LMFDB - Embedded newform 84.2.k.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(5,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("84.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.k (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:	$0.670743376979$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	84.5
Dual form			84.2.k.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-4.50000 + 2.59808i) q^{11} +(-4.50000 + 2.59808i) q^{15} +(1.50000 + 2.59808i) q^{17} +(1.50000 + 0.866025i) q^{19} +(-4.50000 + 0.866025i) q^{21} +(4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.19615i q^{27} +(-1.50000 + 0.866025i) q^{31} +9.00000 q^{33} +(-1.50000 - 7.79423i) q^{35} +(-3.50000 + 6.06218i) q^{37} -6.00000 q^{41} +4.00000 q^{43} +9.00000 q^{45} +(1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} -5.19615i q^{51} +(4.50000 - 2.59808i) q^{53} +15.5885i q^{55} +(-1.50000 - 2.59808i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(-10.5000 - 6.06218i) q^{61} +(7.50000 + 2.59808i) q^{63} +(-2.50000 - 4.33013i) q^{67} +(-4.50000 - 7.79423i) q^{69} +10.3923i q^{71} +(-10.5000 + 6.06218i) q^{73} +6.92820i q^{75} +(-4.50000 + 12.9904i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(-4.50000 + 7.79423i) q^{89} +3.00000 q^{93} +(4.50000 - 2.59808i) q^{95} -6.92820i q^{97} +(-13.5000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 3 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 3 * q^5 + 4 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} + 3 q^{5} + 4 q^{7} + 3 q^{9} - 9 q^{11} - 9 q^{15} + 3 q^{17} + 3 q^{19} - 9 q^{21} + 9 q^{23} - 4 q^{25} - 3 q^{31} + 18 q^{33} - 3 q^{35} - 7 q^{37} - 12 q^{41} + 8 q^{43} + 18 q^{45} + 3 q^{47} + 2 q^{49} + 9 q^{53} - 3 q^{57} - 3 q^{59} - 21 q^{61} + 15 q^{63} - 5 q^{67} - 9 q^{69} - 21 q^{73} - 9 q^{77} + q^{79} - 9 q^{81} + 24 q^{83} + 18 q^{85} - 9 q^{89} + 6 q^{93} + 9 q^{95} - 27 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 3 * q^5 + 4 * q^7 + 3 * q^9 - 9 * q^11 - 9 * q^15 + 3 * q^17 + 3 * q^19 - 9 * q^21 + 9 * q^23 - 4 * q^25 - 3 * q^31 + 18 * q^33 - 3 * q^35 - 7 * q^37 - 12 * q^41 + 8 * q^43 + 18 * q^45 + 3 * q^47 + 2 * q^49 + 9 * q^53 - 3 * q^57 - 3 * q^59 - 21 * q^61 + 15 * q^63 - 5 * q^67 - 9 * q^69 - 21 * q^73 - 9 * q^77 + q^79 - 9 * q^81 + 24 * q^83 + 18 * q^85 - 9 * q^89 + 6 * q^93 + 9 * q^95 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.367610	+	0.929980i	$0.619824\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	−4.50000	+	2.59808i	−1.16190	+	0.670820i
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$	−4.50000	+	0.866025i	−0.981981	+	0.188982i
$22$		0			0
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.889432	−	0.457068i	$-0.151100\pi$
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.0488832	+	0.998805i	$0.484434\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	9.00000			1.56670
$34$		0			0
$35$	−1.50000	−	7.79423i	−0.253546	−	1.31747i
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$		0			0
$39$		0			0
$40$		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
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	9.00000			1.34164
$46$		0			0
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		−	5.19615i		−	0.727607i
$52$		0			0
$53$	4.50000	−	2.59808i	0.618123	−	0.356873i	−0.158015	−	0.987437i	$-0.550509\pi$
$53$	4.50000	−	2.59808i	0.618123	−	0.356873i	0.776138	+	0.630563i	$0.217176\pi$
$54$		0			0
$55$			15.5885i			2.10195i
$56$		0			0
$57$	−1.50000	−	2.59808i	−0.198680	−	0.344124i
$58$		0			0
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	−10.5000	−	6.06218i	−1.34439	−	0.776182i	−0.356939	−	0.934128i	$-0.616180\pi$
$61$	−10.5000	−	6.06218i	−1.34439	−	0.776182i	−0.987448	+	0.157945i	$0.949513\pi$
$62$		0			0
$63$	7.50000	+	2.59808i	0.944911	+	0.327327i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$	−4.50000	−	7.79423i	−0.541736	−	0.938315i
$70$		0			0
$71$			10.3923i			1.23334i	0.787222	+	0.616670i	$0.211519\pi$
$71$			10.3923i			1.23334i	−0.787222	+	0.616670i	$0.788481\pi$
$72$		0			0
$73$	−10.5000	+	6.06218i	−1.22893	+	0.709524i	−0.966807	−	0.255510i	$-0.917757\pi$
$73$	−10.5000	+	6.06218i	−1.22893	+	0.709524i	−0.262126	+	0.965034i	$0.584423\pi$
$74$		0			0
$75$			6.92820i			0.800000i
$76$		0			0
$77$	−4.50000	+	12.9904i	−0.512823	+	1.48039i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.00000			0.311086
$94$		0			0
$95$	4.50000	−	2.59808i	0.461690	−	0.266557i
$96$		0			0
$97$		−	6.92820i		−	0.703452i	−0.936103	−	0.351726i	$-0.885595\pi$
$97$		−	6.92820i		−	0.703452i	0.936103	−	0.351726i	$-0.114405\pi$
$98$		0			0
$99$	−13.5000	−	7.79423i	−1.35680	−	0.783349i
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	−4.50000	−	2.59808i	−0.443398	−	0.255996i	0.261640	−	0.965166i	$-0.415737\pi$
$103$	−4.50000	−	2.59808i	−0.443398	−	0.255996i	−0.705038	+	0.709170i	$0.749070\pi$
$104$		0			0
$105$	−4.50000	+	12.9904i	−0.439155	+	1.26773i
$106$		0			0
$107$	−13.5000	−	7.79423i	−1.30509	−	0.753497i	−0.323821	−	0.946118i	$-0.604968\pi$
$107$	−13.5000	−	7.79423i	−1.30509	−	0.753497i	−0.981273	+	0.192622i	$0.938301\pi$
$108$		0			0
$109$	8.50000	+	14.7224i	0.814152	+	1.41015i	0.909935	+	0.414751i	$0.136131\pi$
$109$	8.50000	+	14.7224i	0.814152	+	1.41015i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	10.5000	−	6.06218i	0.996616	−	0.575396i
$112$		0			0
$113$		−	20.7846i		−	1.95525i	−0.210352	−	0.977626i	$-0.567461\pi$
$113$		−	20.7846i		−	1.95525i	0.210352	−	0.977626i	$-0.432539\pi$
$114$		0			0
$115$	13.5000	−	7.79423i	1.25888	−	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.50000	+	2.59808i	0.687524	+	0.238165i
$120$		0			0
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$		0			0
$123$	9.00000	+	5.19615i	0.811503	+	0.468521i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−6.00000	−	3.46410i	−0.528271	−	0.304997i
$130$		0			0
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$	4.50000	−	0.866025i	0.390199	−	0.0750939i
$134$		0			0
$135$	−13.5000	−	7.79423i	−1.16190	−	0.670820i
$136$		0			0
$137$	4.50000	−	2.59808i	0.384461	−	0.221969i	−0.295296	−	0.955406i	$-0.595418\pi$
$137$	4.50000	−	2.59808i	0.384461	−	0.221969i	0.679757	+	0.733437i	$0.262085\pi$
$138$		0			0
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$		0			0
$141$	−4.50000	+	2.59808i	−0.378968	+	0.218797i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.50000	+	9.52628i	−0.618590	+	0.785714i
$148$		0			0
$149$	4.50000	+	2.59808i	0.368654	+	0.212843i	0.672870	−	0.739760i	$-0.265061\pi$
$149$	4.50000	+	2.59808i	0.368654	+	0.212843i	−0.304216	+	0.952603i	$0.598394\pi$
$150$		0			0
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	−0.999430	−	0.0337724i	$-0.989248\pi$
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	0.470467	−	0.882418i	$-0.344085\pi$
$152$		0			0
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$			5.19615i			0.417365i
$156$		0			0
$157$	−4.50000	+	2.59808i	−0.359139	+	0.207349i	−0.668703	−	0.743530i	$-0.733150\pi$
$157$	−4.50000	+	2.59808i	−0.359139	+	0.207349i	0.309564	+	0.950879i	$0.399817\pi$
$158$		0			0
$159$	−9.00000			−0.713746
$160$		0			0
$161$	13.5000	−	2.59808i	1.06395	−	0.204757i
$162$		0			0
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$		0			0
$165$	13.5000	−	23.3827i	1.05097	−	1.82034i
$166$		0			0
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$			5.19615i			0.397360i
$172$		0			0
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$		0			0
$177$			5.19615i			0.390567i
$178$		0			0
$179$	−4.50000	+	2.59808i	−0.336346	+	0.194189i	−0.658655	−	0.752445i	$-0.728874\pi$
$179$	−4.50000	+	2.59808i	−0.336346	+	0.194189i	0.322309	+	0.946634i	$0.395541\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$	10.5000	+	18.1865i	0.776182	+	1.34439i
$184$		0			0
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$	−13.5000	−	7.79423i	−0.987218	−	0.569970i
$188$		0			0
$189$	−9.00000	−	10.3923i	−0.654654	−	0.755929i
$190$		0			0
$191$	−13.5000	−	7.79423i	−0.976826	−	0.563971i	−0.0755154	−	0.997145i	$-0.524060\pi$
$191$	−13.5000	−	7.79423i	−0.976826	−	0.563971i	−0.901310	+	0.433174i	$0.857394\pi$
$192$		0			0
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−1.50000	+	0.866025i	−0.106332	+	0.0613909i	−0.552223	−	0.833696i	$-0.686220\pi$
$199$	−1.50000	+	0.866025i	−0.106332	+	0.0613909i	0.445891	+	0.895087i	$0.352887\pi$
$200$		0			0
$201$			8.66025i			0.610847i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−9.00000	+	15.5885i	−0.628587	+	1.08875i
$206$		0			0
$207$			15.5885i			1.08347i
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$	9.00000	−	15.5885i	0.616670	−	1.06810i
$214$		0			0
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$		0			0
$217$	−1.50000	+	4.33013i	−0.101827	+	0.293948i
$218$		0			0
$219$	21.0000			1.41905
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$		0			0
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$		0			0
$229$	19.5000	+	11.2583i	1.28860	+	0.743971i	0.978404	−	0.206702i	$-0.0662732\pi$
$229$	19.5000	+	11.2583i	1.28860	+	0.743971i	0.310192	+	0.950674i	$0.399607\pi$
$230$		0			0
$231$	18.0000	−	15.5885i	1.18431	−	1.02565i
$232$		0			0
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	0.640107	−	0.768286i	$-0.278890\pi$
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	−0.345302	+	0.938492i	$0.612223\pi$
$234$		0			0
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$		0			0
$237$	−1.50000	+	0.866025i	−0.0974355	+	0.0562544i
$238$		0			0
$239$		−	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
$241$	1.50000	−	0.866025i	0.0966235	−	0.0557856i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	1.50000	−	0.866025i	0.0966235	−	0.0557856i	0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		0			0
$245$	−16.5000	−	12.9904i	−1.05415	−	0.829925i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−18.0000	−	10.3923i	−1.14070	−	0.658586i
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	−27.0000			−1.69748
$254$		0			0
$255$	−13.5000	−	7.79423i	−0.845403	−	0.488094i
$256$		0			0
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	−0.0460033	−	0.998941i	$-0.514648\pi$
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	0.888110	−	0.459631i	$-0.152018\pi$
$258$		0			0
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.50000	+	2.59808i	−0.277482	+	0.160204i	−0.632283	−	0.774738i	$-0.717882\pi$
$263$	−4.50000	+	2.59808i	−0.277482	+	0.160204i	0.354801	+	0.934942i	$0.384549\pi$
$264$		0			0
$265$		−	15.5885i		−	0.957591i
$266$		0			0
$267$	13.5000	−	7.79423i	0.826187	−	0.476999i
$268$		0			0
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	19.5000	+	11.2583i	1.18454	+	0.683895i	0.957061	−	0.289888i	$-0.0936180\pi$
$271$	19.5000	+	11.2583i	1.18454	+	0.683895i	0.227480	+	0.973783i	$0.426951\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	18.0000	+	10.3923i	1.08544	+	0.626680i
$276$		0			0
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	0.992522	−	0.122068i	$-0.0389525\pi$
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	−0.601975	+	0.798515i	$0.705619\pi$
$278$		0			0
$279$	−4.50000	−	2.59808i	−0.269408	−	0.155543i
$280$		0			0
$281$			20.7846i			1.23991i	0.784639	+	0.619953i	$0.212848\pi$
$281$			20.7846i			1.23991i	−0.784639	+	0.619953i	$0.787152\pi$
$282$		0			0
$283$	−7.50000	+	4.33013i	−0.445829	+	0.257399i	−0.706067	−	0.708145i	$-0.749532\pi$
$283$	−7.50000	+	4.33013i	−0.445829	+	0.257399i	0.260238	+	0.965544i	$0.416199\pi$
$284$		0			0
$285$	−9.00000			−0.533114
$286$		0			0
$287$	−12.0000	+	10.3923i	−0.708338	+	0.613438i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−6.00000	+	10.3923i	−0.351726	+	0.609208i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−9.00000			−0.524000
$296$		0			0
$297$	13.5000	+	23.3827i	0.783349	+	1.35680i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	8.00000	−	6.92820i	0.461112	−	0.399335i
$302$		0			0
$303$			15.5885i			0.895533i
$304$		0			0
$305$	−31.5000	+	18.1865i	−1.80368	+	1.04136i
$306$		0			0
$307$		−	17.3205i		−	0.988534i	−0.869310	−	0.494267i	$-0.835437\pi$
$307$		−	17.3205i		−	0.988534i	0.869310	−	0.494267i	$-0.164563\pi$
$308$		0			0
$309$	4.50000	+	7.79423i	0.255996	+	0.443398i
$310$		0			0
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	0.571161	−	0.820838i	$-0.306493\pi$
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	−0.996447	+	0.0842210i	$0.973160\pi$
$312$		0			0
$313$	−10.5000	−	6.06218i	−0.593495	−	0.342655i	0.172983	−	0.984925i	$-0.444659\pi$
$313$	−10.5000	−	6.06218i	−0.593495	−	0.342655i	−0.766478	+	0.642270i	$0.777993\pi$
$314$		0			0
$315$	18.0000	−	15.5885i	1.01419	−	0.878310i
$316$		0			0
$317$	22.5000	+	12.9904i	1.26373	+	0.729612i	0.973793	−	0.227435i	$-0.0730338\pi$
$317$	22.5000	+	12.9904i	1.26373	+	0.729612i	0.289933	+	0.957047i	$0.406367\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	13.5000	+	23.3827i	0.753497	+	1.30509i
$322$		0			0
$323$			5.19615i			0.289122i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	29.4449i		−	1.62830i
$328$		0			0
$329$	−1.50000	−	7.79423i	−0.0826977	−	0.429710i
$330$		0			0
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	0.0274825	+	0.999622i	$0.491251\pi$
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$	−21.0000			−1.15079
$334$		0			0
$335$	−15.0000			−0.819538
$336$		0			0
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$		0			0
$339$	−18.0000	+	31.1769i	−0.977626	+	1.69330i
$340$		0			0
$341$	4.50000	−	7.79423i	0.243689	−	0.422081i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	−27.0000			−1.45363
$346$		0			0
$347$	13.5000	−	7.79423i	0.724718	−	0.418416i	−0.0917687	−	0.995780i	$-0.529252\pi$
$347$	13.5000	−	7.79423i	0.724718	−	0.418416i	0.816487	+	0.577364i	$0.195919\pi$
$348$		0			0
$349$		−	13.8564i		−	0.741716i	−0.928689	−	0.370858i	$-0.879064\pi$
$349$		−	13.8564i		−	0.741716i	0.928689	−	0.370858i	$-0.120936\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$	27.0000	+	15.5885i	1.43301	+	0.827349i
$356$		0			0
$357$	−9.00000	−	10.3923i	−0.476331	−	0.550019i
$358$		0			0
$359$	22.5000	+	12.9904i	1.18750	+	0.685606i	0.957739	−	0.287640i	$-0.0928706\pi$
$359$	22.5000	+	12.9904i	1.18750	+	0.685606i	0.229766	+	0.973246i	$0.426204\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$	−24.0000	+	13.8564i	−1.25967	+	0.727273i
$364$		0			0
$365$			36.3731i			1.90385i
$366$		0			0
$367$	28.5000	−	16.4545i	1.48769	−	0.858917i	0.487787	−	0.872963i	$-0.337804\pi$
$367$	28.5000	−	16.4545i	1.48769	−	0.858917i	0.999901	+	0.0140459i	$0.00447111\pi$
$368$		0			0
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$		0			0
$371$	4.50000	−	12.9904i	0.233628	−	0.674427i
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$		0			0
$375$	−4.50000	−	2.59808i	−0.232379	−	0.134164i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$	−12.0000	−	6.92820i	−0.614779	−	0.354943i
$382$		0			0
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$		0			0
$385$	27.0000	+	31.1769i	1.37605	+	1.58892i
$386$		0			0
$387$	6.00000	+	10.3923i	0.304997	+	0.528271i
$388$		0			0
$389$	22.5000	−	12.9904i	1.14080	−	0.658638i	0.194168	−	0.980968i	$-0.437799\pi$
$389$	22.5000	−	12.9904i	1.14080	−	0.658638i	0.946627	+	0.322330i	$0.104466\pi$
$390$		0			0
$391$			15.5885i			0.788342i
$392$		0			0
$393$	13.5000	−	7.79423i	0.680985	−	0.393167i
$394$		0			0
$395$	−1.50000	−	2.59808i	−0.0754732	−	0.130723i
$396$		0			0
$397$	7.50000	+	4.33013i	0.376414	+	0.217323i	0.676257	−	0.736666i	$-0.263601\pi$
$397$	7.50000	+	4.33013i	0.376414	+	0.217323i	−0.299843	+	0.953989i	$0.596934\pi$
$398$		0			0
$399$	−7.50000	−	2.59808i	−0.375470	−	0.130066i
$400$		0			0
$401$	−31.5000	−	18.1865i	−1.57303	−	0.908192i	−0.995794	−	0.0916181i	$-0.970796\pi$
$401$	−31.5000	−	18.1865i	−1.57303	−	0.908192i	−0.577241	−	0.816574i	$-0.695871\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$		0			0
$407$		−	36.3731i		−	1.80295i
$408$		0			0
$409$	−4.50000	+	2.59808i	−0.222511	+	0.128467i	−0.607112	−	0.794616i	$-0.707672\pi$
$409$	−4.50000	+	2.59808i	−0.222511	+	0.128467i	0.384602	+	0.923083i	$0.374339\pi$
$410$		0			0
$411$	−9.00000			−0.443937
$412$		0			0
$413$	−7.50000	−	2.59808i	−0.369051	−	0.127843i
$414$		0			0
$415$	18.0000	−	31.1769i	0.883585	−	1.53041i
$416$		0			0
$417$	9.00000	−	15.5885i	0.440732	−	0.763370i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$	9.00000			0.437595
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−31.5000	+	6.06218i	−1.52439	+	0.293369i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.5000	−	7.79423i	0.650272	−	0.375435i	−0.138288	−	0.990392i	$-0.544160\pi$
$431$	13.5000	−	7.79423i	0.650272	−	0.375435i	0.788560	+	0.614957i	$0.210827\pi$
$432$		0			0
$433$		−	34.6410i		−	1.66474i	−0.554220	−	0.832370i	$-0.686983\pi$
$433$		−	34.6410i		−	1.66474i	0.554220	−	0.832370i	$-0.313017\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.50000	+	7.79423i	0.215264	+	0.372849i
$438$		0			0
$439$	13.5000	+	7.79423i	0.644320	+	0.371998i	0.786277	−	0.617875i	$-0.212006\pi$
$439$	13.5000	+	7.79423i	0.644320	+	0.371998i	−0.141957	+	0.989873i	$0.545339\pi$
$440$		0			0
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$		0			0
$443$	−13.5000	−	7.79423i	−0.641404	−	0.370315i	0.143751	−	0.989614i	$-0.454084\pi$
$443$	−13.5000	−	7.79423i	−0.641404	−	0.370315i	−0.785155	+	0.619299i	$0.787417\pi$
$444$		0			0
$445$	13.5000	+	23.3827i	0.639961	+	1.10845i
$446$		0			0
$447$	−4.50000	−	7.79423i	−0.212843	−	0.368654i
$448$		0			0
$449$		−	20.7846i		−	0.980886i	−0.871473	−	0.490443i	$-0.836835\pi$
$449$		−	20.7846i		−	0.980886i	0.871473	−	0.490443i	$-0.163165\pi$
$450$		0			0
$451$	27.0000	−	15.5885i	1.27138	−	0.734032i
$452$		0			0
$453$			22.5167i			1.05792i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$		0			0
$459$	13.5000	−	7.79423i	0.630126	−	0.363803i
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	4.50000	−	7.79423i	0.208683	−	0.361449i
$466$		0			0
$467$	−4.50000	+	7.79423i	−0.208235	+	0.360674i	−0.951159	−	0.308702i	$-0.900105\pi$
$467$	−4.50000	+	7.79423i	−0.208235	+	0.360674i	0.742923	+	0.669376i	$0.233439\pi$
$468$		0			0
$469$	−12.5000	−	4.33013i	−0.577196	−	0.199947i
$470$		0			0
$471$	9.00000			0.414698
$472$		0			0
$473$	−18.0000	+	10.3923i	−0.827641	+	0.477839i
$474$		0			0
$475$		−	6.92820i		−	0.317888i
$476$		0			0
$477$	13.5000	+	7.79423i	0.618123	+	0.356873i
$478$		0			0
$479$	16.5000	+	28.5788i	0.753904	+	1.30580i	0.945917	+	0.324408i	$0.105165\pi$
$479$	16.5000	+	28.5788i	0.753904	+	1.30580i	−0.192013	+	0.981392i	$0.561502\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−22.5000	−	7.79423i	−1.02379	−	0.354650i
$484$		0			0
$485$	−18.0000	−	10.3923i	−0.817338	−	0.471890i
$486$		0			0
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$		0			0
$489$	−1.50000	+	0.866025i	−0.0678323	+	0.0391630i
$490$		0			0
$491$			10.3923i			0.468998i	0.972116	+	0.234499i	$0.0753450\pi$
$491$			10.3923i			0.468998i	−0.972116	+	0.234499i	$0.924655\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−40.5000	+	23.3827i	−1.82034	+	1.05097i
$496$		0			0
$497$	18.0000	+	20.7846i	0.807410	+	0.932317i
$498$		0			0
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	−0.933670	−	0.358134i	$-0.883413\pi$
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	0.776989	+	0.629515i	$0.216746\pi$
$500$		0			0
$501$	18.0000	+	10.3923i	0.804181	+	0.464294i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	−27.0000			−1.20148
$506$		0			0
$507$	−19.5000	−	11.2583i	−0.866025	−	0.500000i
$508$		0			0
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	−0.999220	−	0.0394971i	$-0.987424\pi$
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	0.533815	+	0.845601i	$0.320758\pi$
$510$		0			0
$511$	−10.5000	+	30.3109i	−0.464493	+	1.34087i
$512$		0			0
$513$	4.50000	−	7.79423i	0.198680	−	0.344124i
$514$		0			0
$515$	−13.5000	+	7.79423i	−0.594881	+	0.343455i
$516$		0			0
$517$			15.5885i			0.685580i
$518$		0			0
$519$	13.5000	−	7.79423i	0.592584	−	0.342129i
$520$		0			0
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	0.982231	−	0.187678i	$-0.0600963\pi$
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	−0.653650	+	0.756797i	$0.726763\pi$
$522$		0			0
$523$	−22.5000	−	12.9904i	−0.983856	−	0.568030i	−0.0804241	−	0.996761i	$-0.525627\pi$
$523$	−22.5000	−	12.9904i	−0.983856	−	0.568030i	−0.903432	+	0.428731i	$0.858961\pi$
$524$		0			0
$525$	12.0000	+	13.8564i	0.523723	+	0.604743i
$526$		0			0
$527$	−4.50000	−	2.59808i	−0.196023	−	0.113174i
$528$		0			0
$529$	2.00000	+	3.46410i	0.0869565	+	0.150613i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−40.5000	+	23.3827i	−1.75097	+	1.01092i
$536$		0			0
$537$	9.00000			0.388379
$538$		0			0
$539$	13.5000	+	33.7750i	0.581486	+	1.45479i
$540$		0			0
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	−0.127222	−	0.991874i	$-0.540606\pi$
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	0.922599	−	0.385759i	$-0.126061\pi$
$542$		0			0
$543$	6.00000	−	10.3923i	0.257485	−	0.445976i
$544$		0			0
$545$	51.0000			2.18460
$546$		0			0
$547$	32.0000			1.36822			0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000			1.36822			0.684111	+	0.729378i	$0.260191\pi$
$548$		0			0
$549$		−	36.3731i		−	1.55236i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$		0			0
$555$		−	36.3731i		−	1.54395i
$556$		0			0
$557$	22.5000	−	12.9904i	0.953356	−	0.550420i	0.0592339	−	0.998244i	$-0.481134\pi$
$557$	22.5000	−	12.9904i	0.953356	−	0.550420i	0.894122	+	0.447824i	$0.147801\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	13.5000	+	23.3827i	0.569970	+	0.987218i
$562$		0			0
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	−0.996669	−	0.0815478i	$-0.974014\pi$
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	0.427712	−	0.903915i	$-0.359320\pi$
$564$		0			0
$565$	−54.0000	−	31.1769i	−2.27180	−	1.31162i
$566$		0			0
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$		0			0
$569$	−13.5000	−	7.79423i	−0.565949	−	0.326751i	0.189580	−	0.981865i	$-0.439287\pi$
$569$	−13.5000	−	7.79423i	−0.565949	−	0.326751i	−0.755530	+	0.655114i	$0.772621\pi$
$570$		0			0
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	0.929921	−	0.367760i	$-0.119875\pi$
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	−0.783450	+	0.621455i	$0.786542\pi$
$572$		0			0
$573$	13.5000	+	23.3827i	0.563971	+	0.976826i
$574$		0			0
$575$		−	20.7846i		−	0.866778i
$576$		0			0
$577$	−22.5000	+	12.9904i	−0.936687	+	0.540797i	−0.888920	−	0.458062i	$-0.848544\pi$
$577$	−22.5000	+	12.9904i	−0.936687	+	0.540797i	−0.0477669	+	0.998859i	$0.515210\pi$
$578$		0			0
$579$		−	8.66025i		−	0.359908i
$580$		0			0
$581$	24.0000	−	20.7846i	0.995688	−	0.862291i
$582$		0			0
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$		0			0
$589$	−3.00000			−0.123613
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$	18.0000	−	15.5885i	0.737928	−	0.639064i
$596$		0			0
$597$	3.00000			0.122782
$598$		0			0
$599$	−4.50000	+	2.59808i	−0.183865	+	0.106155i	−0.589107	−	0.808055i	$-0.700520\pi$
$599$	−4.50000	+	2.59808i	−0.183865	+	0.106155i	0.405242	+	0.914209i	$0.367187\pi$
$600$		0			0
$601$			34.6410i			1.41304i	0.707695	+	0.706518i	$0.249735\pi$
$601$			34.6410i			1.41304i	−0.707695	+	0.706518i	$0.750265\pi$
$602$		0			0
$603$	7.50000	−	12.9904i	0.305424	−	0.529009i
$604$		0			0
$605$	−24.0000	−	41.5692i	−0.975739	−	1.69003i
$606$		0			0
$607$	25.5000	+	14.7224i	1.03501	+	0.597565i	0.918417	−	0.395614i	$-0.129468\pi$
$607$	25.5000	+	14.7224i	1.03501	+	0.597565i	0.116596	+	0.993179i	$0.462802\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.500000	+	0.866025i	0.0201948	+	0.0349784i	0.875946	−	0.482409i	$-0.160238\pi$
$613$	0.500000	+	0.866025i	0.0201948	+	0.0349784i	−0.855751	+	0.517387i	$0.826905\pi$
$614$		0			0
$615$	27.0000	−	15.5885i	1.08875	−	0.628587i
$616$		0			0
$617$		−	20.7846i		−	0.836757i	−0.908273	−	0.418378i	$-0.862599\pi$
$617$		−	20.7846i		−	0.836757i	0.908273	−	0.418378i	$-0.137401\pi$
$618$		0			0
$619$	22.5000	−	12.9904i	0.904351	−	0.522127i	0.0257420	−	0.999669i	$-0.491805\pi$
$619$	22.5000	−	12.9904i	0.904351	−	0.522127i	0.878609	+	0.477541i	$0.158472\pi$
$620$		0			0
$621$	13.5000	−	23.3827i	0.541736	−	0.938315i
$622$		0			0
$623$	4.50000	+	23.3827i	0.180289	+	0.936808i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	13.5000	+	7.79423i	0.539138	+	0.311272i
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	30.0000	+	17.3205i	1.19239	+	0.688428i
$634$		0			0
$635$	12.0000	−	20.7846i	0.476205	−	0.824812i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−27.0000	+	15.5885i	−1.06810	+	0.616670i
$640$		0			0
$641$	−13.5000	+	7.79423i	−0.533218	+	0.307854i	−0.742326	−	0.670039i	$-0.766277\pi$
$641$	−13.5000	+	7.79423i	−0.533218	+	0.307854i	0.209108	+	0.977893i	$0.432944\pi$
$642$		0			0
$643$		−	3.46410i		−	0.136611i	−0.997664	−	0.0683054i	$-0.978241\pi$
$643$		−	3.46410i		−	0.136611i	0.997664	−	0.0683054i	$-0.0217592\pi$
$644$		0			0
$645$	−18.0000	+	10.3923i	−0.708749	+	0.409197i
$646$		0			0
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$		0			0
$649$	13.5000	+	7.79423i	0.529921	+	0.305950i
$650$		0			0
$651$	6.00000	−	5.19615i	0.235159	−	0.203653i
$652$		0			0
$653$	−13.5000	−	7.79423i	−0.528296	−	0.305012i	0.212026	−	0.977264i	$-0.431994\pi$
$653$	−13.5000	−	7.79423i	−0.528296	−	0.305012i	−0.740322	+	0.672252i	$0.765327\pi$
$654$		0			0
$655$	13.5000	+	23.3827i	0.527489	+	0.913637i
$656$		0			0
$657$	−31.5000	−	18.1865i	−1.22893	−	0.709524i
$658$		0			0
$659$		−	10.3923i		−	0.404827i	−0.979300	−	0.202413i	$-0.935122\pi$
$659$		−	10.3923i		−	0.404827i	0.979300	−	0.202413i	$-0.0648785\pi$
$660$		0			0
$661$	19.5000	−	11.2583i	0.758462	−	0.437898i	−0.0702812	−	0.997527i	$-0.522390\pi$
$661$	19.5000	−	11.2583i	0.758462	−	0.437898i	0.828743	+	0.559629i	$0.189056\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.50000	−	12.9904i	0.174503	−	0.503745i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−9.00000	+	15.5885i	−0.347960	+	0.602685i
$670$		0			0
$671$	63.0000			2.43209
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$		0			0
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$		0			0
$677$	−22.5000	+	38.9711i	−0.864745	+	1.49778i	0.00255466	+	0.999997i	$0.499187\pi$
$677$	−22.5000	+	38.9711i	−0.864745	+	1.49778i	−0.867300	+	0.497786i	$0.834147\pi$
$678$		0			0
$679$	−12.0000	−	13.8564i	−0.460518	−	0.531760i
$680$		0			0
$681$		−	15.5885i		−	0.597351i
$682$		0			0
$683$	31.5000	−	18.1865i	1.20531	−	0.695888i	0.243582	−	0.969880i	$-0.421677\pi$
$683$	31.5000	−	18.1865i	1.20531	−	0.695888i	0.961732	+	0.273992i	$0.0883442\pi$
$684$		0			0
$685$		−	15.5885i		−	0.595604i
$686$		0			0
$687$	−19.5000	−	33.7750i	−0.743971	−	1.28860i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−28.5000	−	16.4545i	−1.08419	−	0.625958i	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−28.5000	−	16.4545i	−1.08419	−	0.625958i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		0			0
$693$	−40.5000	+	7.79423i	−1.53847	+	0.296078i
$694$		0			0
$695$	27.0000	+	15.5885i	1.02417	+	0.591304i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$	−4.50000	−	7.79423i	−0.170206	−	0.294805i
$700$		0			0
$701$			20.7846i			0.785024i	0.919747	+	0.392512i	$0.128394\pi$
$701$			20.7846i			0.785024i	−0.919747	+	0.392512i	$0.871606\pi$
$702$		0			0
$703$	−10.5000	+	6.06218i	−0.396015	+	0.228639i
$704$		0			0
$705$			15.5885i			0.587095i
$706$		0			0
$707$	−22.5000	−	7.79423i	−0.846200	−	0.293132i
$708$		0			0
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	0.413114	+	0.910679i	$0.364441\pi$
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	3.00000			0.112509
$712$		0			0
$713$	−9.00000			−0.337053
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−9.00000	+	15.5885i	−0.336111	+	0.582162i
$718$		0			0
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		0			0
$721$	−13.5000	+	2.59808i	−0.502766	+	0.0967574i
$722$		0			0
$723$	−3.00000			−0.111571
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	24.2487i		−	0.899335i	−0.893196	−	0.449667i	$-0.851542\pi$
$727$		−	24.2487i		−	0.899335i	0.893196	−	0.449667i	$-0.148458\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$	25.5000	+	14.7224i	0.941864	+	0.543785i	0.890544	−	0.454897i	$-0.150324\pi$
$733$	25.5000	+	14.7224i	0.941864	+	0.543785i	0.0513199	+	0.998682i	$0.483657\pi$
$734$		0			0
$735$	13.5000	+	33.7750i	0.497955	+	1.24581i
$736$		0			0
$737$	22.5000	+	12.9904i	0.828798	+	0.478507i
$738$		0			0
$739$	−8.50000	−	14.7224i	−0.312678	−	0.541573i	0.666264	−	0.745716i	$-0.267893\pi$
$739$	−8.50000	−	14.7224i	−0.312678	−	0.541573i	−0.978941	+	0.204143i	$0.934559\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			51.9615i			1.90628i	0.302524	+	0.953142i	$0.402171\pi$
$743$			51.9615i			1.90628i	−0.302524	+	0.953142i	$0.597829\pi$
$744$		0			0
$745$	13.5000	−	7.79423i	0.494602	−	0.285558i
$746$		0			0
$747$	18.0000	+	31.1769i	0.658586	+	1.14070i
$748$		0			0
$749$	−40.5000	+	7.79423i	−1.47984	+	0.284795i
$750$		0			0
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	−0.470311	−	0.882501i	$-0.655858\pi$
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	0.999424	−	0.0339490i	$-0.0108084\pi$
$752$		0			0
$753$	−36.0000	−	20.7846i	−1.31191	−	0.757433i
$754$		0			0
$755$	−39.0000			−1.41936
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$		0			0
$759$	40.5000	+	23.3827i	1.47006	+	0.848738i
$760$		0			0
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	−0.991152	−	0.132734i	$-0.957624\pi$
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	0.610527	+	0.791995i	$0.290958\pi$
$762$		0			0
$763$	42.5000	+	14.7224i	1.53860	+	0.532988i
$764$		0			0
$765$	13.5000	+	23.3827i	0.488094	+	0.845403i
$766$		0			0
$767$		0			0
$768$		0			0
$769$			34.6410i			1.24919i	0.780950	+	0.624593i	$0.214735\pi$
$769$			34.6410i			1.24919i	−0.780950	+	0.624593i	$0.785265\pi$
$770$		0			0
$771$	−40.5000	+	23.3827i	−1.45857	+	0.842107i
$772$		0			0
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$		0			0
$775$	6.00000	+	3.46410i	0.215526	+	0.124434i
$776$		0			0
$777$	10.5000	−	30.3109i	0.376685	−	1.08740i
$778$		0			0
$779$	−9.00000	−	5.19615i	−0.322458	−	0.186171i
$780$		0			0
$781$	−27.0000	−	46.7654i	−0.966136	−	1.67340i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			15.5885i			0.556376i
$786$		0			0
$787$	−1.50000	+	0.866025i	−0.0534692	+	0.0308705i	−0.526496	−	0.850177i	$-0.676495\pi$
$787$	−1.50000	+	0.866025i	−0.0534692	+	0.0308705i	0.473027	+	0.881048i	$0.343161\pi$
$788$		0			0
$789$	9.00000			0.320408
$790$		0			0
$791$	−36.0000	−	41.5692i	−1.28001	−	1.47803i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−13.5000	+	23.3827i	−0.478796	+	0.829298i
$796$		0			0
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	−27.0000			−0.953998
$802$		0			0
$803$	31.5000	−	54.5596i	1.11161	−	1.92537i
$804$		0			0
$805$	13.5000	−	38.9711i	0.475812	−	1.37355i
$806$		0			0
$807$			36.3731i			1.28039i
$808$		0			0
$809$	22.5000	−	12.9904i	0.791058	−	0.456717i	−0.0492770	−	0.998785i	$-0.515692\pi$
$809$	22.5000	−	12.9904i	0.791058	−	0.456717i	0.840335	+	0.542068i	$0.182358\pi$
$810$		0			0
$811$			51.9615i			1.82462i	0.409505	+	0.912308i	$0.365701\pi$
$811$			51.9615i			1.82462i	−0.409505	+	0.912308i	$0.634299\pi$
$812$		0			0
$813$	−19.5000	−	33.7750i	−0.683895	−	1.18454i
$814$		0			0
$815$	−1.50000	−	2.59808i	−0.0525427	−	0.0910066i
$816$		0			0
$817$	6.00000	+	3.46410i	0.209913	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4.50000	+	2.59808i	0.157051	+	0.0906735i	0.576466	−	0.817121i	$-0.304431\pi$
$821$	4.50000	+	2.59808i	0.157051	+	0.0906735i	−0.419415	+	0.907795i	$0.637765\pi$
$822$		0			0
$823$	3.50000	+	6.06218i	0.122002	+	0.211314i	0.920557	−	0.390608i	$-0.127735\pi$
$823$	3.50000	+	6.06218i	0.122002	+	0.211314i	−0.798555	+	0.601922i	$0.794402\pi$
$824$		0			0
$825$	−18.0000	−	31.1769i	−0.626680	−	1.08544i
$826$		0			0
$827$		−	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
$829$	1.50000	−	0.866025i	0.0520972	−	0.0300783i	−0.473725	−	0.880673i	$-0.657091\pi$
$829$	1.50000	−	0.866025i	0.0520972	−	0.0300783i	0.525822	+	0.850594i	$0.323758\pi$
$830$		0			0
$831$		−	22.5167i		−	0.781094i
$832$		0			0
$833$	19.5000	−	7.79423i	0.675635	−	0.270054i
$834$		0			0
$835$	−18.0000	+	31.1769i	−0.622916	+	1.07892i
$836$		0			0
$837$	4.50000	+	7.79423i	0.155543	+	0.269408i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	18.0000	−	31.1769i	0.619953	−	1.07379i
$844$		0			0
$845$	19.5000	−	33.7750i	0.670820	−	1.16190i
$846$		0			0
$847$	−8.00000	−	41.5692i	−0.274883	−	1.42834i
$848$		0			0
$849$	15.0000			0.514799
$850$		0			0
$851$	−31.5000	+	18.1865i	−1.07981	+	0.623426i
$852$		0			0
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$		0			0
$855$	13.5000	+	7.79423i	0.461690	+	0.266557i
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	−34.5000	−	19.9186i	−1.17712	−	0.679613i	−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−34.5000	−	19.9186i	−1.17712	−	0.679613i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$	27.0000	−	5.19615i	0.920158	−	0.177084i
$862$		0			0
$863$	4.50000	+	2.59808i	0.153182	+	0.0884395i	0.574632	−	0.818412i	$-0.305145\pi$
$863$	4.50000	+	2.59808i	0.153182	+	0.0884395i	−0.421450	+	0.906852i	$0.638479\pi$
$864$		0			0
$865$	13.5000	+	23.3827i	0.459014	+	0.795035i
$866$		0			0
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$		0			0
$869$			5.19615i			0.176267i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	18.0000	−	10.3923i	0.609208	−	0.351726i
$874$		0			0
$875$	6.00000	−	5.19615i	0.202837	−	0.175662i
$876$		0			0
$877$	−5.50000	+	9.52628i	−0.185722	+	0.321680i	−0.943820	−	0.330461i	$-0.892796\pi$
$877$	−5.50000	+	9.52628i	−0.185722	+	0.321680i	0.758098	+	0.652141i	$0.226129\pi$
$878$		0			0
$879$	9.00000	+	5.19615i	0.303562	+	0.175262i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$		0			0
$885$	13.5000	+	7.79423i	0.453798	+	0.262000i
$886$		0			0
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	−0.839744	−	0.542983i	$-0.817295\pi$
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	0.890109	+	0.455748i	$0.150628\pi$
$888$		0			0
$889$	16.0000	−	13.8564i	0.536623	−	0.464729i
$890$		0			0
$891$		−	46.7654i		−	1.56670i
$892$		0			0
$893$	4.50000	−	2.59808i	0.150587	−	0.0869413i
$894$		0			0
$895$			15.5885i			0.521065i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	13.5000	+	7.79423i	0.449750	+	0.259663i
$902$		0			0
$903$	−18.0000	+	3.46410i	−0.599002	+	0.115278i
$904$		0			0
$905$	18.0000	+	10.3923i	0.598340	+	0.345452i
$906$		0			0
$907$	−18.5000	−	32.0429i	−0.614282	−	1.06397i	−0.990510	−	0.137441i	$-0.956112\pi$
$907$	−18.5000	−	32.0429i	−0.614282	−	1.06397i	0.376228	−	0.926527i	$-0.377221\pi$
$908$		0			0
$909$	13.5000	−	23.3827i	0.447767	−	0.775555i
$910$		0			0
$911$			10.3923i			0.344312i	0.985070	+	0.172156i	$0.0550734\pi$
$911$			10.3923i			0.344312i	−0.985070	+	0.172156i	$0.944927\pi$
$912$		0			0
$913$	−54.0000	+	31.1769i	−1.78714	+	1.03181i
$914$		0			0
$915$	63.0000			2.08272
$916$		0			0
$917$	4.50000	+	23.3827i	0.148603	+	0.772164i
$918$		0			0
$919$	−9.50000	+	16.4545i	−0.313376	+	0.542783i	−0.979091	−	0.203423i	$-0.934793\pi$
$919$	−9.50000	+	16.4545i	−0.313376	+	0.542783i	0.665715	+	0.746206i	$0.268127\pi$
$920$		0			0
$921$	−15.0000	+	25.9808i	−0.494267	+	0.856095i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	28.0000			0.920634
$926$		0			0
$927$		−	15.5885i		−	0.511992i
$928$		0			0
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	−0.345708	−	0.938342i	$-0.612361\pi$
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543055\pi$
$930$		0			0
$931$	7.50000	−	9.52628i	0.245803	−	0.312211i
$932$		0			0
$933$			25.9808i			0.850572i
$934$		0			0
$935$	−40.5000	+	23.3827i	−1.32449	+	0.764696i
$936$		0			0
$937$			41.5692i			1.35801i	0.734135	+	0.679004i	$0.237588\pi$
$937$			41.5692i			1.35801i	−0.734135	+	0.679004i	$0.762412\pi$
$938$		0			0
$939$	10.5000	+	18.1865i	0.342655	+	0.593495i
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$	−27.0000	−	15.5885i	−0.879241	−	0.507630i
$944$		0			0
$945$	−40.5000	+	7.79423i	−1.31747	+	0.253546i
$946$		0			0
$947$	40.5000	+	23.3827i	1.31607	+	0.759835i	0.983094	−	0.183099i	$-0.0586129\pi$
$947$	40.5000	+	23.3827i	1.31607	+	0.759835i	0.332979	+	0.942934i	$0.391946\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−22.5000	−	38.9711i	−0.729612	−	1.26373i
$952$		0			0
$953$		−	20.7846i		−	0.673280i	−0.941634	−	0.336640i	$-0.890710\pi$
$953$		−	20.7846i		−	0.673280i	0.941634	−	0.336640i	$-0.109290\pi$
$954$		0			0
$955$	−40.5000	+	23.3827i	−1.31055	+	0.756646i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.50000	−	12.9904i	0.145313	−	0.419481i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$		−	46.7654i		−	1.50699i
$964$		0			0
$965$	15.0000			0.482867
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$	4.50000	−	7.79423i	0.144561	−	0.250387i
$970$		0			0
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.107135	+	0.994244i	$0.534168\pi$
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.807473	+	0.589904i	$0.799166\pi$
$972$		0			0
$973$	18.0000	+	20.7846i	0.577054	+	0.666324i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−31.5000	+	18.1865i	−1.00777	+	0.581839i	−0.910539	−	0.413423i	$-0.864333\pi$
$977$	−31.5000	+	18.1865i	−1.00777	+	0.581839i	−0.0972351	+	0.995261i	$0.531000\pi$
$978$		0			0
$979$		−	46.7654i		−	1.49463i
$980$		0			0
$981$	−25.5000	+	44.1673i	−0.814152	+	1.41015i
$982$		0			0
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.50000	+	12.9904i	−0.143237	+	0.413488i
$988$		0			0
$989$	18.0000	+	10.3923i	0.572367	+	0.330456i
$990$		0			0
$991$	−12.5000	−	21.6506i	−0.397076	−	0.687755i	0.596288	−	0.802771i	$-0.296642\pi$
$991$	−12.5000	−	21.6506i	−0.397076	−	0.687755i	−0.993364	+	0.115015i	$0.963308\pi$
$992$		0			0
$993$	46.5000	−	26.8468i	1.47563	−	0.851957i
$994$		0			0
$995$			5.19615i			0.164729i
$996$		0			0
$997$	19.5000	−	11.2583i	0.617571	−	0.356555i	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	19.5000	−	11.2583i	0.617571	−	0.356555i	0.775923	+	0.630828i	$0.217285\pi$
$998$		0			0
$999$	31.5000	+	18.1865i	0.996616	+	0.575396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.k.a.5.1	✓	2
3.2	odd	2		84.2.k.b.5.1	yes	2
4.3	odd	2		336.2.bc.d.257.1		2
5.2	odd	4		2100.2.bo.a.1349.1		4
5.3	odd	4		2100.2.bo.a.1349.2		4
5.4	even	2		2100.2.bi.f.1601.1		2
7.2	even	3		588.2.f.c.293.1		2
7.3	odd	6		84.2.k.b.17.1	yes	2
7.4	even	3		588.2.k.c.521.1		2
7.5	odd	6		588.2.f.a.293.2		2
7.6	odd	2		588.2.k.d.509.1		2
9.2	odd	6		2268.2.w.a.1349.1		2
9.4	even	3		2268.2.bm.a.593.1		2
9.5	odd	6		2268.2.bm.f.593.1		2
9.7	even	3		2268.2.w.f.1349.1		2
12.11	even	2		336.2.bc.b.257.1		2
15.2	even	4		2100.2.bo.f.1349.2		4
15.8	even	4		2100.2.bo.f.1349.1		4
15.14	odd	2		2100.2.bi.e.1601.1		2
21.2	odd	6		588.2.f.a.293.1		2
21.5	even	6		588.2.f.c.293.2		2
21.11	odd	6		588.2.k.d.521.1		2
21.17	even	6	inner	84.2.k.a.17.1	yes	2
21.20	even	2		588.2.k.c.509.1		2
28.3	even	6		336.2.bc.b.17.1		2
28.19	even	6		2352.2.k.d.881.1		2
28.23	odd	6		2352.2.k.a.881.2		2
35.3	even	12		2100.2.bo.f.1949.2		4
35.17	even	12		2100.2.bo.f.1949.1		4
35.24	odd	6		2100.2.bi.e.101.1		2
63.31	odd	6		2268.2.w.a.269.1		2
63.38	even	6		2268.2.bm.a.1025.1		2
63.52	odd	6		2268.2.bm.f.1025.1		2
63.59	even	6		2268.2.w.f.269.1		2
84.23	even	6		2352.2.k.d.881.2		2
84.47	odd	6		2352.2.k.a.881.1		2
84.59	odd	6		336.2.bc.d.17.1		2
105.17	odd	12		2100.2.bo.a.1949.2		4
105.38	odd	12		2100.2.bo.a.1949.1		4
105.59	even	6		2100.2.bi.f.101.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.k.a.5.1	✓	2	1.1	even	1	trivial
84.2.k.a.17.1	yes	2	21.17	even	6	inner
84.2.k.b.5.1	yes	2	3.2	odd	2
84.2.k.b.17.1	yes	2	7.3	odd	6
336.2.bc.b.17.1		2	28.3	even	6
336.2.bc.b.257.1		2	12.11	even	2
336.2.bc.d.17.1		2	84.59	odd	6
336.2.bc.d.257.1		2	4.3	odd	2
588.2.f.a.293.1		2	21.2	odd	6
588.2.f.a.293.2		2	7.5	odd	6
588.2.f.c.293.1		2	7.2	even	3
588.2.f.c.293.2		2	21.5	even	6
588.2.k.c.509.1		2	21.20	even	2
588.2.k.c.521.1		2	7.4	even	3
588.2.k.d.509.1		2	7.6	odd	2
588.2.k.d.521.1		2	21.11	odd	6
2100.2.bi.e.101.1		2	35.24	odd	6
2100.2.bi.e.1601.1		2	15.14	odd	2
2100.2.bi.f.101.1		2	105.59	even	6
2100.2.bi.f.1601.1		2	5.4	even	2
2100.2.bo.a.1349.1		4	5.2	odd	4
2100.2.bo.a.1349.2		4	5.3	odd	4
2100.2.bo.a.1949.1		4	105.38	odd	12
2100.2.bo.a.1949.2		4	105.17	odd	12
2100.2.bo.f.1349.1		4	15.8	even	4
2100.2.bo.f.1349.2		4	15.2	even	4
2100.2.bo.f.1949.1		4	35.17	even	12
2100.2.bo.f.1949.2		4	35.3	even	12
2268.2.w.a.269.1		2	63.31	odd	6
2268.2.w.a.1349.1		2	9.2	odd	6
2268.2.w.f.269.1		2	63.59	even	6
2268.2.w.f.1349.1		2	9.7	even	3
2268.2.bm.a.593.1		2	9.4	even	3
2268.2.bm.a.1025.1		2	63.38	even	6
2268.2.bm.f.593.1		2	9.5	odd	6
2268.2.bm.f.1025.1		2	63.52	odd	6
2352.2.k.a.881.1		2	84.47	odd	6
2352.2.k.a.881.2		2	28.23	odd	6
2352.2.k.d.881.1		2	28.19	even	6
2352.2.k.d.881.2		2	84.23	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-4.50000 + 2.59808i) q^{11} +(-4.50000 + 2.59808i) q^{15} +(1.50000 + 2.59808i) q^{17} +(1.50000 + 0.866025i) q^{19} +(-4.50000 + 0.866025i) q^{21} +(4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.19615i q^{27} +(-1.50000 + 0.866025i) q^{31} +9.00000 q^{33} +(-1.50000 - 7.79423i) q^{35} +(-3.50000 + 6.06218i) q^{37} -6.00000 q^{41} +4.00000 q^{43} +9.00000 q^{45} +(1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} -5.19615i q^{51} +(4.50000 - 2.59808i) q^{53} +15.5885i q^{55} +(-1.50000 - 2.59808i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(-10.5000 - 6.06218i) q^{61} +(7.50000 + 2.59808i) q^{63} +(-2.50000 - 4.33013i) q^{67} +(-4.50000 - 7.79423i) q^{69} +10.3923i q^{71} +(-10.5000 + 6.06218i) q^{73} +6.92820i q^{75} +(-4.50000 + 12.9904i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(-4.50000 + 7.79423i) q^{89} +3.00000 q^{93} +(4.50000 - 2.59808i) q^{95} -6.92820i q^{97} +(-13.5000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 3 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 3 * q^5 + 4 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} + 3 q^{5} + 4 q^{7} + 3 q^{9} - 9 q^{11} - 9 q^{15} + 3 q^{17} + 3 q^{19} - 9 q^{21} + 9 q^{23} - 4 q^{25} - 3 q^{31} + 18 q^{33} - 3 q^{35} - 7 q^{37} - 12 q^{41} + 8 q^{43} + 18 q^{45} + 3 q^{47} + 2 q^{49} + 9 q^{53} - 3 q^{57} - 3 q^{59} - 21 q^{61} + 15 q^{63} - 5 q^{67} - 9 q^{69} - 21 q^{73} - 9 q^{77} + q^{79} - 9 q^{81} + 24 q^{83} + 18 q^{85} - 9 q^{89} + 6 q^{93} + 9 q^{95} - 27 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 3 * q^5 + 4 * q^7 + 3 * q^9 - 9 * q^11 - 9 * q^15 + 3 * q^17 + 3 * q^19 - 9 * q^21 + 9 * q^23 - 4 * q^25 - 3 * q^31 + 18 * q^33 - 3 * q^35 - 7 * q^37 - 12 * q^41 + 8 * q^43 + 18 * q^45 + 3 * q^47 + 2 * q^49 + 9 * q^53 - 3 * q^57 - 3 * q^59 - 21 * q^61 + 15 * q^63 - 5 * q^67 - 9 * q^69 - 21 * q^73 - 9 * q^77 + q^79 - 9 * q^81 + 24 * q^83 + 18 * q^85 - 9 * q^89 + 6 * q^93 + 9 * q^95 - 27 * q^99

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