−	8.66025i	0.211857	−	0.366947i	−0.740439	−	0.672124i	$-0.765382\pi$
$557$	5.00000	−	8.66025i	0.211857	−	0.366947i	0.952296	+	0.305177i	$0.0987156\pi$
$558$		0			0
$559$	3.00000			0.126886
$560$		0			0
$561$	24.0000			1.01328
$562$		0			0
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	0.450535	+	0.892759i	$0.351233\pi$
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	−0.998419	+	0.0562051i	$0.982100\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$	2.00000	+	1.73205i	0.0839921	+	0.0727393i
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−1.50000	+	2.59808i	−0.0627730	+	0.108726i	−0.895704	−	0.444651i	$-0.853328\pi$
$571$	−1.50000	+	2.59808i	−0.0627730	+	0.108726i	0.832931	+	0.553377i	$0.186661\pi$
$572$		0			0
$573$	10.0000			0.417756
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	14.5000	−	25.1147i	0.603643	−	1.04554i	−0.388621	−	0.921397i	$-0.627049\pi$
$577$	14.5000	−	25.1147i	0.603643	−	1.04554i	0.992264	−	0.124143i	$-0.0396180\pi$
$578$		0			0
$579$	−4.50000	−	7.79423i	−0.187014	−	0.323917i
$580$		0			0
$581$	−1.00000	+	5.19615i	−0.0414870	+	0.215573i
$582$		0			0
$583$	−12.0000	−	20.7846i	−0.496989	−	0.860811i
$584$		0			0
$585$	1.50000	−	2.59808i	0.0620174	−	0.107417i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	1.00000			0.0412043
$590$		0			0
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$		0			0
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	0.989501	−	0.144528i	$-0.0461663\pi$
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	−0.619915	+	0.784669i	$0.712833\pi$
$594$		0			0
$595$	−2.00000	+	10.3923i	−0.0819920	+	0.426043i
$596$		0			0
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$		0			0
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	−0.903988	−	0.427558i	$-0.859374\pi$
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	0.822270	+	0.569097i	$0.192707\pi$
$600$		0			0
$601$	−33.0000			−1.34610			−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000			−1.34610			−0.673049	+	0.739598i	$0.735016\pi$
$602$		0			0
$603$	−7.00000			−0.285062
$604$		0			0
$605$	−12.5000	+	21.6506i	−0.508197	+	0.880223i
$606$		0			0
$607$	17.5000	+	30.3109i	0.710303	+	1.23028i	0.964743	+	0.263193i	$0.0847754\pi$
$607$	17.5000	+	30.3109i	0.710303	+	1.23028i	−0.254440	+	0.967088i	$0.581891\pi$
$608$		0			0
$609$	16.0000	+	13.8564i	0.648353	+	0.561490i
$610$		0			0
$611$	−3.00000	−	5.19615i	−0.121367	−	0.210214i
$612$		0			0
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	−0.386073	−	0.922468i	$-0.626169\pi$
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	0.991917	−	0.126885i	$-0.0404979\pi$
$614$		0			0
$615$	6.00000			0.241943
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	1.50000	−	2.59808i	0.0602901	−	0.104425i	−0.834305	−	0.551303i	$-0.814131\pi$
$619$	1.50000	−	2.59808i	0.0602901	−	0.104425i	0.894595	+	0.446878i	$0.147464\pi$
$620$		0			0
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$		0			0
$623$	30.0000	−	10.3923i	1.20192	−	0.416359i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$		0			0
$629$	−28.0000			−1.11643
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$		0			0
$633$	10.0000	−	17.3205i	0.397464	−	0.688428i
$634$		0			0
$635$	2.50000	+	4.33013i	0.0992095	+	0.171836i
$636$		0			0
$637$	19.5000	+	7.79423i	0.772618	+	0.308819i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	0.722862	+	0.690992i	$0.242826\pi$
$642$		0			0
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$		0			0
$645$	1.00000			0.0393750
$646$		0			0
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	−0.404559	−	0.914512i	$-0.632575\pi$
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	0.994270	−	0.106897i	$-0.0340916\pi$
$648$		0			0
$649$	−24.0000	−	41.5692i	−0.942082	−	1.63173i
$650$		0			0
$651$	−2.50000	+	0.866025i	−0.0979827	+	0.0339422i
$652$		0			0
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	0.695934	−	0.718106i	$-0.254991\pi$
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	−0.969865	+	0.243643i	$0.921657\pi$
$654$		0			0
$655$	1.00000	−	1.73205i	0.0390732	−	0.0676768i
$656$		0			0
$657$	1.00000			0.0390137
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$		0			0
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$		0			0
$665$	−2.00000	−	1.73205i	−0.0775567	−	0.0671660i
$666$		0			0
$667$	16.0000	+	27.7128i	0.619522	+	1.07304i
$668$		0			0
$669$	12.0000	−	20.7846i	0.463947	−	0.803579i
$670$		0			0
$671$	−84.0000			−3.24278
$672$		0			0
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	−8.00000	−	13.8564i	−0.307465	−	0.532545i	0.670342	−	0.742052i	$-0.266147\pi$
$677$	−8.00000	−	13.8564i	−0.307465	−	0.532545i	−0.977807	+	0.209507i	$0.932814\pi$
$678$		0			0
$679$	−3.00000	+	15.5885i	−0.115129	+	0.598230i
$680$		0			0
$681$	5.00000	+	8.66025i	0.191600	+	0.331862i
$682$		0			0
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.116390	+	0.993204i	$0.537132\pi$
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.801945	+	0.597398i	$0.796201\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$		0			0
$687$	−13.0000			−0.495981
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	13.5000	+	23.3827i	0.513564	+	0.889519i	0.999876	+	0.0157341i	$0.00500851\pi$
$691$	13.5000	+	23.3827i	0.513564	+	0.889519i	−0.486312	+	0.873785i	$0.661658\pi$
$692$		0			0
$693$	3.00000	−	15.5885i	0.113961	−	0.592157i
$694$		0			0
$695$	10.5000	+	18.1865i	0.398288	+	0.689855i
$696$		0			0
$697$	−12.0000	+	20.7846i	−0.454532	+	0.787273i
$698$		0			0
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$		0			0
$703$	3.50000	−	6.06218i	0.132005	−	0.228639i
$704$		0			0
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$		0			0
$707$	−20.0000	−	17.3205i	−0.752177	−	0.651405i
$708$		0			0
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$		0			0
$711$	−0.500000	+	0.866025i	−0.0187515	+	0.0324785i
$712$		0			0
$713$	−4.00000			−0.149801
$714$		0			0
$715$	−18.0000			−0.673162
$716$		0			0
$717$	−7.00000	+	12.1244i	−0.261420	+	0.452792i
$718$		0			0
$719$	−17.0000	−	29.4449i	−0.633993	−	1.09811i	−0.986728	−	0.162385i	$-0.948081\pi$
$719$	−17.0000	−	29.4449i	−0.633993	−	1.09811i	0.352735	−	0.935723i	$-0.385252\pi$
$720$		0			0
$721$	−47.5000	+	16.4545i	−1.76899	+	0.612797i
$722$		0			0
$723$	−9.00000	−	15.5885i	−0.334714	−	0.579741i
$724$		0			0
$725$	4.00000	−	6.92820i	0.148556	−	0.257307i
$726$		0			0
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$		0			0
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	0.923396	+	0.383849i	$0.125402\pi$
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	−0.129275	+	0.991609i	$0.541265\pi$
$734$		0			0
$735$	6.50000	+	2.59808i	0.239756	+	0.0958315i
$736$		0			0
$737$	21.0000	+	36.3731i	0.773545	+	1.33982i
$738$		0			0
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	−0.191714	−	0.981451i	$-0.561404\pi$
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	0.945818	−	0.324697i	$-0.105262\pi$
$740$		0			0
$741$	−3.00000			−0.110208
$742$		0			0
$743$	−6.00000			−0.220119			−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000			−0.220119			−0.110059	+	0.993925i	$0.535104\pi$
$744$		0			0
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$		0			0
$747$	1.00000	+	1.73205i	0.0365881	+	0.0633724i
$748$		0			0
$749$	30.0000	−	10.3923i	1.09618	−	0.379727i
$750$		0			0
$751$	14.5000	+	25.1147i	0.529113	+	0.916450i	0.999424	+	0.0339490i	$0.0108084\pi$
$751$	14.5000	+	25.1147i	0.529113	+	0.916450i	−0.470311	+	0.882501i	$0.655858\pi$
$752$		0			0
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$		0			0
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$	12.0000	−	20.7846i	0.435572	−	0.754434i
$760$		0			0
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		0			0
$763$	−30.0000	−	25.9808i	−1.08607	−	0.940567i
$764$		0			0
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$		0			0
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$		0			0
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$		0			0
$775$	0.500000	+	0.866025i	0.0179605	+	0.0311086i
$776$		0			0
$777$	−3.50000	+	18.1865i	−0.125562	+	0.652438i
$778$		0			0
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$	8.00000			0.285897
$784$		0			0
$785$	10.0000			0.356915
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$		0			0
$789$	−2.00000	−	3.46410i	−0.0712019	−	0.123325i
$790$		0			0
$791$	−3.00000	+	15.5885i	−0.106668	+	0.554262i
$792$		0			0
$793$	−21.0000	−	36.3731i	−0.745732	−	1.29165i
$794$		0			0
$795$	2.00000	−	3.46410i	0.0709327	−	0.122859i
$796$		0			0
$797$	−36.0000			−1.27519			−0.637593	−	0.770374i	$-0.720070\pi$
$797$	−36.0000			−1.27519			−0.637593	+	0.770374i	$0.720070\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$		0			0
$801$	6.00000	−	10.3923i	0.212000	−	0.367194i
$802$		0			0
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$	8.00000	+	6.92820i	0.281963	+	0.244187i
$806$		0			0
$807$	−5.00000	−	8.66025i	−0.176008	−	0.304855i
$808$		0			0
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	−0.214930	−	0.976629i	$-0.568952\pi$
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	0.953251	−	0.302180i	$-0.0977142\pi$
$810$		0			0
$811$	48.0000			1.68551			0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000			1.68551			0.842754	+	0.538299i	$0.180933\pi$
$812$		0			0
$813$	−24.0000			−0.841717
$814$		0			0
$815$	−6.00000	+	10.3923i	−0.210171	+	0.364027i
$816$		0			0
$817$	−0.500000	−	0.866025i	−0.0174928	−	0.0302984i
$818$		0			0
$819$	7.50000	−	2.59808i	0.262071	−	0.0907841i
$820$		0			0
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.761056	−	0.648686i	$-0.775319\pi$
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.181250	−	0.983437i	$-0.558014\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		0			0
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	−28.5000	+	49.3634i	−0.989846	+	1.71446i	−0.371822	+	0.928304i	$0.621267\pi$
$829$	−28.5000	+	49.3634i	−0.989846	+	1.71446i	−0.618024	+	0.786159i	$0.712066\pi$
$830$		0			0
$831$	−3.50000	−	6.06218i	−0.121414	−	0.210295i
$832$		0			0
$833$	−22.0000	+	17.3205i	−0.762255	+	0.600120i
$834$		0			0
$835$	−5.00000	−	8.66025i	−0.173032	−	0.299700i
$836$		0			0
$837$	−0.500000	+	0.866025i	−0.0172825	+	0.0299342i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$		0			0
$843$	−6.00000	+	10.3923i	−0.206651	+	0.357930i
$844$		0			0
$845$	2.00000	+	3.46410i	0.0688021	+	0.119169i
$846$		0			0
$847$	−62.5000	+	21.6506i	−2.14753	+	0.743925i
$848$		0			0
$849$	3.50000	+	6.06218i	0.120120	+	0.208053i
$850$		0			0
$851$	−14.0000	+	24.2487i	−0.479914	+	0.831235i
$852$		0			0
$853$	−9.00000			−0.308154			−0.154077	−	0.988059i	$-0.549240\pi$
$853$	−9.00000			−0.308154			−0.154077	+	0.988059i	$0.549240\pi$
$854$		0			0
$855$	−1.00000			−0.0341993
$856$		0			0
$857$	6.00000	−	10.3923i	0.204956	−	0.354994i	−0.745163	−	0.666883i	$-0.767628\pi$
$857$	6.00000	−	10.3923i	0.204956	−	0.354994i	0.950119	+	0.311888i	$0.100962\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$		0			0
$861$	12.0000	+	10.3923i	0.408959	+	0.354169i
$862$		0			0
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	0.810437	−	0.585826i	$-0.199230\pi$
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	−0.912558	+	0.408946i	$0.865896\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	6.00000			0.203536
$870$		0			0
$871$	−10.5000	+	18.1865i	−0.355779	+	0.616227i
$872$		0			0
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$		0			0
$875$	0.500000	−	2.59808i	0.0169031	−	0.0878310i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	−8.00000	+	13.8564i	−0.269833	+	0.467365i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$		0			0
$885$	4.00000	−	6.92820i	0.134459	−	0.232889i
$886$		0			0
$887$	5.00000	+	8.66025i	0.167884	+	0.290783i	0.937676	−	0.347512i	$-0.112973\pi$
$887$	5.00000	+	8.66025i	0.167884	+	0.290783i	−0.769792	+	0.638295i	$0.779640\pi$
$888$		0			0
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$		0			0
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$		0			0
$893$	−1.00000	+	1.73205i	−0.0334637	+	0.0579609i
$894$		0			0
$895$	−18.0000			−0.601674
$896$		0			0
$897$	12.0000			0.400668
$898$		0			0
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	8.00000	+	13.8564i	0.266519	+	0.461624i
$902$		0			0
$903$	2.00000	+	1.73205i	0.0665558	+	0.0576390i
$904$		0			0
$905$	−6.50000	−	11.2583i	−0.216067	−	0.374240i
$906$		0			0
$907$	15.5000	−	26.8468i	0.514669	−	0.891433i	−0.485186	−	0.874411i	$-0.661248\pi$
$907$	15.5000	−	26.8468i	0.514669	−	0.891433i	0.999855	−	0.0170220i	$-0.00541854\pi$
$908$		0			0
$909$	−10.0000			−0.331679
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$		0			0
$915$	−7.00000	−	12.1244i	−0.231413	−	0.400819i
$916$		0			0
$917$	5.00000	−	1.73205i	0.165115	−	0.0571974i
$918$		0			0
$919$	−4.50000	−	7.79423i	−0.148441	−	0.257108i	0.782210	−	0.623015i	$-0.214092\pi$
$919$	−4.50000	−	7.79423i	−0.148441	−	0.257108i	−0.930652	+	0.365907i	$0.880759\pi$
$920$		0			0
$921$	−1.50000	+	2.59808i	−0.0494267	+	0.0856095i
$922$		0			0
$923$	18.0000			0.592477
$924$		0			0
$925$	7.00000			0.230159
$926$		0			0
$927$	−9.50000	+	16.4545i	−0.312021	+	0.540436i
$928$		0			0
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$		0			0
$933$	−3.00000	−	5.19615i	−0.0982156	−	0.170114i
$934$		0			0
$935$	12.0000	−	20.7846i	0.392442	−	0.679729i
$936$		0			0
$937$	−29.0000			−0.947389			−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000			−0.947389			−0.473694	+	0.880689i	$0.657080\pi$
$938$		0			0
$939$	−11.0000			−0.358971
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	12.0000	+	20.7846i	0.390774	+	0.676840i
$944$		0			0
$945$	2.50000	−	0.866025i	0.0813250	−	0.0281718i
$946$		0			0
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	0.996178	−	0.0873481i	$-0.0278392\pi$
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	−0.573735	+	0.819041i	$0.694506\pi$
$948$		0			0
$949$	1.50000	−	2.59808i	0.0486921	−	0.0843371i
$950$		0			0
$951$	−20.0000			−0.648544
$952$		0			0
$953$	4.00000			0.129573			0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000			0.129573			0.0647864	+	0.997899i	$0.479363\pi$
$954$		0			0
$955$	5.00000	−	8.66025i	0.161796	−	0.280239i
$956$		0			0
$957$	−24.0000	−	41.5692i	−0.775810	−	1.34374i
$958$		0			0
$959$	16.0000	+	13.8564i	0.516667	+	0.447447i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$		0			0
$965$	−9.00000			−0.289720
$966$		0			0
$967$	−55.0000			−1.76868			−0.884340	−	0.466843i	$-0.845391\pi$
$967$	−55.0000			−1.76868			−0.884340	+	0.466843i	$0.845391\pi$
$968$		0			0
$969$	2.00000	−	3.46410i	0.0642493	−	0.111283i
$970$		0			0
$971$	−26.0000	−	45.0333i	−0.834380	−	1.44519i	−0.894534	−	0.446999i	$-0.852493\pi$
$971$	−26.0000	−	45.0333i	−0.834380	−	1.44519i	0.0601548	−	0.998189i	$-0.480841\pi$
$972$		0			0
$973$	−10.5000	+	54.5596i	−0.336615	+	1.74910i
$974$		0			0
$975$	−1.50000	−	2.59808i	−0.0480384	−	0.0832050i
$976$		0			0
$977$	11.0000	−	19.0526i	0.351921	−	0.609545i	−0.634665	−	0.772787i	$-0.718862\pi$
$977$	11.0000	−	19.0526i	0.351921	−	0.609545i	0.986586	+	0.163242i	$0.0521952\pi$
$978$		0			0
$979$	−72.0000			−2.30113
$980$		0			0
$981$	−15.0000			−0.478913
$982$		0			0
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	−0.489608	−	0.871943i	$-0.662860\pi$
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	0.999928	−	0.0119587i	$-0.00380665\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$	1.00000	−	5.19615i	0.0318304	−	0.165395i
$988$		0			0
$989$	2.00000	+	3.46410i	0.0635963	+	0.110152i
$990$		0			0
$991$	−7.50000	+	12.9904i	−0.238245	+	0.412653i	−0.960211	−	0.279276i	$-0.909906\pi$
$991$	−7.50000	+	12.9904i	−0.238245	+	0.412653i	0.721966	+	0.691929i	$0.243239\pi$
$992$		0			0
$993$	−9.00000			−0.285606
$994$		0			0
$995$	−8.00000			−0.253617
$996$		0			0
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	−0.597334	−	0.801993i	$-0.703773\pi$
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	0.993213	+	0.116310i	$0.0371066\pi$
$998$		0			0
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.l.1201.1		2
4.3	odd	2		105.2.i.b.46.1	yes	2
7.2	even	3	inner	1680.2.bg.l.961.1		2
12.11	even	2		315.2.j.a.46.1		2
20.3	even	4		525.2.r.d.424.2		4
20.7	even	4		525.2.r.d.424.1		4
20.19	odd	2		525.2.i.a.151.1		2
28.3	even	6		735.2.a.a.1.1		1
28.11	odd	6		735.2.a.b.1.1		1
28.19	even	6		735.2.i.f.226.1		2
28.23	odd	6		105.2.i.b.16.1	✓	2
28.27	even	2		735.2.i.f.361.1		2
84.11	even	6		2205.2.a.k.1.1		1
84.23	even	6		315.2.j.a.226.1		2
84.59	odd	6		2205.2.a.m.1.1		1
140.23	even	12		525.2.r.d.499.1		4
140.39	odd	6		3675.2.a.o.1.1		1
140.59	even	6		3675.2.a.p.1.1		1
140.79	odd	6		525.2.i.a.226.1		2
140.107	even	12		525.2.r.d.499.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.b.16.1	✓	2	28.23	odd	6
105.2.i.b.46.1	yes	2	4.3	odd	2
315.2.j.a.46.1		2	12.11	even	2
315.2.j.a.226.1		2	84.23	even	6
525.2.i.a.151.1		2	20.19	odd	2
525.2.i.a.226.1		2	140.79	odd	6
525.2.r.d.424.1		4	20.7	even	4
525.2.r.d.424.2		4	20.3	even	4
525.2.r.d.499.1		4	140.23	even	12
525.2.r.d.499.2		4	140.107	even	12
735.2.a.a.1.1		1	28.3	even	6
735.2.a.b.1.1		1	28.11	odd	6
735.2.i.f.226.1		2	28.19	even	6
735.2.i.f.361.1		2	28.27	even	2
1680.2.bg.l.961.1		2	7.2	even	3	inner
1680.2.bg.l.1201.1		2	1.1	even	1	trivial
2205.2.a.k.1.1		1	84.11	even	6
2205.2.a.m.1.1		1	84.59	odd	6
3675.2.a.o.1.1		1	140.39	odd	6
3675.2.a.p.1.1		1	140.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} -3.00000 q^{13} -1.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-2.50000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-1.50000 + 2.59808i) q^{39} -6.00000 q^{41} -1.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 + 3.46410i) q^{53} +6.00000 q^{55} +1.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(1.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} -4.00000 q^{69} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(0.500000 + 0.866025i) q^{75} +(12.0000 + 10.3923i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000 q^{83} -4.00000 q^{85} +(-4.00000 + 6.92820i) q^{87} +(6.00000 + 10.3923i) q^{89} +(-1.50000 + 7.79423i) q^{91} +(-0.500000 - 0.866025i) q^{93} +(0.500000 - 0.866025i) q^{95} -6.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{5} + q^{7} - q^{9}+O(q^{10}) \) 2 * q + q^3 - q^5 + q^7 - q^9	\( 2 q + q^{3} - q^{5} + q^{7} - q^{9} - 6 q^{11} - 6 q^{13} - 2 q^{15} + 4 q^{17} + q^{19} - 4 q^{21} - 4 q^{23} - q^{25} - 2 q^{27} - 16 q^{29} + q^{31} + 6 q^{33} - 5 q^{35} - 7 q^{37} - 3 q^{39} - 12 q^{41} - 2 q^{43} - q^{45} + 2 q^{47} - 13 q^{49} - 4 q^{51} - 4 q^{53} + 12 q^{55} + 2 q^{57} - 8 q^{59} + 14 q^{61} - 5 q^{63} + 3 q^{65} + 7 q^{67} - 8 q^{69} - 12 q^{71} - q^{73} + q^{75} + 24 q^{77} - q^{79} - q^{81} - 4 q^{83} - 8 q^{85} - 8 q^{87} + 12 q^{89} - 3 q^{91} - q^{93} + q^{95} - 12 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^5 + q^7 - q^9 - 6 * q^11 - 6 * q^13 - 2 * q^15 + 4 * q^17 + q^19 - 4 * q^21 - 4 * q^23 - q^25 - 2 * q^27 - 16 * q^29 + q^31 + 6 * q^33 - 5 * q^35 - 7 * q^37 - 3 * q^39 - 12 * q^41 - 2 * q^43 - q^45 + 2 * q^47 - 13 * q^49 - 4 * q^51 - 4 * q^53 + 12 * q^55 + 2 * q^57 - 8 * q^59 + 14 * q^61 - 5 * q^63 + 3 * q^65 + 7 * q^67 - 8 * q^69 - 12 * q^71 - q^73 + q^75 + 24 * q^77 - q^79 - q^81 - 4 * q^83 - 8 * q^85 - 8 * q^87 + 12 * q^89 - 3 * q^91 - q^93 + q^95 - 12 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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