LMFDB - Embedded newform 819.2.do.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	819.361
Dual form			819.2.do.c.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.73205i q^{8} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.73205i q^{8} +3.00000 q^{10} -5.19615i q^{11} +(-1.00000 - 3.46410i) q^{13} +(-3.00000 - 3.46410i) q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} -1.73205i q^{19} +(1.50000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.00000 + 1.73205i) q^{25} +(1.50000 - 6.06218i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.50000 + 0.866025i) q^{31} +(4.50000 - 2.59808i) q^{32} +10.3923i q^{34} +(-4.50000 + 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(4.50000 - 2.59808i) q^{44} +(7.50000 - 4.33013i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-3.00000 + 1.73205i) q^{50} +(2.50000 - 2.59808i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 - 7.79423i) q^{55} +(-1.50000 + 4.33013i) q^{56} +5.19615i q^{58} +(3.00000 - 1.73205i) q^{59} +7.00000 q^{61} +(1.50000 + 2.59808i) q^{62} -1.00000 q^{64} +(-4.50000 - 4.33013i) q^{65} -8.66025i q^{67} +(-3.00000 + 5.19615i) q^{68} +(-7.50000 - 2.59808i) q^{70} +(-1.50000 - 0.866025i) q^{71} +(-7.50000 - 4.33013i) q^{73} +(1.50000 - 0.866025i) q^{76} +(-4.50000 + 12.9904i) q^{77} +(2.50000 + 4.33013i) q^{79} -8.66025i q^{80} +9.00000 q^{82} -3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +(-16.5000 + 9.52628i) q^{86} -9.00000 q^{88} +(6.00000 + 3.46410i) q^{89} +(-0.500000 + 9.52628i) q^{91} +15.0000 q^{94} +(-1.50000 - 2.59808i) q^{95} +(-4.50000 - 2.59808i) q^{97} +(4.50000 + 11.2583i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{4} + 3 q^{5} - 5 q^{7}+O(q^{10}) $ 2 * q + 3 * q^2 + q^4 + 3 * q^5 - 5 * q^7	$ 2 q + 3 q^{2} + q^{4} + 3 q^{5} - 5 q^{7} + 6 q^{10} - 2 q^{13} - 6 q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{20} + 9 q^{22} - 2 q^{25} + 3 q^{26} - q^{28} + 3 q^{29} + 3 q^{31} + 9 q^{32} - 9 q^{35} + 3 q^{38} - 3 q^{40} + 9 q^{41} - 11 q^{43} + 9 q^{44} + 15 q^{47} + 11 q^{49} - 6 q^{50} + 5 q^{52} - 9 q^{53} - 9 q^{55} - 3 q^{56} + 6 q^{59} + 14 q^{61} + 3 q^{62} - 2 q^{64} - 9 q^{65} - 6 q^{68} - 15 q^{70} - 3 q^{71} - 15 q^{73} + 3 q^{76} - 9 q^{77} + 5 q^{79} + 18 q^{82} + 18 q^{85} - 33 q^{86} - 18 q^{88} + 12 q^{89} - q^{91} + 30 q^{94} - 3 q^{95} - 9 q^{97} + 9 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + q^4 + 3 * q^5 - 5 * q^7 + 6 * q^10 - 2 * q^13 - 6 * q^14 + 5 * q^16 + 6 * q^17 + 3 * q^20 + 9 * q^22 - 2 * q^25 + 3 * q^26 - q^28 + 3 * q^29 + 3 * q^31 + 9 * q^32 - 9 * q^35 + 3 * q^38 - 3 * q^40 + 9 * q^41 - 11 * q^43 + 9 * q^44 + 15 * q^47 + 11 * q^49 - 6 * q^50 + 5 * q^52 - 9 * q^53 - 9 * q^55 - 3 * q^56 + 6 * q^59 + 14 * q^61 + 3 * q^62 - 2 * q^64 - 9 * q^65 - 6 * q^68 - 15 * q^70 - 3 * q^71 - 15 * q^73 + 3 * q^76 - 9 * q^77 + 5 * q^79 + 18 * q^82 + 18 * q^85 - 33 * q^86 - 18 * q^88 + 12 * q^89 - q^91 + 30 * q^94 - 3 * q^95 - 9 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	3.00000			0.948683
$11$		−	5.19615i		−	1.56670i	−0.621582	−	0.783349i	$-0.713510\pi$
$11$		−	5.19615i		−	1.56670i	0.621582	−	0.783349i	$-0.286490\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	−3.00000	−	3.46410i	−0.801784	−	0.925820i
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$		−	1.73205i		−	0.397360i	−0.980064	−	0.198680i	$-0.936335\pi$
$19$		−	1.73205i		−	0.397360i	0.980064	−	0.198680i	$-0.0636654\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$		0			0
$22$	4.50000	−	7.79423i	0.959403	−	1.66174i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	1.50000	−	6.06218i	0.294174	−	1.18889i
$27$		0			0
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$		0			0
$34$			10.3923i			1.78227i
$35$	−4.50000	+	0.866025i	−0.760639	+	0.146385i
$36$		0			0
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$		0			0
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	4.50000	−	2.59808i	0.678401	−	0.391675i
$45$		0			0
$46$		0			0
$47$	7.50000	−	4.33013i	1.09399	−	0.631614i	0.159352	−	0.987222i	$-0.449059\pi$
$47$	7.50000	−	4.33013i	1.09399	−	0.631614i	0.934635	+	0.355608i	$0.115726\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−3.00000	+	1.73205i	−0.424264	+	0.244949i
$51$		0			0
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	−4.50000	−	7.79423i	−0.606780	−	1.05097i
$56$	−1.50000	+	4.33013i	−0.200446	+	0.578638i
$57$		0			0
$58$			5.19615i			0.682288i
$59$	3.00000	−	1.73205i	0.390567	−	0.225494i	−0.291839	−	0.956467i	$-0.594267\pi$
$59$	3.00000	−	1.73205i	0.390567	−	0.225494i	0.682406	+	0.730974i	$0.260934\pi$
$60$		0			0
$61$	7.00000			0.896258			0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000			0.896258			0.448129	+	0.893969i	$0.352090\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.50000	−	4.33013i	−0.558156	−	0.537086i
$66$		0			0
$67$		−	8.66025i		−	1.05802i	−0.848616	−	0.529009i	$-0.822564\pi$
$67$		−	8.66025i		−	1.05802i	0.848616	−	0.529009i	$-0.177436\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$	−7.50000	−	2.59808i	−0.896421	−	0.310530i
$71$	−1.50000	−	0.866025i	−0.178017	−	0.102778i	0.408344	−	0.912828i	$-0.366107\pi$
$71$	−1.50000	−	0.866025i	−0.178017	−	0.102778i	−0.586361	+	0.810050i	$0.699440\pi$
$72$		0			0
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$		0			0
$75$		0			0
$76$	1.50000	−	0.866025i	0.172062	−	0.0993399i
$77$	−4.50000	+	12.9904i	−0.512823	+	1.48039i
$78$		0			0
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$		−	8.66025i		−	0.968246i
$81$		0			0
$82$	9.00000			0.993884
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$		0			0
$85$	9.00000	+	5.19615i	0.976187	+	0.563602i
$86$	−16.5000	+	9.52628i	−1.77924	+	1.02725i
$87$		0			0
$88$	−9.00000			−0.959403
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	0.783072	−	0.621932i	$-0.213652\pi$
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	−0.147073	+	0.989126i	$0.546985\pi$
$90$		0			0
$91$	−0.500000	+	9.52628i	−0.0524142	+	0.998625i
$92$		0			0
$93$		0			0
$94$	15.0000			1.54713
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$		0			0
$97$	−4.50000	−	2.59808i	−0.456906	−	0.263795i	0.253837	−	0.967247i	$-0.418307\pi$
$97$	−4.50000	−	2.59808i	−0.456906	−	0.263795i	−0.710742	+	0.703452i	$0.751641\pi$
$98$	4.50000	+	11.2583i	0.454569	+	1.13726i
$99$		0			0
$100$	−2.00000			−0.200000
$101$	9.00000			0.895533			0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000			0.895533			0.447767	+	0.894150i	$0.352219\pi$
$102$		0			0
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	−13.5000	+	7.79423i	−1.31124	+	0.757042i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	4.50000	+	2.59808i	0.431022	+	0.248851i	0.699782	−	0.714357i	$-0.253281\pi$
$109$	4.50000	+	2.59808i	0.431022	+	0.248851i	−0.268760	+	0.963207i	$0.586614\pi$
$110$		−	15.5885i		−	1.48630i
$111$		0			0
$112$	−10.0000	+	8.66025i	−0.944911	+	0.818317i
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$		0			0
$115$		0			0
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$		0			0
$118$	6.00000			0.552345
$119$	−3.00000	−	15.5885i	−0.275010	−	1.42899i
$120$		0			0
$121$	−16.0000			−1.45455
$122$	10.5000	+	6.06218i	0.950625	+	0.548844i
$123$		0			0
$124$			1.73205i			0.155543i
$125$			12.1244i			1.08444i
$126$		0			0
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	−0.995846	−	0.0910585i	$-0.970975\pi$
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	0.419064	−	0.907957i	$-0.362358\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$		0			0
$130$	−3.00000	−	10.3923i	−0.263117	−	0.911465i
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$		0			0
$133$	−1.50000	+	4.33013i	−0.130066	+	0.375470i
$134$	7.50000	−	12.9904i	0.647901	−	1.12220i
$135$		0			0
$136$	9.00000	−	5.19615i	0.771744	−	0.445566i
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$	−3.00000	−	3.46410i	−0.253546	−	0.292770i
$141$		0			0
$142$	−1.50000	−	2.59808i	−0.125877	−	0.218026i
$143$	−18.0000	+	5.19615i	−1.50524	+	0.434524i
$144$		0			0
$145$	4.50000	+	2.59808i	0.373705	+	0.215758i
$146$	−7.50000	−	12.9904i	−0.620704	−	1.07509i
$147$		0			0
$148$		0			0
$149$			19.0526i			1.56085i	0.625252	+	0.780423i	$0.284996\pi$
$149$			19.0526i			1.56085i	−0.625252	+	0.780423i	$0.715004\pi$
$150$		0			0
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	0.00768132	−	0.999970i	$-0.497555\pi$
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	−0.862159	+	0.506637i	$0.830888\pi$
$152$	−3.00000			−0.243332
$153$		0			0
$154$	−18.0000	+	15.5885i	−1.45048	+	1.25615i
$155$	3.00000			0.240966
$156$		0			0
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.115050	+	0.993360i	$0.536703\pi$
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.802749	+	0.596316i	$0.796630\pi$
$158$			8.66025i			0.688973i
$159$		0			0
$160$	4.50000	−	7.79423i	0.355756	−	0.616188i
$161$		0			0
$162$		0			0
$163$			12.1244i			0.949653i	0.880079	+	0.474826i	$0.157489\pi$
$163$			12.1244i			0.949653i	−0.880079	+	0.474826i	$0.842511\pi$
$164$	4.50000	+	2.59808i	0.351391	+	0.202876i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	1.50000	−	0.866025i	0.116073	−	0.0670151i	−0.440839	−	0.897586i	$-0.645319\pi$
$167$	1.50000	−	0.866025i	0.116073	−	0.0670151i	0.556913	+	0.830571i	$0.311986\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	9.00000	+	15.5885i	0.690268	+	1.19558i
$171$		0			0
$172$	−11.0000			−0.838742
$173$	−15.0000			−1.14043			−0.570214	−	0.821496i	$-0.693140\pi$
$173$	−15.0000			−1.14043			−0.570214	+	0.821496i	$0.693140\pi$
$174$		0			0
$175$	4.00000	−	3.46410i	0.302372	−	0.261861i
$176$	−22.5000	−	12.9904i	−1.69600	−	0.979187i
$177$		0			0
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−9.00000	+	13.8564i	−0.667124	+	1.02711i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	27.0000	−	15.5885i	1.97444	−	1.13994i
$188$	7.50000	+	4.33013i	0.546994	+	0.315807i
$189$		0			0
$190$		−	5.19615i		−	0.376969i
$191$	15.0000			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$192$		0			0
$193$		−	1.73205i		−	0.124676i	−0.998055	−	0.0623379i	$-0.980144\pi$
$193$		−	1.73205i		−	0.124676i	0.998055	−	0.0623379i	$-0.0198556\pi$
$194$	−4.50000	−	7.79423i	−0.323081	−	0.559593i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$	−19.5000	+	11.2583i	−1.38932	+	0.802123i	−0.993238	−	0.116094i	$-0.962963\pi$
$197$	−19.5000	+	11.2583i	−1.38932	+	0.802123i	−0.396079	+	0.918216i	$0.629629\pi$
$198$		0			0
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	3.00000	+	1.73205i	0.212132	+	0.122474i
$201$		0			0
$202$	13.5000	+	7.79423i	0.949857	+	0.548400i
$203$	−1.50000	−	7.79423i	−0.105279	−	0.547048i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$			22.5167i			1.56881i
$207$		0			0
$208$	−17.5000	−	4.33013i	−1.21341	−	0.300240i
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−9.00000			−0.618123
$213$		0			0
$214$		0			0
$215$			19.0526i			1.29937i
$216$		0			0
$217$	−3.00000	−	3.46410i	−0.203653	−	0.235159i
$218$	4.50000	+	7.79423i	0.304778	+	0.527892i
$219$		0			0
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$	15.0000	−	15.5885i	1.00901	−	1.04859i
$222$		0			0
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	−0.341703	−	0.939808i	$-0.611004\pi$
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	0.643046	+	0.765828i	$0.277671\pi$
$224$	−13.5000	+	2.59808i	−0.902007	+	0.173591i
$225$		0			0
$226$	22.5000	−	12.9904i	1.49668	−	0.864107i
$227$	15.0000	−	8.66025i	0.995585	−	0.574801i	0.0886460	−	0.996063i	$-0.471746\pi$
$227$	15.0000	−	8.66025i	0.995585	−	0.574801i	0.906939	+	0.421262i	$0.138413\pi$
$228$		0			0
$229$	10.5000	−	6.06218i	0.693860	−	0.400600i	−0.111197	−	0.993798i	$-0.535468\pi$
$229$	10.5000	−	6.06218i	0.693860	−	0.400600i	0.805056	+	0.593198i	$0.202135\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	−	2.59808i	0.295439	−	0.170572i
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	0.910968	−	0.412477i	$-0.135336\pi$
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	−0.812700	+	0.582683i	$0.802003\pi$
$234$		0			0
$235$	7.50000	−	12.9904i	0.489246	−	0.847399i
$236$	3.00000	+	1.73205i	0.195283	+	0.112747i
$237$		0			0
$238$	9.00000	−	25.9808i	0.583383	−	1.68408i
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	−6.00000	+	3.46410i	−0.386494	+	0.223142i	−0.680640	−	0.732618i	$-0.738298\pi$
$241$	−6.00000	+	3.46410i	−0.386494	+	0.223142i	0.294146	+	0.955761i	$0.404965\pi$
$242$	−24.0000	−	13.8564i	−1.54278	−	0.890724i
$243$		0			0
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$	12.0000	+	1.73205i	0.766652	+	0.110657i
$246$		0			0
$247$	−6.00000	+	1.73205i	−0.381771	+	0.110208i
$248$	1.50000	−	2.59808i	0.0952501	−	0.164978i
$249$		0			0
$250$	−10.5000	+	18.1865i	−0.664078	+	1.15022i
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$		0			0
$253$		0			0
$254$		−	22.5167i		−	1.41282i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.162247	−	0.986750i	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$		0			0
$259$		0			0
$260$	1.50000	−	6.06218i	0.0930261	−	0.375960i
$261$		0			0
$262$			25.9808i			1.60510i
$263$	−3.00000			−0.184988			−0.0924940	−	0.995713i	$-0.529484\pi$
$263$	−3.00000			−0.184988			−0.0924940	+	0.995713i	$0.529484\pi$
$264$		0			0
$265$			15.5885i			0.957591i
$266$	−6.00000	+	5.19615i	−0.367884	+	0.318597i
$267$		0			0
$268$	7.50000	−	4.33013i	0.458135	−	0.264505i
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−15.0000	−	8.66025i	−0.911185	−	0.526073i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−15.0000	−	8.66025i	−0.911185	−	0.526073i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$		0			0
$275$	9.00000	+	5.19615i	0.542720	+	0.313340i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	19.5000	−	11.2583i	1.16953	−	0.675230i
$279$		0			0
$280$	1.50000	+	7.79423i	0.0896421	+	0.465794i
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$		0			0
$283$	19.0000			1.12943			0.564716	−	0.825285i	$-0.308986\pi$
$283$	19.0000			1.12943			0.564716	+	0.825285i	$0.308986\pi$
$284$		−	1.73205i		−	0.102778i
$285$		0			0
$286$	−31.5000	−	7.79423i	−1.86263	−	0.460882i
$287$	−13.5000	+	2.59808i	−0.796880	+	0.153360i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$		0			0
$292$		−	8.66025i		−	0.506803i
$293$	22.5000	+	12.9904i	1.31446	+	0.758906i	0.982832	−	0.184503i	$-0.0590674\pi$
$293$	22.5000	+	12.9904i	1.31446	+	0.758906i	0.331632	+	0.943409i	$0.392401\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$		0			0
$297$		0			0
$298$	−16.5000	+	28.5788i	−0.955819	+	1.65553i
$299$		0			0
$300$		0			0
$301$	22.0000	−	19.0526i	1.26806	−	1.09817i
$302$	−10.5000	−	18.1865i	−0.604207	−	1.04652i
$303$		0			0
$304$	−7.50000	−	4.33013i	−0.430155	−	0.248350i
$305$	10.5000	−	6.06218i	0.601228	−	0.347119i
$306$		0			0
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$	−13.5000	+	2.59808i	−0.769234	+	0.148039i
$309$		0			0
$310$	4.50000	+	2.59808i	0.255583	+	0.147561i
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	−0.996447	−	0.0842210i	$-0.973160\pi$
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	0.571161	+	0.820838i	$0.306493\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$	−34.5000	+	19.9186i	−1.94695	+	1.12407i
$315$		0			0
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	−4.50000	+	2.59808i	−0.252745	+	0.145922i	−0.621021	−	0.783794i	$-0.713282\pi$
$317$	−4.50000	+	2.59808i	−0.252745	+	0.145922i	0.368275	+	0.929717i	$0.379948\pi$
$318$		0			0
$319$	13.5000	−	7.79423i	0.755855	−	0.436393i
$320$	−1.50000	+	0.866025i	−0.0838525	+	0.0484123i
$321$		0			0
$322$		0			0
$323$	9.00000	−	5.19615i	0.500773	−	0.289122i
$324$		0			0
$325$	7.00000	+	1.73205i	0.388290	+	0.0960769i
$326$	−10.5000	+	18.1865i	−0.581541	+	1.00726i
$327$		0			0
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	−22.5000	+	4.33013i	−1.24047	+	0.238728i
$330$		0			0
$331$			32.9090i			1.80884i	0.426643	+	0.904420i	$0.359696\pi$
$331$			32.9090i			1.80884i	−0.426643	+	0.904420i	$0.640304\pi$
$332$	3.00000	−	1.73205i	0.164646	−	0.0950586i
$333$		0			0
$334$	3.00000			0.164153
$335$	−7.50000	−	12.9904i	−0.409769	−	0.709740i
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	−22.5000	+	0.866025i	−1.22384	+	0.0471056i
$339$		0			0
$340$			10.3923i			0.563602i
$341$	4.50000	−	7.79423i	0.243689	−	0.422081i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	16.5000	+	9.52628i	0.889620	+	0.513623i
$345$		0			0
$346$	−22.5000	−	12.9904i	−1.20961	−	0.698367i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$	−4.50000	+	2.59808i	−0.240879	+	0.139072i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	−4.50000	+	2.59808i	−0.240879	+	0.139072i	0.374701	+	0.927146i	$0.377745\pi$
$350$	9.00000	−	1.73205i	0.481070	−	0.0925820i
$351$		0			0
$352$	−13.5000	−	23.3827i	−0.719552	−	1.24630i
$353$			1.73205i			0.0921878i	0.998937	+	0.0460939i	$0.0146773\pi$
$353$			1.73205i			0.0921878i	−0.998937	+	0.0460939i	$0.985323\pi$
$354$		0			0
$355$	−3.00000			−0.159223
$356$			6.92820i			0.367194i
$357$		0			0
$358$	−4.50000	−	2.59808i	−0.237832	−	0.137313i
$359$	−16.5000	+	9.52628i	−0.870837	+	0.502778i	−0.867626	−	0.497217i	$-0.834355\pi$
$359$	−16.5000	+	9.52628i	−0.870837	+	0.502778i	−0.00321050	+	0.999995i	$0.501022\pi$
$360$		0			0
$361$	16.0000			0.842105
$362$	3.00000	+	1.73205i	0.157676	+	0.0910346i
$363$		0			0
$364$	−8.50000	+	4.33013i	−0.445521	+	0.226960i
$365$	−15.0000			−0.785136
$366$		0			0
$367$	23.0000			1.20059			0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000			1.20059			0.600295	+	0.799779i	$0.295050\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.0000	−	15.5885i	0.934513	−	0.809312i
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	54.0000			2.79227
$375$		0			0
$376$	−7.50000	−	12.9904i	−0.386783	−	0.669928i
$377$	7.50000	−	7.79423i	0.386270	−	0.401423i
$378$		0			0
$379$	−1.50000	+	0.866025i	−0.0770498	+	0.0444847i	−0.538030	−	0.842926i	$-0.680831\pi$
$379$	−1.50000	+	0.866025i	−0.0770498	+	0.0444847i	0.460980	+	0.887410i	$0.347498\pi$
$380$	1.50000	−	2.59808i	0.0769484	−	0.133278i
$381$		0			0
$382$	22.5000	+	12.9904i	1.15120	+	0.664646i
$383$			15.5885i			0.796533i	0.917270	+	0.398266i	$0.130388\pi$
$383$			15.5885i			0.796533i	−0.917270	+	0.398266i	$0.869612\pi$
$384$		0			0
$385$	4.50000	+	23.3827i	0.229341	+	1.19169i
$386$	1.50000	−	2.59808i	0.0763480	−	0.132239i
$387$		0			0
$388$		−	5.19615i		−	0.263795i
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$		0			0
$391$		0			0
$392$	7.50000	−	9.52628i	0.378807	−	0.481150i
$393$		0			0
$394$	−39.0000			−1.96479
$395$	7.50000	+	4.33013i	0.377366	+	0.217872i
$396$		0			0
$397$			36.3731i			1.82551i	0.408505	+	0.912756i	$0.366050\pi$
$397$			36.3731i			1.82551i	−0.408505	+	0.912756i	$0.633950\pi$
$398$		−	6.92820i		−	0.347279i
$399$		0			0
$400$	5.00000	+	8.66025i	0.250000	+	0.433013i
$401$	6.00000	+	3.46410i	0.299626	+	0.172989i	0.642275	−	0.766475i	$-0.277991\pi$
$401$	6.00000	+	3.46410i	0.299626	+	0.172989i	−0.342649	+	0.939463i	$0.611324\pi$
$402$		0			0
$403$	1.50000	−	6.06218i	0.0747203	−	0.301979i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$		0			0
$406$	4.50000	−	12.9904i	0.223331	−	0.644702i
$407$		0			0
$408$		0			0
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	−0.344270	−	0.938871i	$-0.611874\pi$
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	0.640951	+	0.767582i	$0.278540\pi$
$410$	13.5000	−	7.79423i	0.666717	−	0.384930i
$411$		0			0
$412$	−6.50000	+	11.2583i	−0.320232	+	0.554658i
$413$	−9.00000	+	1.73205i	−0.442861	+	0.0852286i
$414$		0			0
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	−13.5000	−	12.9904i	−0.661892	−	0.636906i
$417$		0			0
$418$	−13.5000	−	7.79423i	−0.660307	−	0.381228i
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	0.999887	+	0.0150285i	$0.00478389\pi$
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	−0.486928	+	0.873442i	$0.661883\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		−	22.5167i		−	1.09609i
$423$		0			0
$424$	13.5000	+	7.79423i	0.655618	+	0.378521i
$425$	−12.0000			−0.582086
$426$		0			0
$427$	−17.5000	−	6.06218i	−0.846884	−	0.293369i
$428$		0			0
$429$		0			0
$430$	−16.5000	+	28.5788i	−0.795701	+	1.37819i
$431$		−	32.9090i		−	1.58517i	−0.609762	−	0.792585i	$-0.708735\pi$
$431$		−	32.9090i		−	1.58517i	0.609762	−	0.792585i	$-0.291265\pi$
$432$		0			0
$433$	−9.50000	+	16.4545i	−0.456541	+	0.790752i	−0.998775	−	0.0494752i	$-0.984245\pi$
$433$	−9.50000	+	16.4545i	−0.456541	+	0.790752i	0.542234	+	0.840227i	$0.317578\pi$
$434$	−1.50000	−	7.79423i	−0.0720023	−	0.374135i
$435$		0			0
$436$			5.19615i			0.248851i
$437$		0			0
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	−13.5000	+	7.79423i	−0.643587	+	0.371575i
$441$		0			0
$442$	36.0000	−	10.3923i	1.71235	−	0.494312i
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	0.987346	−	0.158583i	$-0.0506926\pi$
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	−0.631010	+	0.775775i	$0.717359\pi$
$444$		0			0
$445$	12.0000			0.568855
$446$	9.00000			0.426162
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	−1.50000	−	0.866025i	−0.0707894	−	0.0408703i	0.464188	−	0.885737i	$-0.346346\pi$
$449$	−1.50000	−	0.866025i	−0.0707894	−	0.0408703i	−0.534977	+	0.844867i	$0.679680\pi$
$450$		0			0
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	15.0000			0.705541
$453$		0			0
$454$	30.0000			1.40797
$455$	7.50000	+	14.7224i	0.351605	+	0.690198i
$456$		0			0
$457$	−30.0000	−	17.3205i	−1.40334	−	0.810219i	−0.408607	−	0.912710i	$-0.633985\pi$
$457$	−30.0000	−	17.3205i	−1.40334	−	0.810219i	−0.994734	+	0.102491i	$0.967319\pi$
$458$	21.0000			0.981266
$459$		0			0
$460$		0			0
$461$	−25.5000	−	14.7224i	−1.18765	−	0.685692i	−0.229881	−	0.973219i	$-0.573834\pi$
$461$	−25.5000	−	14.7224i	−1.18765	−	0.685692i	−0.957773	+	0.287527i	$0.907167\pi$
$462$		0			0
$463$		−	24.2487i		−	1.12693i	−0.826139	−	0.563467i	$-0.809467\pi$
$463$		−	24.2487i		−	1.12693i	0.826139	−	0.563467i	$-0.190533\pi$
$464$	15.0000			0.696358
$465$		0			0
$466$			5.19615i			0.240707i
$467$	−10.5000	−	18.1865i	−0.485882	−	0.841572i	0.513986	−	0.857798i	$-0.328168\pi$
$467$	−10.5000	−	18.1865i	−0.485882	−	0.841572i	−0.999868	+	0.0162260i	$0.994835\pi$
$468$		0			0
$469$	−7.50000	+	21.6506i	−0.346318	+	0.999733i
$470$	22.5000	−	12.9904i	1.03785	−	0.599202i
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	49.5000	+	28.5788i	2.27601	+	1.31406i
$474$		0			0
$475$	3.00000	+	1.73205i	0.137649	+	0.0794719i
$476$	12.0000	−	10.3923i	0.550019	−	0.476331i
$477$		0			0
$478$	9.00000	−	15.5885i	0.411650	−	0.712999i
$479$			29.4449i			1.34537i	0.739929	+	0.672685i	$0.234859\pi$
$479$			29.4449i			1.34537i	−0.739929	+	0.672685i	$0.765141\pi$
$480$		0			0
$481$		0			0
$482$	−12.0000			−0.546585
$483$		0			0
$484$	−8.00000	−	13.8564i	−0.363636	−	0.629837i
$485$	−9.00000			−0.408669
$486$		0			0
$487$	−21.0000	+	12.1244i	−0.951601	+	0.549407i	−0.893578	−	0.448908i	$-0.851813\pi$
$487$	−21.0000	+	12.1244i	−0.951601	+	0.549407i	−0.0580230	+	0.998315i	$0.518480\pi$
$488$		−	12.1244i		−	0.548844i
$489$		0			0
$490$	16.5000	+	12.9904i	0.745394	+	0.586846i
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	−0.991365	−	0.131132i	$-0.958139\pi$
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	0.382118	−	0.924113i	$-0.375195\pi$
$492$		0			0
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	−10.5000	−	2.59808i	−0.472417	−	0.116893i
$495$		0			0
$496$	7.50000	−	4.33013i	0.336760	−	0.194428i
$497$	3.00000	+	3.46410i	0.134568	+	0.155386i
$498$		0			0
$499$	−1.50000	+	0.866025i	−0.0671492	+	0.0387686i	−0.533199	−	0.845990i	$-0.679010\pi$
$499$	−1.50000	+	0.866025i	−0.0671492	+	0.0387686i	0.466049	+	0.884759i	$0.345677\pi$
$500$	−10.5000	+	6.06218i	−0.469574	+	0.271109i
$501$		0			0
$502$	4.50000	−	2.59808i	0.200845	−	0.115958i
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	−0.948736	−	0.316068i	$-0.897637\pi$
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	0.748091	+	0.663596i	$0.230970\pi$
$504$		0			0
$505$	13.5000	−	7.79423i	0.600742	−	0.346839i
$506$		0			0
$507$		0			0
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	6.00000	+	3.46410i	0.265945	+	0.153544i	0.627044	−	0.778984i	$-0.284265\pi$
$509$	6.00000	+	3.46410i	0.265945	+	0.153544i	−0.361098	+	0.932528i	$0.617598\pi$
$510$		0			0
$511$	15.0000	+	17.3205i	0.663561	+	0.766214i
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	45.0000	−	25.9808i	1.98486	−	1.14596i
$515$	19.5000	+	11.2583i	0.859273	+	0.496101i
$516$		0			0
$517$	−22.5000	−	38.9711i	−0.989549	−	1.71395i
$518$		0			0
$519$		0			0
$520$	−7.50000	+	7.79423i	−0.328897	+	0.341800i
$521$	19.5000	−	33.7750i	0.854311	−	1.47971i	−0.0229727	−	0.999736i	$-0.507313\pi$
$521$	19.5000	−	33.7750i	0.854311	−	1.47971i	0.877283	−	0.479973i	$-0.159354\pi$
$522$		0			0
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−4.50000	−	2.59808i	−0.196209	−	0.113282i
$527$			10.3923i			0.452696i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−13.5000	+	23.3827i	−0.586403	+	1.01568i
$531$		0			0
$532$	−4.50000	+	0.866025i	−0.195100	+	0.0375470i
$533$	−13.5000	−	12.9904i	−0.584750	−	0.562676i
$534$		0			0
$535$		0			0
$536$	−15.0000			−0.647901
$537$		0			0
$538$		−	10.3923i		−	0.448044i
$539$	22.5000	−	28.5788i	0.969144	−	1.23098i
$540$		0			0
$541$	10.5000	−	6.06218i	0.451430	−	0.260633i	−0.257004	−	0.966410i	$-0.582735\pi$
$541$	10.5000	−	6.06218i	0.451430	−	0.260633i	0.708434	+	0.705777i	$0.249402\pi$
$542$	−15.0000	−	25.9808i	−0.644305	−	1.11597i
$543$		0			0
$544$	27.0000	+	15.5885i	1.15762	+	0.668350i
$545$	9.00000			0.385518
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$		0			0
$550$	9.00000	+	15.5885i	0.383761	+	0.664694i
$551$	4.50000	−	2.59808i	0.191706	−	0.110682i
$552$		0			0
$553$	−2.50000	−	12.9904i	−0.106311	−	0.552407i
$554$			17.3205i			0.735878i
$555$		0			0
$556$	13.0000			0.551323
$557$			15.5885i			0.660504i	0.943893	+	0.330252i	$0.107134\pi$
$557$			15.5885i			0.660504i	−0.943893	+	0.330252i	$0.892866\pi$
$558$		0			0
$559$	38.5000	+	9.52628i	1.62838	+	0.402919i
$560$	−7.50000	+	21.6506i	−0.316933	+	0.914906i
$561$		0			0
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$		0			0
$565$		−	25.9808i		−	1.09302i
$566$	28.5000	+	16.4545i	1.19794	+	0.691633i
$567$		0			0
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	11.5000	−	19.9186i	0.481260	−	0.833567i	−0.518509	−	0.855072i	$-0.673513\pi$
$571$	11.5000	−	19.9186i	0.481260	−	0.833567i	0.999769	+	0.0215055i	$0.00684595\pi$
$572$	−13.5000	−	12.9904i	−0.564463	−	0.543155i
$573$		0			0
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$		0			0
$576$		0			0
$577$	−13.5000	−	7.79423i	−0.562012	−	0.324478i	0.191940	−	0.981407i	$-0.438522\pi$
$577$	−13.5000	−	7.79423i	−0.562012	−	0.324478i	−0.753953	+	0.656929i	$0.771855\pi$
$578$	−28.5000	+	16.4545i	−1.18544	+	0.684416i
$579$		0			0
$580$			5.19615i			0.215758i
$581$	−3.00000	+	8.66025i	−0.124461	+	0.359288i
$582$		0			0
$583$	40.5000	+	23.3827i	1.67734	+	0.968412i
$584$	−7.50000	+	12.9904i	−0.310352	+	0.537546i
$585$		0			0
$586$	22.5000	+	38.9711i	0.929466	+	1.60988i
$587$	13.5000	−	7.79423i	0.557205	−	0.321702i	−0.194818	−	0.980839i	$-0.562412\pi$
$587$	13.5000	−	7.79423i	0.557205	−	0.321702i	0.752023	+	0.659137i	$0.229078\pi$
$588$		0			0
$589$	1.50000	−	2.59808i	0.0618064	−	0.107052i
$590$	9.00000	−	5.19615i	0.370524	−	0.213922i
$591$		0			0
$592$		0			0
$593$	−4.50000	+	2.59808i	−0.184793	+	0.106690i	−0.589543	−	0.807737i	$-0.700692\pi$
$593$	−4.50000	+	2.59808i	−0.184793	+	0.106690i	0.404750	+	0.914428i	$0.367359\pi$
$594$		0			0
$595$	−18.0000	−	20.7846i	−0.737928	−	0.852086i
$596$	−16.5000	+	9.52628i	−0.675866	+	0.390212i
$597$		0			0
$598$		0			0
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$	49.5000	−	9.52628i	2.01747	−	0.388262i
$603$		0			0
$604$		−	12.1244i		−	0.493333i
$605$	−24.0000	+	13.8564i	−0.975739	+	0.563343i
$606$		0			0
$607$	−43.0000			−1.74532			−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000			−1.74532			−0.872658	+	0.488332i	$0.837606\pi$
$608$	−4.50000	−	7.79423i	−0.182499	−	0.316098i
$609$		0			0
$610$	21.0000			0.850265
$611$	−22.5000	−	21.6506i	−0.910253	−	0.875891i
$612$		0			0
$613$		−	36.3731i		−	1.46909i	−0.678558	−	0.734547i	$-0.737395\pi$
$613$		−	36.3731i		−	1.46909i	0.678558	−	0.734547i	$-0.262605\pi$
$614$	−21.0000	+	36.3731i	−0.847491	+	1.46790i
$615$		0			0
$616$	22.5000	+	7.79423i	0.906551	+	0.314038i
$617$	−37.5000	−	21.6506i	−1.50969	−	0.871622i	−0.999936	−	0.0113033i	$-0.996402\pi$
$617$	−37.5000	−	21.6506i	−1.50969	−	0.871622i	−0.509757	−	0.860318i	$-0.670265\pi$
$618$		0			0
$619$	−16.5000	−	9.52628i	−0.663191	−	0.382893i	0.130301	−	0.991475i	$-0.458406\pi$
$619$	−16.5000	−	9.52628i	−0.663191	−	0.382893i	−0.793492	+	0.608581i	$0.791739\pi$
$620$	1.50000	+	2.59808i	0.0602414	+	0.104341i
$621$		0			0
$622$	−22.5000	+	12.9904i	−0.902168	+	0.520867i
$623$	−12.0000	−	13.8564i	−0.480770	−	0.555145i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		−	32.9090i		−	1.31531i
$627$		0			0
$628$	−23.0000			−0.917800
$629$		0			0
$630$		0			0
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.988841	−	0.148978i	$-0.952402\pi$
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.623439	−	0.781872i	$-0.714265\pi$
$632$	7.50000	−	4.33013i	0.298334	−	0.172243i
$633$		0			0
$634$	−9.00000			−0.357436
$635$	−19.5000	−	11.2583i	−0.773834	−	0.446773i
$636$		0			0
$637$	9.50000	−	23.3827i	0.376404	−	0.926456i
$638$	27.0000			1.06894
$639$		0			0
$640$	−21.0000			−0.830098
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	−4.50000	−	2.59808i	−0.177463	−	0.102458i	0.408637	−	0.912697i	$-0.366004\pi$
$643$	−4.50000	−	2.59808i	−0.177463	−	0.102458i	−0.586100	+	0.810239i	$0.699337\pi$
$644$		0			0
$645$		0			0
$646$	18.0000			0.708201
$647$	9.00000			0.353827			0.176913	−	0.984226i	$-0.443389\pi$
$647$	9.00000			0.353827			0.176913	+	0.984226i	$0.443389\pi$
$648$		0			0
$649$	−9.00000	−	15.5885i	−0.353281	−	0.611900i
$650$	9.00000	+	8.66025i	0.353009	+	0.339683i
$651$		0			0
$652$	−10.5000	+	6.06218i	−0.411212	+	0.237413i
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$		0			0
$655$	22.5000	+	12.9904i	0.879148	+	0.507576i
$656$		−	25.9808i		−	1.01438i
$657$		0			0
$658$	−37.5000	−	12.9904i	−1.46190	−	0.506418i
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$		0			0
$661$		−	36.3731i		−	1.41475i	−0.706839	−	0.707374i	$-0.749880\pi$
$661$		−	36.3731i		−	1.41475i	0.706839	−	0.707374i	$-0.250120\pi$
$662$	−28.5000	+	49.3634i	−1.10768	+	1.91856i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	1.50000	+	7.79423i	0.0581675	+	0.302247i
$666$		0			0
$667$		0			0
$668$	1.50000	+	0.866025i	0.0580367	+	0.0335075i
$669$		0			0
$670$		−	25.9808i		−	1.00372i
$671$		−	36.3731i		−	1.40417i
$672$		0			0
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	33.0000	+	19.0526i	1.27111	+	0.733877i
$675$		0			0
$676$	−11.5000	−	6.06218i	−0.442308	−	0.233161i
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$		0			0
$679$	9.00000	+	10.3923i	0.345388	+	0.398820i
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$		0			0
$682$	13.5000	−	7.79423i	0.516942	−	0.298456i
$683$	−21.0000	+	12.1244i	−0.803543	+	0.463926i	−0.844708	−	0.535227i	$-0.820226\pi$
$683$	−21.0000	+	12.1244i	−0.803543	+	0.463926i	0.0411658	+	0.999152i	$0.486893\pi$
$684$		0			0
$685$		0			0
$686$	−1.50000	−	32.0429i	−0.0572703	−	1.22341i
$687$		0			0
$688$	27.5000	+	47.6314i	1.04843	+	1.81593i
$689$	31.5000	+	7.79423i	1.20005	+	0.296936i
$690$		0			0
$691$	27.0000	+	15.5885i	1.02713	+	0.593013i	0.916161	−	0.400811i	$-0.131272\pi$
$691$	27.0000	+	15.5885i	1.02713	+	0.593013i	0.110968	+	0.993824i	$0.464605\pi$
$692$	−7.50000	−	12.9904i	−0.285107	−	0.493820i
$693$		0			0
$694$		0			0
$695$		−	22.5167i		−	0.854106i
$696$		0			0
$697$	27.0000	+	15.5885i	1.02270	+	0.590455i
$698$	−9.00000			−0.340655
$699$		0			0
$700$	5.00000	+	1.73205i	0.188982	+	0.0654654i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$		0			0
$704$			5.19615i			0.195837i
$705$		0			0
$706$	−1.50000	+	2.59808i	−0.0564532	+	0.0977799i
$707$	−22.5000	−	7.79423i	−0.846200	−	0.293132i
$708$		0			0
$709$		−	12.1244i		−	0.455340i	−0.973738	−	0.227670i	$-0.926889\pi$
$709$		−	12.1244i		−	0.455340i	0.973738	−	0.227670i	$-0.0731107\pi$
$710$	−4.50000	−	2.59808i	−0.168882	−	0.0975041i
$711$		0			0
$712$	6.00000	−	10.3923i	0.224860	−	0.389468i
$713$		0			0
$714$		0			0
$715$	−22.5000	+	23.3827i	−0.841452	+	0.874463i
$716$	−1.50000	−	2.59808i	−0.0560576	−	0.0970947i
$717$		0			0
$718$	−33.0000			−1.23155
$719$	15.0000			0.559406			0.279703	−	0.960087i	$-0.409764\pi$
$719$	15.0000			0.559406			0.279703	+	0.960087i	$0.409764\pi$
$720$		0			0
$721$	−6.50000	−	33.7750i	−0.242073	−	1.25785i
$722$	24.0000	+	13.8564i	0.893188	+	0.515682i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	−6.00000			−0.222834
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$	16.5000	+	0.866025i	0.611531	+	0.0320970i
$729$		0			0
$730$	−22.5000	−	12.9904i	−0.832762	−	0.480796i
$731$	−66.0000			−2.44110
$732$		0			0
$733$	−43.5000	+	25.1147i	−1.60671	+	0.927634i	−0.616609	+	0.787269i	$0.711494\pi$
$733$	−43.5000	+	25.1147i	−1.60671	+	0.927634i	−0.990100	+	0.140365i	$0.955173\pi$
$734$	34.5000	+	19.9186i	1.27342	+	0.735208i
$735$		0			0
$736$		0			0
$737$	−45.0000			−1.65760
$738$		0			0
$739$			39.8372i			1.46543i	0.680534	+	0.732717i	$0.261748\pi$
$739$			39.8372i			1.46543i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$		0			0
$742$	40.5000	−	7.79423i	1.48680	−	0.286135i
$743$	1.50000	−	0.866025i	0.0550297	−	0.0317714i	−0.472233	−	0.881474i	$-0.656552\pi$
$743$	1.50000	−	0.866025i	0.0550297	−	0.0317714i	0.527262	+	0.849703i	$0.323218\pi$
$744$		0			0
$745$	16.5000	+	28.5788i	0.604513	+	1.04705i
$746$	28.5000	+	16.4545i	1.04346	+	0.602441i
$747$		0			0
$748$	27.0000	+	15.5885i	0.987218	+	0.569970i
$749$		0			0
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$		−	43.3013i		−	1.57903i
$753$		0			0
$754$	18.0000	−	5.19615i	0.655521	−	0.189233i
$755$	−21.0000			−0.764268
$756$		0			0
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	0.978130	−	0.207993i	$-0.0666932\pi$
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	−0.669193	+	0.743089i	$0.733360\pi$
$758$	−3.00000			−0.108965
$759$		0			0
$760$	−4.50000	+	2.59808i	−0.163232	+	0.0942421i
$761$		−	29.4449i		−	1.06738i	−0.845682	−	0.533688i	$-0.820806\pi$
$761$		−	29.4449i		−	1.06738i	0.845682	−	0.533688i	$-0.179194\pi$
$762$		0			0
$763$	−9.00000	−	10.3923i	−0.325822	−	0.376227i
$764$	7.50000	+	12.9904i	0.271340	+	0.469975i
$765$		0			0
$766$	−13.5000	+	23.3827i	−0.487775	+	0.844851i
$767$	−9.00000	−	8.66025i	−0.324971	−	0.312704i
$768$		0			0
$769$	−16.5000	+	9.52628i	−0.595005	+	0.343526i	−0.767074	−	0.641558i	$-0.778288\pi$
$769$	−16.5000	+	9.52628i	−0.595005	+	0.343526i	0.172069	+	0.985085i	$0.444955\pi$
$770$	−13.5000	+	38.9711i	−0.486506	+	1.40442i
$771$		0			0
$772$	1.50000	−	0.866025i	0.0539862	−	0.0311689i
$773$	12.0000	−	6.92820i	0.431610	−	0.249190i	−0.268422	−	0.963301i	$-0.586502\pi$
$773$	12.0000	−	6.92820i	0.431610	−	0.249190i	0.700032	+	0.714111i	$0.253169\pi$
$774$		0			0
$775$	−3.00000	+	1.73205i	−0.107763	+	0.0622171i
$776$	−4.50000	+	7.79423i	−0.161541	+	0.279797i
$777$		0			0
$778$	4.50000	−	2.59808i	0.161333	−	0.0931455i
$779$	−4.50000	−	7.79423i	−0.161229	−	0.279257i
$780$		0			0
$781$	−4.50000	+	7.79423i	−0.161023	+	0.278899i
$782$		0			0
$783$		0			0
$784$	32.5000	−	12.9904i	1.16071	−	0.463942i
$785$			39.8372i			1.42185i
$786$		0			0
$787$	−27.0000	+	15.5885i	−0.962446	+	0.555668i	−0.896925	−	0.442183i	$-0.854204\pi$
$787$	−27.0000	+	15.5885i	−0.962446	+	0.555668i	−0.0655211	+	0.997851i	$0.520871\pi$
$788$	−19.5000	−	11.2583i	−0.694659	−	0.401061i
$789$		0			0
$790$	7.50000	+	12.9904i	0.266838	+	0.462177i
$791$	−30.0000	+	25.9808i	−1.06668	+	0.923770i
$792$		0			0
$793$	−7.00000	−	24.2487i	−0.248577	−	0.861097i
$794$	−31.5000	+	54.5596i	−1.11789	+	1.93625i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	0.410483	+	0.911868i	$0.365360\pi$
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	−0.994943	+	0.100446i	$0.967973\pi$
$798$		0			0
$799$	45.0000	+	25.9808i	1.59199	+	0.919133i
$800$			10.3923i			0.367423i
$801$		0			0
$802$	6.00000	+	10.3923i	0.211867	+	0.366965i
$803$	−22.5000	+	38.9711i	−0.794008	+	1.37526i
$804$		0			0
$805$		0			0
$806$	7.50000	−	7.79423i	0.264176	−	0.274540i
$807$		0			0
$808$		−	15.5885i		−	0.548400i
$809$	21.0000			0.738321			0.369160	−	0.929366i	$-0.379645\pi$
$809$	21.0000			0.738321			0.369160	+	0.929366i	$0.379645\pi$
$810$		0			0
$811$		−	3.46410i		−	0.121641i	−0.998149	−	0.0608205i	$-0.980628\pi$
$811$		−	3.46410i		−	0.121641i	0.998149	−	0.0608205i	$-0.0193717\pi$
$812$	6.00000	−	5.19615i	0.210559	−	0.182349i
$813$		0			0
$814$		0			0
$815$	10.5000	+	18.1865i	0.367799	+	0.637046i
$816$		0			0
$817$	16.5000	+	9.52628i	0.577262	+	0.333282i
$818$	12.0000			0.419570
$819$		0			0
$820$	9.00000			0.314294
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	19.5000	−	11.2583i	0.679315	−	0.392203i
$825$		0			0
$826$	−15.0000	−	5.19615i	−0.521917	−	0.180797i
$827$		−	10.3923i		−	0.361376i	−0.983540	−	0.180688i	$-0.942168\pi$
$827$		−	10.3923i		−	0.361376i	0.983540	−	0.180688i	$-0.0578324\pi$
$828$		0			0
$829$	7.00000			0.243120			0.121560	−	0.992584i	$-0.461210\pi$
$829$	7.00000			0.243120			0.121560	+	0.992584i	$0.461210\pi$
$830$		−	10.3923i		−	0.360722i
$831$		0			0
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$	−6.00000	+	41.5692i	−0.207888	+	1.44029i
$834$		0			0
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	−4.50000	−	7.79423i	−0.155636	−	0.269569i
$837$		0			0
$838$			36.3731i			1.25649i
$839$	−1.50000	−	0.866025i	−0.0517858	−	0.0298985i	0.473884	−	0.880587i	$-0.342852\pi$
$839$	−1.50000	−	0.866025i	−0.0517858	−	0.0298985i	−0.525669	+	0.850689i	$0.676185\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$		0			0
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$	−10.5000	+	19.9186i	−0.361211	+	0.685220i
$846$		0			0
$847$	40.0000	+	13.8564i	1.37442	+	0.476112i
$848$	22.5000	+	38.9711i	0.772653	+	1.33827i
$849$		0			0
$850$	−18.0000	−	10.3923i	−0.617395	−	0.356453i
$851$		0			0
$852$		0			0
$853$			41.5692i			1.42330i	0.702533	+	0.711651i	$0.252052\pi$
$853$			41.5692i			1.42330i	−0.702533	+	0.711651i	$0.747948\pi$
$854$	−21.0000	−	24.2487i	−0.718605	−	0.829774i
$855$		0			0
$856$		0			0
$857$	−16.5000	+	28.5788i	−0.563629	+	0.976235i	0.433546	+	0.901131i	$0.357262\pi$
$857$	−16.5000	+	28.5788i	−0.563629	+	0.976235i	−0.997176	+	0.0751033i	$0.976071\pi$
$858$		0			0
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	0.999982	−	0.00607046i	$-0.00193230\pi$
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	−0.505248	+	0.862974i	$0.668599\pi$
$860$	−16.5000	+	9.52628i	−0.562645	+	0.324843i
$861$		0			0
$862$	28.5000	−	49.3634i	0.970714	−	1.68133i
$863$	1.50000	−	0.866025i	0.0510606	−	0.0294798i	−0.474252	−	0.880389i	$-0.657282\pi$
$863$	1.50000	−	0.866025i	0.0510606	−	0.0294798i	0.525313	+	0.850909i	$0.323948\pi$
$864$		0			0
$865$	−22.5000	+	12.9904i	−0.765023	+	0.441686i
$866$	−28.5000	+	16.4545i	−0.968469	+	0.559146i
$867$		0			0
$868$	1.50000	−	4.33013i	0.0509133	−	0.146974i
$869$	22.5000	−	12.9904i	0.763260	−	0.440668i
$870$		0			0
$871$	−30.0000	+	8.66025i	−1.01651	+	0.293442i
$872$	4.50000	−	7.79423i	0.152389	−	0.263946i
$873$		0			0
$874$		0			0
$875$	10.5000	−	30.3109i	0.354965	−	1.02470i
$876$		0			0
$877$			1.73205i			0.0584872i	0.999572	+	0.0292436i	$0.00930985\pi$
$877$			1.73205i			0.0584872i	−0.999572	+	0.0292436i	$0.990690\pi$
$878$	−12.0000	+	6.92820i	−0.404980	+	0.233816i
$879$		0			0
$880$	−45.0000			−1.51695
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	−0.997833	−	0.0657979i	$-0.979041\pi$
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	0.441934	−	0.897048i	$-0.354293\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	21.0000	+	5.19615i	0.706306	+	0.174766i
$885$		0			0
$886$			25.9808i			0.872841i
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$		0			0
$889$	6.50000	+	33.7750i	0.218003	+	1.13278i
$890$	18.0000	+	10.3923i	0.603361	+	0.348351i
$891$		0			0
$892$	4.50000	+	2.59808i	0.150671	+	0.0869900i
$893$	−7.50000	−	12.9904i	−0.250978	−	0.434707i
$894$		0			0
$895$	−4.50000	+	2.59808i	−0.150418	+	0.0868441i
$896$	21.0000	+	24.2487i	0.701561	+	0.810093i
$897$		0			0
$898$	−1.50000	−	2.59808i	−0.0500556	−	0.0866989i
$899$			5.19615i			0.173301i
$900$		0			0
$901$	−54.0000			−1.79900
$902$		−	46.7654i		−	1.55712i
$903$		0			0
$904$	−22.5000	−	12.9904i	−0.748339	−	0.432054i
$905$	3.00000	−	1.73205i	0.0997234	−	0.0575753i
$906$		0			0
$907$	−29.0000			−0.962929			−0.481465	−	0.876466i	$-0.659895\pi$
$907$	−29.0000			−0.962929			−0.481465	+	0.876466i	$0.659895\pi$
$908$	15.0000	+	8.66025i	0.497792	+	0.287401i
$909$		0			0
$910$	−1.50000	+	28.5788i	−0.0497245	+	0.947379i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−18.0000			−0.595713
$914$	−30.0000	−	51.9615i	−0.992312	−	1.71873i
$915$		0			0
$916$	10.5000	+	6.06218i	0.346930	+	0.200300i
$917$	−7.50000	−	38.9711i	−0.247672	−	1.28694i
$918$		0			0
$919$	−47.0000			−1.55039			−0.775193	−	0.631724i	$-0.782348\pi$
$919$	−47.0000			−1.55039			−0.775193	+	0.631724i	$0.782348\pi$
$920$		0			0
$921$		0			0
$922$	−25.5000	−	44.1673i	−0.839798	−	1.45457i
$923$	−1.50000	+	6.06218i	−0.0493731	+	0.199539i
$924$		0			0
$925$		0			0
$926$	21.0000	−	36.3731i	0.690103	−	1.19529i
$927$		0			0
$928$	13.5000	+	7.79423i	0.443159	+	0.255858i
$929$			46.7654i			1.53432i	0.641455	+	0.767161i	$0.278331\pi$
$929$			46.7654i			1.53432i	−0.641455	+	0.767161i	$0.721669\pi$
$930$		0			0
$931$	7.50000	−	9.52628i	0.245803	−	0.312211i
$932$	−1.50000	+	2.59808i	−0.0491341	+	0.0851028i
$933$		0			0
$934$		−	36.3731i		−	1.19016i
$935$	27.0000	−	46.7654i	0.882994	−	1.52939i
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	−30.0000	+	25.9808i	−0.979535	+	0.848302i
$939$		0			0
$940$	15.0000			0.489246
$941$	−4.50000	−	2.59808i	−0.146696	−	0.0846949i	0.424856	−	0.905261i	$-0.360325\pi$
$941$	−4.50000	−	2.59808i	−0.146696	−	0.0846949i	−0.571551	+	0.820566i	$0.693658\pi$
$942$		0			0
$943$		0			0
$944$		−	17.3205i		−	0.563735i
$945$		0			0
$946$	49.5000	+	85.7365i	1.60938	+	2.78753i
$947$	33.0000	+	19.0526i	1.07236	+	0.619125i	0.928824	−	0.370521i	$-0.120821\pi$
$947$	33.0000	+	19.0526i	1.07236	+	0.619125i	0.143532	+	0.989646i	$0.454154\pi$
$948$		0			0
$949$	−7.50000	+	30.3109i	−0.243460	+	0.983933i
$950$	3.00000	+	5.19615i	0.0973329	+	0.168585i
$951$		0			0
$952$	−27.0000	+	5.19615i	−0.875075	+	0.168408i
$953$	−28.5000	+	49.3634i	−0.923206	+	1.59904i	−0.128784	+	0.991673i	$0.541107\pi$
$953$	−28.5000	+	49.3634i	−0.923206	+	1.59904i	−0.794422	+	0.607366i	$0.792226\pi$
$954$		0			0
$955$	22.5000	−	12.9904i	0.728083	−	0.420359i
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$		0			0
$958$	−25.5000	+	44.1673i	−0.823868	+	1.42698i
$959$		0			0
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$		0			0
$963$		0			0
$964$	−6.00000	−	3.46410i	−0.193247	−	0.111571i
$965$	−1.50000	−	2.59808i	−0.0482867	−	0.0836350i
$966$		0			0
$967$		−	10.3923i		−	0.334194i	−0.985940	−	0.167097i	$-0.946561\pi$
$967$		−	10.3923i		−	0.334194i	0.985940	−	0.167097i	$-0.0534393\pi$
$968$			27.7128i			0.890724i
$969$		0			0
$970$	−13.5000	−	7.79423i	−0.433459	−	0.250258i
$971$	−21.0000			−0.673922			−0.336961	−	0.941519i	$-0.609399\pi$
$971$	−21.0000			−0.673922			−0.336961	+	0.941519i	$0.609399\pi$
$972$		0			0
$973$	−26.0000	+	22.5167i	−0.833522	+	0.721851i
$974$	−42.0000			−1.34577
$975$		0			0
$976$	17.5000	−	30.3109i	0.560161	−	0.970228i
$977$		−	19.0526i		−	0.609545i	−0.952425	−	0.304773i	$-0.901420\pi$
$977$		−	19.0526i		−	0.609545i	0.952425	−	0.304773i	$-0.0985805\pi$
$978$		0			0
$979$	18.0000	−	31.1769i	0.575282	−	0.996419i
$980$	4.50000	+	11.2583i	0.143747	+	0.359634i
$981$		0			0
$982$		−	46.7654i		−	1.49234i
$983$	−31.5000	−	18.1865i	−1.00469	−	0.580060i	−0.0950602	−	0.995472i	$-0.530304\pi$
$983$	−31.5000	−	18.1865i	−1.00469	−	0.580060i	−0.909634	+	0.415411i	$0.863638\pi$
$984$		0			0
$985$	−19.5000	+	33.7750i	−0.621322	+	1.07616i
$986$	−27.0000	+	15.5885i	−0.859855	+	0.496438i
$987$		0			0
$988$	−4.50000	−	4.33013i	−0.143164	−	0.137760i
$989$		0			0
$990$		0			0
$991$	59.0000			1.87420			0.937098	−	0.349065i	$-0.113501\pi$
$991$	59.0000			1.87420			0.937098	+	0.349065i	$0.113501\pi$
$992$	9.00000			0.285750
$993$		0			0
$994$	1.50000	+	7.79423i	0.0475771	+	0.247218i
$995$	−6.00000	−	3.46410i	−0.190213	−	0.109819i
$996$		0			0
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	−3.00000			−0.0949633
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.c.361.1		2
3.2	odd	2		91.2.u.a.88.1	yes	2
7.2	even	3		819.2.bm.a.478.1		2
13.4	even	6		819.2.bm.a.550.1		2
21.2	odd	6		91.2.k.a.23.1	yes	2
21.5	even	6		637.2.k.b.569.1		2
21.11	odd	6		637.2.q.c.491.1		2
21.17	even	6		637.2.q.b.491.1		2
21.20	even	2		637.2.u.a.361.1		2
39.2	even	12		1183.2.e.e.508.1		4
39.11	even	12		1183.2.e.e.508.2		4
39.17	odd	6		91.2.k.a.4.1	✓	2
91.30	even	6	inner	819.2.do.c.667.1		2
273.2	even	12		1183.2.e.e.170.1		4
273.11	even	12		8281.2.a.s.1.1		2
273.17	even	6		637.2.q.b.589.1		2
273.80	odd	12		8281.2.a.w.1.2		2
273.95	odd	6		637.2.q.c.589.1		2
273.128	even	12		1183.2.e.e.170.2		4
273.158	even	12		8281.2.a.s.1.2		2
273.173	even	6		637.2.u.a.30.1		2
273.206	odd	12		8281.2.a.w.1.1		2
273.212	odd	6		91.2.u.a.30.1	yes	2
273.251	even	6		637.2.k.b.459.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.a.4.1	✓	2	39.17	odd	6
91.2.k.a.23.1	yes	2	21.2	odd	6
91.2.u.a.30.1	yes	2	273.212	odd	6
91.2.u.a.88.1	yes	2	3.2	odd	2
637.2.k.b.459.1		2	273.251	even	6
637.2.k.b.569.1		2	21.5	even	6
637.2.q.b.491.1		2	21.17	even	6
637.2.q.b.589.1		2	273.17	even	6
637.2.q.c.491.1		2	21.11	odd	6
637.2.q.c.589.1		2	273.95	odd	6
637.2.u.a.30.1		2	273.173	even	6
637.2.u.a.361.1		2	21.20	even	2
819.2.bm.a.478.1		2	7.2	even	3
819.2.bm.a.550.1		2	13.4	even	6
819.2.do.c.361.1		2	1.1	even	1	trivial
819.2.do.c.667.1		2	91.30	even	6	inner
1183.2.e.e.170.1		4	273.2	even	12
1183.2.e.e.170.2		4	273.128	even	12
1183.2.e.e.508.1		4	39.2	even	12
1183.2.e.e.508.2		4	39.11	even	12
8281.2.a.s.1.1		2	273.11	even	12
8281.2.a.s.1.2		2	273.158	even	12
8281.2.a.w.1.1		2	273.206	odd	12
8281.2.a.w.1.2		2	273.80	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.73205i q^{8} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.73205i q^{8} +3.00000 q^{10} -5.19615i q^{11} +(-1.00000 - 3.46410i) q^{13} +(-3.00000 - 3.46410i) q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} -1.73205i q^{19} +(1.50000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.00000 + 1.73205i) q^{25} +(1.50000 - 6.06218i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.50000 + 0.866025i) q^{31} +(4.50000 - 2.59808i) q^{32} +10.3923i q^{34} +(-4.50000 + 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(4.50000 - 2.59808i) q^{44} +(7.50000 - 4.33013i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-3.00000 + 1.73205i) q^{50} +(2.50000 - 2.59808i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 - 7.79423i) q^{55} +(-1.50000 + 4.33013i) q^{56} +5.19615i q^{58} +(3.00000 - 1.73205i) q^{59} +7.00000 q^{61} +(1.50000 + 2.59808i) q^{62} -1.00000 q^{64} +(-4.50000 - 4.33013i) q^{65} -8.66025i q^{67} +(-3.00000 + 5.19615i) q^{68} +(-7.50000 - 2.59808i) q^{70} +(-1.50000 - 0.866025i) q^{71} +(-7.50000 - 4.33013i) q^{73} +(1.50000 - 0.866025i) q^{76} +(-4.50000 + 12.9904i) q^{77} +(2.50000 + 4.33013i) q^{79} -8.66025i q^{80} +9.00000 q^{82} -3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +(-16.5000 + 9.52628i) q^{86} -9.00000 q^{88} +(6.00000 + 3.46410i) q^{89} +(-0.500000 + 9.52628i) q^{91} +15.0000 q^{94} +(-1.50000 - 2.59808i) q^{95} +(-4.50000 - 2.59808i) q^{97} +(4.50000 + 11.2583i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{4} + 3 q^{5} - 5 q^{7}+O(q^{10}) \) 2 * q + 3 * q^2 + q^4 + 3 * q^5 - 5 * q^7	\( 2 q + 3 q^{2} + q^{4} + 3 q^{5} - 5 q^{7} + 6 q^{10} - 2 q^{13} - 6 q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{20} + 9 q^{22} - 2 q^{25} + 3 q^{26} - q^{28} + 3 q^{29} + 3 q^{31} + 9 q^{32} - 9 q^{35} + 3 q^{38} - 3 q^{40} + 9 q^{41} - 11 q^{43} + 9 q^{44} + 15 q^{47} + 11 q^{49} - 6 q^{50} + 5 q^{52} - 9 q^{53} - 9 q^{55} - 3 q^{56} + 6 q^{59} + 14 q^{61} + 3 q^{62} - 2 q^{64} - 9 q^{65} - 6 q^{68} - 15 q^{70} - 3 q^{71} - 15 q^{73} + 3 q^{76} - 9 q^{77} + 5 q^{79} + 18 q^{82} + 18 q^{85} - 33 q^{86} - 18 q^{88} + 12 q^{89} - q^{91} + 30 q^{94} - 3 q^{95} - 9 q^{97} + 9 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + q^4 + 3 * q^5 - 5 * q^7 + 6 * q^10 - 2 * q^13 - 6 * q^14 + 5 * q^16 + 6 * q^17 + 3 * q^20 + 9 * q^22 - 2 * q^25 + 3 * q^26 - q^28 + 3 * q^29 + 3 * q^31 + 9 * q^32 - 9 * q^35 + 3 * q^38 - 3 * q^40 + 9 * q^41 - 11 * q^43 + 9 * q^44 + 15 * q^47 + 11 * q^49 - 6 * q^50 + 5 * q^52 - 9 * q^53 - 9 * q^55 - 3 * q^56 + 6 * q^59 + 14 * q^61 + 3 * q^62 - 2 * q^64 - 9 * q^65 - 6 * q^68 - 15 * q^70 - 3 * q^71 - 15 * q^73 + 3 * q^76 - 9 * q^77 + 5 * q^79 + 18 * q^82 + 18 * q^85 - 33 * q^86 - 18 * q^88 + 12 * q^89 - q^91 + 30 * q^94 - 3 * q^95 - 9 * q^97 + 9 * q^98

Introduction

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