LMFDB - Embedded newform 735.2.p.a.509.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(374,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	735.509
Dual form			735.2.p.a.374.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.50000i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.358719 + 2.20711i) q^{5} +(-1.73205 - 2.44949i) q^{6} +1.73205 q^{8} +(-1.94949 - 2.28024i) q^{9} +(3.62132 + 1.37333i) q^{10} +(2.44949 - 1.41421i) q^{11} +(-1.72474 + 0.158919i) q^{12} +4.00000 q^{13} +(3.73205 + 1.03528i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.44949 + 1.41421i) q^{17} +(-5.10867 + 0.949490i) q^{18} +(1.73205 - 1.41421i) q^{20} -4.89898i q^{22} +(1.73205 - 3.00000i) q^{23} +(1.25529 - 2.72474i) q^{24} +(-4.74264 + 1.58346i) q^{25} +(3.46410 - 6.00000i) q^{26} +(-5.00000 + 1.41421i) q^{27} -5.65685i q^{29} +(4.78497 - 4.70150i) q^{30} +(-8.48528 + 4.89898i) q^{31} +(-2.59808 - 4.50000i) q^{32} +(-0.449490 - 4.87832i) q^{33} +4.89898i q^{34} +(-1.00000 + 2.82843i) q^{36} +(2.89898 - 6.29253i) q^{39} +(0.621320 + 3.82282i) q^{40} +3.46410 q^{41} +4.89898i q^{43} +(-2.44949 - 1.41421i) q^{44} +(4.33341 - 5.12070i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(2.44949 + 1.41421i) q^{47} +(-5.00000 - 7.07107i) q^{48} +(-1.73205 + 8.48528i) q^{50} +(0.449490 + 4.87832i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-2.20881 + 8.72474i) q^{54} +(4.00000 + 4.89898i) q^{55} +(-8.48528 - 4.89898i) q^{58} +(3.46410 + 6.00000i) q^{59} +(-0.969450 - 3.74969i) q^{60} +(-8.48528 - 4.89898i) q^{61} +16.9706i q^{62} +1.00000 q^{64} +(1.43488 + 8.82843i) q^{65} +(-7.70674 - 3.55051i) q^{66} +(-4.24264 + 2.44949i) q^{67} +(2.44949 + 1.41421i) q^{68} +(-3.46410 - 4.89898i) q^{69} +2.82843i q^{71} +(-3.37662 - 3.94949i) q^{72} +(4.00000 + 6.92820i) q^{73} +(-0.946206 + 8.60841i) q^{75} +(-6.92820 - 9.79796i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(10.4539 + 3.96447i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(3.00000 - 5.19615i) q^{82} -2.82843i q^{83} +(-4.00000 - 4.89898i) q^{85} +(7.34847 + 4.24264i) q^{86} +(-8.89898 - 4.09978i) q^{87} +(4.24264 - 2.44949i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-3.92820 - 10.9348i) q^{90} -3.46410 q^{92} +(1.55708 + 16.8990i) q^{93} +(4.24264 - 2.44949i) q^{94} +(-8.96204 + 0.825765i) q^{96} -8.00000 q^{97} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{4} + 4 q^{9} + 12 q^{10} - 4 q^{12} + 32 q^{13} + 16 q^{15} + 20 q^{16} - 4 q^{25} - 40 q^{27} + 12 q^{30} + 16 q^{33} - 8 q^{36} - 16 q^{39} - 12 q^{40} - 16 q^{45} - 24 q^{46} - 40 q^{48}+ \cdots - 64 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^4 + 4 * q^9 + 12 * q^10 - 4 * q^12 + 32 * q^13 + 16 * q^15 + 20 * q^16 - 4 * q^25 - 40 * q^27 + 12 * q^30 + 16 * q^33 - 8 * q^36 - 16 * q^39 - 12 * q^40 - 16 * q^45 - 24 * q^46 - 40 * q^48 - 16 * q^51 - 16 * q^52 + 32 * q^55 - 8 * q^60 + 8 * q^64 + 32 * q^73 - 4 * q^75 - 32 * q^79 + 28 * q^81 + 24 * q^82 - 32 * q^85 - 32 * q^87 + 24 * q^90 - 64 * q^97 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	0.990839	−	0.135045i	$-0.0431180\pi$
$3$	0.724745	−	1.57313i	0.418432	−	0.908248i
$3$	0.724745	−	1.57313i	0.418432	−	0.908248i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.358719	+	2.20711i	0.160424	+	0.987048i
$5$	0.358719	+	2.20711i	0.160424	+	0.987048i
$6$	−1.73205	−	2.44949i	−0.707107	−	1.00000i
$7$		0			0
$7$		0			0
$8$	1.73205			0.612372
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$	3.62132	+	1.37333i	1.14516	+	0.434286i
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	0.821541	+	0.570149i	$0.193114\pi$
$12$	−1.72474	+	0.158919i	−0.497891	+	0.0458759i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	3.73205	+	1.03528i	0.963611	+	0.267307i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−2.44949	+	1.41421i	−0.594089	+	0.342997i	−0.766712	−	0.641991i	$-0.778109\pi$
$17$	−2.44949	+	1.41421i	−0.594089	+	0.342997i	0.172624	+	0.984988i	$0.444775\pi$
$18$	−5.10867	+	0.949490i	−1.20412	+	0.223797i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	1.73205	−	1.41421i	0.387298	−	0.316228i
$21$		0			0
$22$		−	4.89898i		−	1.04447i
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	−0.626994	−	0.779024i	$-0.715715\pi$
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	0.988152	+	0.153481i	$0.0490483\pi$
$24$	1.25529	−	2.72474i	0.256236	−	0.556186i
$25$	−4.74264	+	1.58346i	−0.948528	+	0.316693i
$26$	3.46410	−	6.00000i	0.679366	−	1.17670i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$		0			0
$29$		−	5.65685i		−	1.05045i	−0.850963	−	0.525226i	$-0.823981\pi$
$29$		−	5.65685i		−	1.05045i	0.850963	−	0.525226i	$-0.176019\pi$
$30$	4.78497	−	4.70150i	0.873611	−	0.858373i
$31$	−8.48528	+	4.89898i	−1.52400	+	0.879883i	−0.524405	+	0.851469i	$0.675712\pi$
$31$	−8.48528	+	4.89898i	−1.52400	+	0.879883i	−0.999596	+	0.0284139i	$0.990954\pi$
$32$	−2.59808	−	4.50000i	−0.459279	−	0.795495i
$33$	−0.449490	−	4.87832i	−0.0782461	−	0.849206i
$34$			4.89898i			0.840168i
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$	2.89898	−	6.29253i	0.464208	−	1.00761i
$40$	0.621320	+	3.82282i	0.0982394	+	0.604441i
$41$	3.46410			0.541002			0.270501	−	0.962720i	$-0.412811\pi$
$41$	3.46410			0.541002			0.270501	+	0.962720i	$0.412811\pi$
$42$		0			0
$43$			4.89898i			0.747087i	0.927613	+	0.373544i	$0.121857\pi$
$43$			4.89898i			0.747087i	−0.927613	+	0.373544i	$0.878143\pi$
$44$	−2.44949	−	1.41421i	−0.369274	−	0.213201i
$45$	4.33341	−	5.12070i	0.645987	−	0.763349i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	2.44949	+	1.41421i	0.357295	+	0.206284i	0.667893	−	0.744257i	$-0.267196\pi$
$47$	2.44949	+	1.41421i	0.357295	+	0.206284i	−0.310599	+	0.950541i	$0.600530\pi$
$48$	−5.00000	−	7.07107i	−0.721688	−	1.02062i
$49$		0			0
$50$	−1.73205	+	8.48528i	−0.244949	+	1.20000i
$51$	0.449490	+	4.87832i	0.0629412	+	0.683101i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$	−2.20881	+	8.72474i	−0.300581	+	1.18729i
$55$	4.00000	+	4.89898i	0.539360	+	0.660578i
$56$		0			0
$57$		0			0
$58$	−8.48528	−	4.89898i	−1.11417	−	0.643268i
$59$	3.46410	+	6.00000i	0.450988	+	0.781133i	0.998448	−	0.0556984i	$-0.0177385\pi$
$59$	3.46410	+	6.00000i	0.450988	+	0.781133i	−0.547460	+	0.836832i	$0.684405\pi$
$60$	−0.969450	−	3.74969i	−0.125155	−	0.484083i
$61$	−8.48528	−	4.89898i	−1.08643	−	0.627250i	−0.153806	−	0.988101i	$-0.549153\pi$
$61$	−8.48528	−	4.89898i	−1.08643	−	0.627250i	−0.932623	+	0.360851i	$0.882486\pi$
$62$			16.9706i			2.15526i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.43488	+	8.82843i	0.177975	+	1.09503i
$66$	−7.70674	−	3.55051i	−0.948634	−	0.437038i
$67$	−4.24264	+	2.44949i	−0.518321	+	0.299253i	−0.736247	−	0.676712i	$-0.763404\pi$
$67$	−4.24264	+	2.44949i	−0.518321	+	0.299253i	0.217926	+	0.975965i	$0.430071\pi$
$68$	2.44949	+	1.41421i	0.297044	+	0.171499i
$69$	−3.46410	−	4.89898i	−0.417029	−	0.589768i
$70$		0			0
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$	−3.37662	−	3.94949i	−0.397938	−	0.465452i
$73$	4.00000	+	6.92820i	0.468165	+	0.810885i	0.999338	−	0.0363782i	$-0.0115821\pi$
$73$	4.00000	+	6.92820i	0.468165	+	0.810885i	−0.531174	+	0.847263i	$0.678249\pi$
$74$		0			0
$75$	−0.946206	+	8.60841i	−0.109258	+	0.994013i
$76$		0			0
$77$		0			0
$78$	−6.92820	−	9.79796i	−0.784465	−	1.10940i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	10.4539	+	3.96447i	1.16878	+	0.443241i
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$		−	2.82843i		−	0.310460i	−0.987878	−	0.155230i	$-0.950388\pi$
$83$		−	2.82843i		−	0.310460i	0.987878	−	0.155230i	$-0.0496119\pi$
$84$		0			0
$85$	−4.00000	−	4.89898i	−0.433861	−	0.531369i
$86$	7.34847	+	4.24264i	0.792406	+	0.457496i
$87$	−8.89898	−	4.09978i	−0.954071	−	0.439542i
$88$	4.24264	−	2.44949i	0.452267	−	0.261116i
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$	−3.92820	−	10.9348i	−0.414069	−	1.15263i
$91$		0			0
$92$	−3.46410			−0.361158
$93$	1.55708	+	16.8990i	0.161461	+	1.75234i
$94$	4.24264	−	2.44949i	0.437595	−	0.252646i
$95$		0			0
$96$	−8.96204	+	0.825765i	−0.914684	+	0.0842793i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$		0			0
$99$	−8.00000	−	2.82843i	−0.804030	−	0.284268i
$100$	3.74264	+	3.31552i	0.374264	+	0.331552i
$101$	−8.66025	−	15.0000i	−0.861727	−	1.49256i	−0.870260	−	0.492592i	$-0.836049\pi$
$101$	−8.66025	−	15.0000i	−0.861727	−	1.49256i	0.00853278	−	0.999964i	$-0.497284\pi$
$102$	7.70674	+	3.55051i	0.763081	+	0.351553i
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	−0.999964	−	0.00844953i	$-0.997310\pi$
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	0.507300	+	0.861770i	$0.330644\pi$
$104$	6.92820			0.679366
$105$		0			0
$106$		0			0
$107$	−5.19615	+	9.00000i	−0.502331	+	0.870063i	0.497665	+	0.867369i	$0.334191\pi$
$107$	−5.19615	+	9.00000i	−0.502331	+	0.870063i	−0.999996	+	0.00269372i	$0.999143\pi$
$108$	3.72474	+	3.62302i	0.358414	+	0.348625i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	10.8126	−	1.75736i	1.03094	−	0.167558i
$111$		0			0
$112$		0			0
$113$	6.92820			0.651751			0.325875	−	0.945413i	$-0.394341\pi$
$113$	6.92820			0.651751			0.325875	+	0.945413i	$0.394341\pi$
$114$		0			0
$115$	7.24264	+	2.74666i	0.675380	+	0.256128i
$116$	−4.89898	+	2.82843i	−0.454859	+	0.262613i
$117$	−7.79796	−	9.12096i	−0.720922	−	0.843233i
$118$	12.0000			1.10469
$119$		0			0
$120$	6.46410	+	1.79315i	0.590089	+	0.163692i
$121$	−1.50000	+	2.59808i	−0.136364	+	0.236189i
$122$	−14.6969	+	8.48528i	−1.33060	+	0.768221i
$123$	2.51059	−	5.44949i	0.226372	−	0.491364i
$124$	8.48528	+	4.89898i	0.762001	+	0.439941i
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$		0			0
$127$			14.6969i			1.30414i	0.758158	+	0.652071i	$0.226100\pi$
$127$			14.6969i			1.30414i	−0.758158	+	0.652071i	$0.773900\pi$
$128$	6.06218	−	10.5000i	0.535826	−	0.928078i
$129$	7.70674	+	3.55051i	0.678541	+	0.312605i
$130$	14.4853	+	5.49333i	1.27044	+	0.481797i
$131$	3.46410	−	6.00000i	0.302660	−	0.524222i	−0.674078	−	0.738661i	$-0.735459\pi$
$131$	3.46410	−	6.00000i	0.302660	−	0.524222i	0.976738	+	0.214438i	$0.0687920\pi$
$132$	−4.00000	+	2.82843i	−0.348155	+	0.246183i
$133$		0			0
$134$			8.48528i			0.733017i
$135$	−4.91492	−	10.5282i	−0.423009	−	0.906126i
$136$	−4.24264	+	2.44949i	−0.363803	+	0.210042i
$137$	3.46410	+	6.00000i	0.295958	+	0.512615i	0.975207	−	0.221293i	$-0.0710278\pi$
$137$	3.46410	+	6.00000i	0.295958	+	0.512615i	−0.679249	+	0.733908i	$0.737694\pi$
$138$	−10.3485	+	0.953512i	−0.880920	+	0.0811683i
$139$		−	9.79796i		−	0.831052i	−0.909581	−	0.415526i	$-0.863598\pi$
$139$		−	9.79796i		−	0.831052i	0.909581	−	0.415526i	$-0.136402\pi$
$140$		0			0
$141$	4.00000	−	2.82843i	0.336861	−	0.238197i
$142$	4.24264	+	2.44949i	0.356034	+	0.205557i
$143$	9.79796	−	5.65685i	0.819346	−	0.473050i
$144$	−14.7474	+	2.74094i	−1.22895	+	0.228412i
$145$	12.4853	−	2.02922i	1.03685	−	0.168518i
$146$	13.8564			1.14676
$147$		0			0
$148$		0			0
$149$	−9.79796	−	5.65685i	−0.802680	−	0.463428i	0.0417274	−	0.999129i	$-0.486714\pi$
$149$	−9.79796	−	5.65685i	−0.802680	−	0.463428i	−0.844407	+	0.535701i	$0.820047\pi$
$150$	12.0932	+	8.87441i	0.987404	+	0.724592i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$	8.00000	+	2.82843i	0.646762	+	0.228665i
$154$		0			0
$155$	−13.8564	−	16.9706i	−1.11297	−	1.36311i
$156$	−6.89898	+	0.635674i	−0.552360	+	0.0508947i
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	6.92820	+	12.0000i	0.551178	+	0.954669i
$159$		0			0
$160$	9.00000	−	7.34847i	0.711512	−	0.580948i
$161$		0			0
$162$	12.1244	+	9.79796i	0.952579	+	0.769800i
$163$	12.7279	+	7.34847i	0.996928	+	0.575577i	0.907338	−	0.420402i	$-0.138111\pi$
$163$	12.7279	+	7.34847i	0.996928	+	0.575577i	0.0895899	+	0.995979i	$0.471444\pi$
$164$	−1.73205	−	3.00000i	−0.135250	−	0.234261i
$165$	10.6057	−	2.74202i	0.825654	−	0.213466i
$166$	−4.24264	−	2.44949i	−0.329293	−	0.190117i
$167$			14.1421i			1.09435i	0.837018	+	0.547176i	$0.184297\pi$
$167$			14.1421i			1.09435i	−0.837018	+	0.547176i	$0.815703\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	−10.8126	+	1.75736i	−0.829286	+	0.134783i
$171$		0			0
$172$	4.24264	−	2.44949i	0.323498	−	0.186772i
$173$	17.1464	+	9.89949i	1.30362	+	0.752645i	0.981023	−	0.193892i	$-0.0621112\pi$
$173$	17.1464	+	9.89949i	1.30362	+	0.752645i	0.322596	+	0.946537i	$0.395445\pi$
$174$	−13.8564	+	9.79796i	−1.05045	+	0.742781i
$175$		0			0
$176$		−	14.1421i		−	1.06600i
$177$	11.9494	−	1.10102i	0.898171	−	0.0827578i
$178$	−9.00000	−	15.5885i	−0.674579	−	1.16840i
$179$	2.44949	−	1.41421i	0.183083	−	0.105703i	−0.405657	−	0.914025i	$-0.632957\pi$
$179$	2.44949	−	1.41421i	0.183083	−	0.105703i	0.588741	+	0.808322i	$0.299624\pi$
$180$	−6.60136	−	1.19249i	−0.492036	−	0.0888833i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−13.8564	+	9.79796i	−1.02430	+	0.724286i
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$	26.6969	+	12.2993i	1.95751	+	0.901831i
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$		−	2.82843i		−	0.206284i
$189$		0			0
$190$		0			0
$191$	−17.1464	−	9.89949i	−1.24067	−	0.716302i	−0.271441	−	0.962455i	$-0.587500\pi$
$191$	−17.1464	−	9.89949i	−1.24067	−	0.716302i	−0.969231	+	0.246153i	$0.920834\pi$
$192$	0.724745	−	1.57313i	0.0523040	−	0.113531i
$193$	8.48528	−	4.89898i	0.610784	−	0.352636i	−0.162488	−	0.986710i	$-0.551952\pi$
$193$	8.48528	−	4.89898i	0.610784	−	0.352636i	0.773272	+	0.634074i	$0.218619\pi$
$194$	−6.92820	+	12.0000i	−0.497416	+	0.861550i
$195$	14.9282	+	4.14110i	1.06903	+	0.296551i
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−11.1708	+	9.55051i	−0.793877	+	0.678725i
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	−8.21449	+	2.74264i	−0.580852	+	0.193934i
$201$	0.778539	+	8.44949i	0.0549139	+	0.595981i
$202$	−30.0000			−2.11079
$203$		0			0
$204$	4.00000	−	2.82843i	0.280056	−	0.198030i
$205$	1.24264	+	7.64564i	0.0867898	+	0.533995i
$206$	8.66025	+	15.0000i	0.603388	+	1.04510i
$207$	−10.2173	+	1.89898i	−0.710154	+	0.131988i
$208$	10.0000	−	17.3205i	0.693375	−	1.20096i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	4.44949	+	2.04989i	0.304874	+	0.140456i
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$	−10.8126	+	1.75736i	−0.737411	+	0.119851i
$216$	−8.66025	+	2.44949i	−0.589256	+	0.166667i
$217$		0			0
$218$	17.3205			1.17309
$219$	13.7980	−	1.27135i	0.932380	−	0.0859098i
$220$	2.24264	−	5.91359i	0.151199	−	0.398694i
$221$	−9.79796	+	5.65685i	−0.659082	+	0.380521i
$222$		0			0
$223$	−26.0000			−1.74109			−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000			−1.74109			−0.870544	+	0.492090i	$0.836233\pi$
$224$		0			0
$225$	12.8564	+	7.72741i	0.857094	+	0.515160i
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	−2.44949	+	1.41421i	−0.162578	+	0.0938647i	−0.579082	−	0.815270i	$-0.696589\pi$
$227$	−2.44949	+	1.41421i	−0.162578	+	0.0938647i	0.416503	+	0.909134i	$0.363255\pi$
$228$		0			0
$229$	−16.9706	−	9.79796i	−1.12145	−	0.647467i	−0.179677	−	0.983726i	$-0.557505\pi$
$229$	−16.9706	−	9.79796i	−1.12145	−	0.647467i	−0.941770	+	0.336258i	$0.890838\pi$
$230$	10.3923	−	8.48528i	0.685248	−	0.559503i
$231$		0			0
$232$		−	9.79796i		−	0.643268i
$233$	10.3923	−	18.0000i	0.680823	−	1.17922i	−0.293908	−	0.955834i	$-0.594956\pi$
$233$	10.3923	−	18.0000i	0.680823	−	1.17922i	0.974730	−	0.223385i	$-0.0717108\pi$
$234$	−20.4347	+	3.79796i	−1.33586	+	0.248280i
$235$	−2.24264	+	5.91359i	−0.146294	+	0.385760i
$236$	3.46410	−	6.00000i	0.225494	−	0.390567i
$237$	8.00000	+	11.3137i	0.519656	+	0.734904i
$238$		0			0
$239$			2.82843i			0.182956i	0.995807	+	0.0914779i	$0.0291591\pi$
$239$			2.82843i			0.182956i	−0.995807	+	0.0914779i	$0.970841\pi$
$240$	13.8130	−	13.5721i	0.891626	−	0.876073i
$241$	8.48528	−	4.89898i	0.546585	−	0.315571i	−0.201158	−	0.979559i	$-0.564471\pi$
$241$	8.48528	−	4.89898i	0.546585	−	0.315571i	0.747743	+	0.663988i	$0.231137\pi$
$242$	2.59808	+	4.50000i	0.167011	+	0.289271i
$243$	12.9722	+	8.64420i	0.832167	+	0.554526i
$244$			9.79796i			0.627250i
$245$		0			0
$246$	−6.00000	−	8.48528i	−0.382546	−	0.541002i
$247$		0			0
$248$	−14.6969	+	8.48528i	−0.933257	+	0.538816i
$249$	−4.44949	−	2.04989i	−0.281975	−	0.129906i
$250$	−19.3492	−	0.778985i	−1.22375	−	0.0492674i
$251$	−20.7846			−1.31191			−0.655956	−	0.754799i	$-0.727735\pi$
$251$	−20.7846			−1.31191			−0.655956	+	0.754799i	$0.727735\pi$
$252$		0			0
$253$		−	9.79796i		−	0.615992i
$254$	22.0454	+	12.7279i	1.38325	+	0.798621i
$255$	−10.6057	+	2.74202i	−0.664156	+	0.171712i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−12.2474	−	7.07107i	−0.763975	−	0.441081i	0.0667462	−	0.997770i	$-0.478738\pi$
$257$	−12.2474	−	7.07107i	−0.763975	−	0.441081i	−0.830721	+	0.556689i	$0.812072\pi$
$258$	12.0000	−	8.48528i	0.747087	−	0.528271i
$259$		0			0
$260$	6.92820	−	5.65685i	0.429669	−	0.350823i
$261$	−12.8990	+	11.0280i	−0.798427	+	0.682615i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−1.73205	−	3.00000i	−0.106803	−	0.184988i	0.807671	−	0.589634i	$-0.200728\pi$
$263$	−1.73205	−	3.00000i	−0.106803	−	0.184988i	−0.914473	+	0.404646i	$0.867395\pi$
$264$	−0.778539	−	8.44949i	−0.0479158	−	0.520030i
$265$		0			0
$266$		0			0
$267$	−10.3923	−	14.6969i	−0.635999	−	0.899438i
$268$	4.24264	+	2.44949i	0.259161	+	0.149626i
$269$	−5.19615	−	9.00000i	−0.316815	−	0.548740i	0.663007	−	0.748614i	$-0.269280\pi$
$269$	−5.19615	−	9.00000i	−0.316815	−	0.548740i	−0.979822	+	0.199874i	$0.935947\pi$
$270$	−20.0488	−	1.74534i	−1.22013	−	0.106218i
$271$	25.4558	+	14.6969i	1.54633	+	0.892775i	0.998417	+	0.0562416i	$0.0179117\pi$
$271$	25.4558	+	14.6969i	1.54633	+	0.892775i	0.547915	+	0.836534i	$0.315422\pi$
$272$			14.1421i			0.857493i
$273$		0			0
$274$	12.0000			0.724947
$275$	−9.37769	+	10.5858i	−0.565496	+	0.638347i
$276$	−2.51059	+	5.44949i	−0.151120	+	0.328021i
$277$	16.9706	−	9.79796i	1.01966	−	0.588702i	0.105656	−	0.994403i	$-0.466306\pi$
$277$	16.9706	−	9.79796i	1.01966	−	0.588702i	0.914006	+	0.405700i	$0.132972\pi$
$278$	−14.6969	−	8.48528i	−0.881464	−	0.508913i
$279$	27.7128	+	9.79796i	1.65912	+	0.586588i
$280$		0			0
$281$			28.2843i			1.68730i	0.536895	+	0.843649i	$0.319597\pi$
$281$			28.2843i			1.68730i	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−0.778539	−	8.44949i	−0.0463613	−	0.503160i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	2.44949	−	1.41421i	0.145350	−	0.0839181i
$285$		0			0
$286$		−	19.5959i		−	1.15873i
$287$		0			0
$288$	−5.19615	+	14.6969i	−0.306186	+	0.866025i
$289$	−4.50000	+	7.79423i	−0.264706	+	0.458484i
$290$	7.76874	−	20.4853i	0.456196	−	1.20294i
$291$	−5.79796	+	12.5851i	−0.339882	+	0.737749i
$292$	4.00000	−	6.92820i	0.234082	−	0.405442i
$293$		−	2.82843i		−	0.165238i	−0.996581	−	0.0826192i	$-0.973671\pi$
$293$		−	2.82843i		−	0.165238i	0.996581	−	0.0826192i	$-0.0263285\pi$
$294$		0			0
$295$	−12.0000	+	9.79796i	−0.698667	+	0.570459i
$296$		0			0
$297$	−10.2474	+	10.5352i	−0.594617	+	0.611313i
$298$	−16.9706	+	9.79796i	−0.983078	+	0.567581i
$299$	6.92820	−	12.0000i	0.400668	−	0.693978i
$300$	7.92820	−	3.48477i	0.457735	−	0.201193i
$301$		0			0
$302$	−13.8564			−0.797347
$303$	−29.8735	+	2.75255i	−1.71619	+	0.158130i
$304$		0			0
$305$	7.76874	−	20.4853i	0.444836	−	1.17298i
$306$	11.1708	−	9.55051i	0.638595	−	0.545966i
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$		0			0
$309$	10.0000	+	14.1421i	0.568880	+	0.804518i
$310$	−37.4558	+	6.08767i	−2.12735	+	0.345756i
$311$	13.8564	+	24.0000i	0.785725	+	1.36092i	0.928565	+	0.371169i	$0.121043\pi$
$311$	13.8564	+	24.0000i	0.785725	+	1.36092i	−0.142840	+	0.989746i	$0.545624\pi$
$312$	5.02118	−	10.8990i	0.284268	−	0.617033i
$313$	−8.00000	+	13.8564i	−0.452187	+	0.783210i	−0.998522	−	0.0543564i	$-0.982689\pi$
$313$	−8.00000	+	13.8564i	−0.452187	+	0.783210i	0.546335	+	0.837567i	$0.316023\pi$
$314$	−6.92820			−0.390981
$315$		0			0
$316$	8.00000			0.450035
$317$	−6.92820	+	12.0000i	−0.389127	+	0.673987i	−0.992332	−	0.123599i	$-0.960556\pi$
$317$	−6.92820	+	12.0000i	−0.389127	+	0.673987i	0.603206	+	0.797586i	$0.293890\pi$
$318$		0			0
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$	0.358719	+	2.20711i	0.0200530	+	0.123381i
$321$	10.3923	+	14.6969i	0.580042	+	0.820303i
$322$		0			0
$323$		0			0
$324$	8.39898	−	3.23375i	0.466610	−	0.179653i
$325$	−18.9706	+	6.33386i	−1.05230	+	0.351339i
$326$	22.0454	−	12.7279i	1.22098	−	0.704934i
$327$	17.2474	−	1.58919i	0.953786	−	0.0878822i
$328$	6.00000			0.331295
$329$		0			0
$330$	5.07180	−	18.2832i	0.279193	−	1.00646i
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−2.44949	+	1.41421i	−0.134433	+	0.0776151i
$333$		0			0
$334$	21.2132	+	12.2474i	1.16073	+	0.670151i
$335$	−6.92820	−	8.48528i	−0.378528	−	0.463600i
$336$		0			0
$337$		−	19.5959i		−	1.06746i	−0.845656	−	0.533729i	$-0.820790\pi$
$337$		−	19.5959i		−	1.06746i	0.845656	−	0.533729i	$-0.179210\pi$
$338$	2.59808	−	4.50000i	0.141317	−	0.244768i
$339$	5.02118	−	10.8990i	0.272713	−	0.591951i
$340$	−2.24264	+	5.91359i	−0.121624	+	0.320710i
$341$	−13.8564	+	24.0000i	−0.750366	+	1.29967i
$342$		0			0
$343$		0			0
$344$			8.48528i			0.457496i
$345$	9.56993	−	9.40300i	0.515228	−	0.506241i
$346$	29.6985	−	17.1464i	1.59660	−	0.921798i
$347$	−8.66025	−	15.0000i	−0.464907	−	0.805242i	0.534291	−	0.845301i	$-0.320579\pi$
$347$	−8.66025	−	15.0000i	−0.464907	−	0.805242i	−0.999197	+	0.0400587i	$0.987246\pi$
$348$	0.898979	+	9.75663i	0.0481904	+	0.523010i
$349$		−	19.5959i		−	1.04895i	−0.851427	−	0.524473i	$-0.824262\pi$
$349$		−	19.5959i		−	1.04895i	0.851427	−	0.524473i	$-0.175738\pi$
$350$		0			0
$351$	−20.0000	+	5.65685i	−1.06752	+	0.301941i
$352$	−12.7279	−	7.34847i	−0.678401	−	0.391675i
$353$	26.9444	−	15.5563i	1.43411	−	0.827981i	0.436674	−	0.899620i	$-0.356156\pi$
$353$	26.9444	−	15.5563i	1.43411	−	0.827981i	0.997431	+	0.0716387i	$0.0228229\pi$
$354$	8.69694	−	18.8776i	0.462237	−	1.00333i
$355$	−6.24264	+	1.01461i	−0.331325	+	0.0538500i
$356$	−10.3923			−0.550791
$357$		0			0
$358$		−	4.89898i		−	0.258919i
$359$	26.9444	+	15.5563i	1.42207	+	0.821033i	0.996476	−	0.0838812i	$-0.0267316\pi$
$359$	26.9444	+	15.5563i	1.42207	+	0.821033i	0.425595	+	0.904914i	$0.360065\pi$
$360$	7.50569	−	8.86931i	0.395584	−	0.467454i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$		0			0
$363$	3.00000	+	4.24264i	0.157459	+	0.222681i
$364$		0			0
$365$	−13.8564	+	11.3137i	−0.725277	+	0.592187i
$366$	2.69694	+	29.2699i	0.140971	+	1.52996i
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$	−8.66025	−	15.0000i	−0.451447	−	0.781929i
$369$	−6.75323	−	7.89898i	−0.351559	−	0.411204i
$370$		0			0
$371$		0			0
$372$	13.8564	−	9.79796i	0.718421	−	0.508001i
$373$	−8.48528	−	4.89898i	−0.439351	−	0.253660i	0.263971	−	0.964531i	$-0.414968\pi$
$373$	−8.48528	−	4.89898i	−0.439351	−	0.253660i	−0.703322	+	0.710871i	$0.748301\pi$
$374$	6.92820	+	12.0000i	0.358249	+	0.620505i
$375$	−19.3391	+	0.999626i	−0.998667	+	0.0516205i
$376$	4.24264	+	2.44949i	0.218797	+	0.126323i
$377$		−	22.6274i		−	1.16537i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	23.1202	+	10.6515i	1.18449	+	0.545694i
$382$	−29.6985	+	17.1464i	−1.51951	+	0.877288i
$383$	−12.2474	−	7.07107i	−0.625815	−	0.361315i	0.153314	−	0.988177i	$-0.451005\pi$
$383$	−12.2474	−	7.07107i	−0.625815	−	0.361315i	−0.779130	+	0.626863i	$0.784339\pi$
$384$	−12.1244	−	17.1464i	−0.618718	−	0.875000i
$385$		0			0
$386$		−	16.9706i		−	0.863779i
$387$	11.1708	−	9.55051i	0.567846	−	0.485480i
$388$	4.00000	+	6.92820i	0.203069	+	0.351726i
$389$	−19.5959	+	11.3137i	−0.993552	+	0.573628i	−0.906334	−	0.422561i	$-0.861131\pi$
$389$	−19.5959	+	11.3137i	−0.993552	+	0.573628i	−0.0872182	+	0.996189i	$0.527798\pi$
$390$	19.1399	−	18.8060i	0.969185	−	0.952279i
$391$			9.79796i			0.495504i
$392$		0			0
$393$	−6.92820	−	9.79796i	−0.349482	−	0.494242i
$394$		0			0
$395$	−16.7262	−	6.34315i	−0.841585	−	0.319158i
$396$	1.55051	+	8.34242i	0.0779161	+	0.419222i
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	−0.498112	−	0.867113i	$-0.665973\pi$
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	0.999998	−	0.00217869i	$-0.000693499\pi$
$398$		0			0
$399$		0			0
$400$	−5.00000	+	24.4949i	−0.250000	+	1.22474i
$401$	19.5959	+	11.3137i	0.978573	+	0.564980i	0.901839	−	0.432072i	$-0.142217\pi$
$401$	19.5959	+	11.3137i	0.978573	+	0.564980i	0.0767343	+	0.997052i	$0.475551\pi$
$402$	13.3485	+	6.14966i	0.665761	+	0.306717i
$403$	−33.9411	+	19.5959i	−1.69073	+	0.976142i
$404$	−8.66025	+	15.0000i	−0.430864	+	0.746278i
$405$	−20.1244	+	0.101536i	−0.999987	+	0.00504536i
$406$		0			0
$407$		0			0
$408$	0.778539	+	8.44949i	0.0385434	+	0.418312i
$409$	−8.48528	+	4.89898i	−0.419570	+	0.242239i	−0.694893	−	0.719113i	$-0.744548\pi$
$409$	−8.48528	+	4.89898i	−0.419570	+	0.242239i	0.275323	+	0.961352i	$0.411215\pi$
$410$	12.5446	+	4.75736i	0.619535	+	0.234949i
$411$	11.9494	−	1.10102i	0.589420	−	0.0543093i
$412$	10.0000			0.492665
$413$		0			0
$414$	−6.00000	+	16.9706i	−0.294884	+	0.834058i
$415$	6.24264	−	1.01461i	0.306439	−	0.0498053i
$416$	−10.3923	−	18.0000i	−0.509525	−	0.882523i
$417$	−15.4135	−	7.10102i	−0.754802	−	0.347738i
$418$		0			0
$419$	−6.92820			−0.338465			−0.169232	−	0.985576i	$-0.554129\pi$
$419$	−6.92820			−0.338465			−0.169232	+	0.985576i	$0.554129\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	−3.46410	+	6.00000i	−0.168630	+	0.292075i
$423$	−1.55051	−	8.34242i	−0.0753884	−	0.405622i
$424$		0			0
$425$	9.37769	−	10.5858i	0.454885	−	0.513486i
$426$	6.92820	−	4.89898i	0.335673	−	0.237356i
$427$		0			0
$428$	10.3923			0.502331
$429$	−1.79796	−	19.5133i	−0.0868063	−	0.942109i
$430$	−6.72792	+	17.7408i	−0.324449	+	0.855536i
$431$	2.44949	−	1.41421i	0.117988	−	0.0681203i	−0.439845	−	0.898074i	$-0.644967\pi$
$431$	2.44949	−	1.41421i	0.117988	−	0.0681203i	0.557832	+	0.829954i	$0.311633\pi$
$432$	−6.37628	+	25.1862i	−0.306779	+	1.21177i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$		0			0
$435$	5.85641	−	21.1117i	0.280793	−	1.01223i
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$		0			0
$438$	10.0424	−	21.7980i	0.479842	−	1.04155i
$439$	−33.9411	−	19.5959i	−1.61992	−	0.935262i	−0.986939	−	0.161096i	$-0.948497\pi$
$439$	−33.9411	−	19.5959i	−1.61992	−	0.935262i	−0.632983	−	0.774166i	$-0.718170\pi$
$440$	6.92820	+	8.48528i	0.330289	+	0.404520i
$441$		0			0
$442$			19.5959i			0.932083i
$443$	8.66025	−	15.0000i	0.411461	−	0.712672i	−0.583589	−	0.812049i	$-0.698352\pi$
$443$	8.66025	−	15.0000i	0.411461	−	0.712672i	0.995050	+	0.0993779i	$0.0316853\pi$
$444$		0			0
$445$	21.7279	+	8.23999i	1.03000	+	0.390613i
$446$	−22.5167	+	39.0000i	−1.06619	+	1.84670i
$447$	−16.0000	+	11.3137i	−0.756774	+	0.535120i
$448$		0			0
$449$		−	5.65685i		−	0.266963i	−0.991051	−	0.133482i	$-0.957384\pi$
$449$		−	5.65685i		−	0.266963i	0.991051	−	0.133482i	$-0.0426157\pi$
$450$	22.7251	−	12.5925i	1.07127	−	0.593615i
$451$	8.48528	−	4.89898i	0.399556	−	0.230684i
$452$	−3.46410	−	6.00000i	−0.162938	−	0.282216i
$453$	−13.7980	+	1.27135i	−0.648285	+	0.0597332i
$454$			4.89898i			0.229920i
$455$		0			0
$456$		0			0
$457$	−16.9706	−	9.79796i	−0.793849	−	0.458329i	0.0474665	−	0.998873i	$-0.484885\pi$
$457$	−16.9706	−	9.79796i	−0.793849	−	0.458329i	−0.841316	+	0.540544i	$0.818219\pi$
$458$	−29.3939	+	16.9706i	−1.37349	+	0.792982i
$459$	10.2474	−	10.5352i	0.478310	−	0.491740i
$460$	−1.24264	−	7.64564i	−0.0579384	−	0.356480i
$461$	−3.46410			−0.161339			−0.0806696	−	0.996741i	$-0.525706\pi$
$461$	−3.46410			−0.161339			−0.0806696	+	0.996741i	$0.525706\pi$
$462$		0			0
$463$		−	4.89898i		−	0.227675i	−0.993499	−	0.113837i	$-0.963686\pi$
$463$		−	4.89898i		−	0.227675i	0.993499	−	0.113837i	$-0.0363143\pi$
$464$	−24.4949	−	14.1421i	−1.13715	−	0.656532i
$465$	−36.7393	+	9.49863i	−1.70374	+	0.440488i
$466$	−18.0000	−	31.1769i	−0.833834	−	1.44424i
$467$	2.44949	+	1.41421i	0.113349	+	0.0654420i	0.555603	−	0.831448i	$-0.312488\pi$
$467$	2.44949	+	1.41421i	0.113349	+	0.0654420i	−0.442254	+	0.896890i	$0.645821\pi$
$468$	−4.00000	+	11.3137i	−0.184900	+	0.522976i
$469$		0			0
$470$	6.92820	+	8.48528i	0.319574	+	0.391397i
$471$	−6.89898	+	0.635674i	−0.317888	+	0.0292903i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	6.92820	+	12.0000i	0.318559	+	0.551761i
$474$	23.8988	−	2.20204i	1.09771	−	0.101143i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	4.24264	+	2.44949i	0.194054	+	0.112037i
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	−0.986911	−	0.161265i	$-0.948443\pi$
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	0.353796	−	0.935323i	$-0.384891\pi$
$480$	−5.03741	−	19.4840i	−0.229925	−	0.889317i
$481$		0			0
$482$		−	16.9706i		−	0.772988i
$483$		0			0
$484$	3.00000			0.136364
$485$	−2.86976	−	17.6569i	−0.130309	−	0.801756i
$486$	24.2005	−	11.9722i	1.09776	−	0.543070i
$487$	12.7279	−	7.34847i	0.576757	−	0.332991i	−0.183086	−	0.983097i	$-0.558609\pi$
$487$	12.7279	−	7.34847i	0.576757	−	0.332991i	0.759844	+	0.650106i	$0.225275\pi$
$488$	−14.6969	−	8.48528i	−0.665299	−	0.384111i
$489$	20.7846	−	14.6969i	0.939913	−	0.664619i
$490$		0			0
$491$		−	14.1421i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$491$		−	14.1421i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$492$	−5.97469	+	0.550510i	−0.269360	+	0.0248189i
$493$	8.00000	+	13.8564i	0.360302	+	0.624061i
$494$		0			0
$495$	3.37288	−	18.6715i	0.151600	−	0.839220i
$496$			48.9898i			2.19971i
$497$		0			0
$498$	−6.92820	+	4.89898i	−0.310460	+	0.219529i
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−5.97514	+	9.44975i	−0.267216	+	0.422606i
$501$	22.2474	+	10.2494i	0.993943	+	0.457911i
$502$	−18.0000	+	31.1769i	−0.803379	+	1.39149i
$503$		−	19.7990i		−	0.882793i	−0.897312	−	0.441397i	$-0.854483\pi$
$503$		−	19.7990i		−	0.882793i	0.897312	−	0.441397i	$-0.145517\pi$
$504$		0			0
$505$	30.0000	−	24.4949i	1.33498	−	1.09001i
$506$	−14.6969	−	8.48528i	−0.653359	−	0.377217i
$507$	2.17423	−	4.71940i	0.0965611	−	0.209596i
$508$	12.7279	−	7.34847i	0.564710	−	0.326036i
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	−0.901855	−	0.432038i	$-0.857795\pi$
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	0.825084	+	0.565011i	$0.191128\pi$
$510$	−5.07180	+	18.2832i	−0.224583	+	0.809595i
$511$		0			0
$512$	−8.66025			−0.382733
$513$		0			0
$514$	−21.2132	+	12.2474i	−0.935674	+	0.540212i
$515$	−20.9077	−	7.92893i	−0.921303	−	0.349390i
$516$	−0.778539	−	8.44949i	−0.0342733	−	0.371968i
$517$	8.00000			0.351840
$518$		0			0
$519$	28.0000	−	19.7990i	1.22906	−	0.869079i
$520$	2.48528	+	15.2913i	0.108987	+	0.670567i
$521$	−5.19615	−	9.00000i	−0.227648	−	0.394297i	0.729463	−	0.684020i	$-0.239770\pi$
$521$	−5.19615	−	9.00000i	−0.227648	−	0.394297i	−0.957110	+	0.289723i	$0.906437\pi$
$522$	5.37113	+	28.8990i	0.235088	+	1.26487i
$523$	13.0000	−	22.5167i	0.568450	−	0.984585i	−0.428269	−	0.903651i	$-0.640876\pi$
$523$	13.0000	−	22.5167i	0.568450	−	0.984585i	0.996719	−	0.0809336i	$-0.0257902\pi$
$524$	−6.92820			−0.302660
$525$		0			0
$526$	−6.00000			−0.261612
$527$	13.8564	−	24.0000i	0.603595	−	1.04546i
$528$	−22.2474	−	10.2494i	−0.968196	−	0.446050i
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$		0			0
$531$	6.92820	−	19.5959i	0.300658	−	0.850390i
$532$		0			0
$533$	13.8564			0.600188
$534$	−31.0454	+	2.86054i	−1.34347	+	0.123787i
$535$	−21.7279	−	8.23999i	−0.939380	−	0.356246i
$536$	−7.34847	+	4.24264i	−0.317406	+	0.183254i
$537$	−0.449490	−	4.87832i	−0.0193969	−	0.210515i
$538$	−18.0000			−0.776035
$539$		0			0
$540$	−6.66025	+	9.52056i	−0.286612	+	0.409700i
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	44.0908	−	25.4558i	1.89386	−	1.09342i
$543$		0			0
$544$	12.7279	+	7.34847i	0.545705	+	0.315063i
$545$	−17.3205	+	14.1421i	−0.741929	+	0.605783i
$546$		0			0
$547$			34.2929i			1.46626i	0.680090	+	0.733128i	$0.261941\pi$
$547$			34.2929i			1.46626i	−0.680090	+	0.733128i	$0.738059\pi$
$548$	3.46410	−	6.00000i	0.147979	−	0.256307i
$549$	5.37113	+	28.8990i	0.229234	+	1.23338i
$550$	7.75736	+	23.2341i	0.330775	+	0.990705i
$551$		0			0
$552$	−6.00000	−	8.48528i	−0.255377	−	0.361158i
$553$		0			0
$554$		−	33.9411i		−	1.44202i
$555$		0			0
$556$	−8.48528	+	4.89898i	−0.359856	+	0.207763i
$557$	20.7846	+	36.0000i	0.880672	+	1.52537i	0.850595	+	0.525821i	$0.176242\pi$
$557$	20.7846	+	36.0000i	0.880672	+	1.52537i	0.0300772	+	0.999548i	$0.490425\pi$
$558$	38.6969	−	33.0839i	1.63817	−	1.40055i
$559$			19.5959i			0.828819i
$560$		0			0
$561$	8.00000	+	11.3137i	0.337760	+	0.477665i
$562$	42.4264	+	24.4949i	1.78965	+	1.03325i
$563$	12.2474	−	7.07107i	0.516168	−	0.298010i	−0.219197	−	0.975681i	$-0.570344\pi$
$563$	12.2474	−	7.07107i	0.516168	−	0.298010i	0.735366	+	0.677671i	$0.237010\pi$
$564$	−4.44949	−	2.04989i	−0.187357	−	0.0863159i
$565$	2.48528	+	15.2913i	0.104557	+	0.643309i
$566$	24.2487			1.01925
$567$		0			0
$568$			4.89898i			0.205557i
$569$	−24.4949	−	14.1421i	−1.02688	−	0.592869i	−0.110790	−	0.993844i	$-0.535338\pi$
$569$	−24.4949	−	14.1421i	−1.02688	−	0.592869i	−0.916089	+	0.400975i	$0.868672\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	−9.79796	−	5.65685i	−0.409673	−	0.236525i
$573$	−28.0000	+	19.7990i	−1.16972	+	0.827115i
$574$		0			0
$575$	−3.46410	+	16.9706i	−0.144463	+	0.707721i
$576$	−1.94949	−	2.28024i	−0.0812287	−	0.0950100i
$577$	4.00000	+	6.92820i	0.166522	+	0.288425i	0.937195	−	0.348806i	$-0.113413\pi$
$577$	4.00000	+	6.92820i	0.166522	+	0.288425i	−0.770673	+	0.637231i	$0.780080\pi$
$578$	7.79423	+	13.5000i	0.324197	+	0.561526i
$579$	−1.55708	−	16.8990i	−0.0647100	−	0.702298i
$580$	−8.00000	−	9.79796i	−0.332182	−	0.406838i
$581$		0			0
$582$	13.8564	+	19.5959i	0.574367	+	0.812277i
$583$		0			0
$584$	6.92820	+	12.0000i	0.286691	+	0.496564i
$585$	17.3336	−	20.4828i	0.716658	−	0.846859i
$586$	−4.24264	−	2.44949i	−0.175262	−	0.101187i
$587$		−	19.7990i		−	0.817192i	−0.912715	−	0.408596i	$-0.866019\pi$
$587$		−	19.7990i		−	0.817192i	0.912715	−	0.408596i	$-0.133981\pi$
$588$		0			0
$589$		0			0
$590$	4.30463	+	26.4853i	0.177219	+	1.09038i
$591$		0			0
$592$		0			0
$593$	17.1464	+	9.89949i	0.704119	+	0.406524i	0.808880	−	0.587974i	$-0.200074\pi$
$593$	17.1464	+	9.89949i	0.704119	+	0.406524i	−0.104760	+	0.994497i	$0.533408\pi$
$594$	6.92820	+	24.4949i	0.284268	+	1.00504i
$595$		0			0
$596$			11.3137i			0.463428i
$597$		0			0
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$	31.8434	−	18.3848i	1.30108	−	0.751182i	0.320495	−	0.947250i	$-0.396151\pi$
$599$	31.8434	−	18.3848i	1.30108	−	0.751182i	0.980590	+	0.196069i	$0.0628176\pi$
$600$	−1.63888	+	14.9102i	−0.0669069	+	0.608706i
$601$			9.79796i			0.399667i	0.979830	+	0.199834i	$0.0640401\pi$
$601$			9.79796i			0.399667i	−0.979830	+	0.199834i	$0.935960\pi$
$602$		0			0
$603$	13.8564	+	4.89898i	0.564276	+	0.199502i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−6.27231	−	2.37868i	−0.255006	−	0.0967071i
$606$	−21.7423	+	47.1940i	−0.883222	+	1.91712i
$607$	−5.00000	+	8.66025i	−0.202944	+	0.351509i	−0.949476	−	0.313841i	$-0.898384\pi$
$607$	−5.00000	+	8.66025i	−0.202944	+	0.351509i	0.746532	+	0.665350i	$0.231718\pi$
$608$		0			0
$609$		0			0
$610$	−24.0000	−	29.3939i	−0.971732	−	1.19012i
$611$	9.79796	+	5.65685i	0.396383	+	0.228852i
$612$	−1.55051	−	8.34242i	−0.0626757	−	0.337222i
$613$	25.4558	−	14.6969i	1.02815	−	0.593604i	0.111697	−	0.993742i	$-0.464371\pi$
$613$	25.4558	−	14.6969i	1.02815	−	0.593604i	0.916455	+	0.400139i	$0.131038\pi$
$614$	8.66025	−	15.0000i	0.349499	−	0.605351i
$615$	12.9282	+	3.58630i	0.521315	+	0.144614i
$616$		0			0
$617$	48.4974			1.95243			0.976216	−	0.216799i	$-0.0695615\pi$
$617$	48.4974			1.95243			0.976216	+	0.216799i	$0.0695615\pi$
$618$	29.8735	−	2.75255i	1.20169	−	0.110724i
$619$	8.48528	−	4.89898i	0.341052	−	0.196907i	−0.319685	−	0.947524i	$-0.603577\pi$
$619$	8.48528	−	4.89898i	0.341052	−	0.196907i	0.660737	+	0.750617i	$0.270244\pi$
$620$	−7.76874	+	20.4853i	−0.312000	+	0.822709i
$621$	−4.41761	+	17.4495i	−0.177273	+	0.700224i
$622$	48.0000			1.92462
$623$		0			0
$624$	−20.0000	−	28.2843i	−0.800641	−	1.13228i
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	13.8564	+	24.0000i	0.553813	+	0.959233i
$627$		0			0
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.92820	+	12.0000i	−0.275589	+	0.477334i
$633$	−2.89898	+	6.29253i	−0.115224	+	0.250106i
$634$	12.0000	+	20.7846i	0.476581	+	0.825462i
$635$	−32.4377	+	5.27208i	−1.28725	+	0.209216i
$636$		0			0
$637$		0			0
$638$	−27.7128			−1.09716
$639$	6.44949	−	5.51399i	0.255138	−	0.218130i
$640$	25.3492	+	9.61332i	1.00202	+	0.380000i
$641$	−4.89898	+	2.82843i	−0.193498	+	0.111716i	−0.593619	−	0.804746i	$-0.702301\pi$
$641$	−4.89898	+	2.82843i	−0.193498	+	0.111716i	0.400121	+	0.916462i	$0.368968\pi$
$642$	31.0454	−	2.86054i	1.22526	−	0.112896i
$643$	22.0000			0.867595			0.433798	−	0.901010i	$-0.357173\pi$
$643$	22.0000			0.867595			0.433798	+	0.901010i	$0.357173\pi$
$644$		0			0
$645$	−5.07180	+	18.2832i	−0.199702	+	0.719902i
$646$		0			0
$647$	−17.1464	+	9.89949i	−0.674096	+	0.389189i	−0.797627	−	0.603151i	$-0.793911\pi$
$647$	−17.1464	+	9.89949i	−0.674096	+	0.389189i	0.123531	+	0.992341i	$0.460578\pi$
$648$	−2.42310	+	15.3990i	−0.0951885	+	0.604929i
$649$	16.9706	+	9.79796i	0.666153	+	0.384604i
$650$	−6.92820	+	33.9411i	−0.271746	+	1.33128i
$651$		0			0
$652$		−	14.6969i		−	0.575577i
$653$	−13.8564	+	24.0000i	−0.542243	+	0.939193i	0.456532	+	0.889707i	$0.349091\pi$
$653$	−13.8564	+	24.0000i	−0.542243	+	0.939193i	−0.998775	+	0.0494855i	$0.984242\pi$
$654$	12.5529	−	27.2474i	0.490859	−	1.06546i
$655$	14.4853	+	5.49333i	0.565987	+	0.214642i
$656$	8.66025	−	15.0000i	0.338126	−	0.585652i
$657$	8.00000	−	22.6274i	0.312110	−	0.882780i
$658$		0			0
$659$			2.82843i			0.110180i	0.998481	+	0.0550899i	$0.0175446\pi$
$659$			2.82843i			0.110180i	−0.998481	+	0.0550899i	$0.982455\pi$
$660$	−7.67752	−	7.81382i	−0.298847	−	0.304152i
$661$	−8.48528	+	4.89898i	−0.330039	+	0.190548i	−0.655859	−	0.754884i	$-0.727693\pi$
$661$	−8.48528	+	4.89898i	−0.330039	+	0.190548i	0.325819	+	0.945432i	$0.394360\pi$
$662$	−24.2487	−	42.0000i	−0.942453	−	1.63238i
$663$	1.79796	+	19.5133i	0.0698269	+	0.757832i
$664$		−	4.89898i		−	0.190117i
$665$		0			0
$666$		0			0
$667$	−16.9706	−	9.79796i	−0.657103	−	0.379378i
$668$	12.2474	−	7.07107i	0.473868	−	0.273588i
$669$	−18.8434	+	40.9014i	−0.728527	+	1.58134i
$670$	−18.7279	+	3.04384i	−0.723523	+	0.117594i
$671$	−27.7128			−1.06984
$672$		0			0
$673$		−	9.79796i		−	0.377684i	−0.982008	−	0.188842i	$-0.939527\pi$
$673$		−	9.79796i		−	0.377684i	0.982008	−	0.188842i	$-0.0604733\pi$
$674$	−29.3939	−	16.9706i	−1.13221	−	0.653682i
$675$	21.4738	−	14.6244i	0.826529	−	0.562895i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	2.44949	+	1.41421i	0.0941415	+	0.0543526i	0.546332	−	0.837569i	$-0.316024\pi$
$677$	2.44949	+	1.41421i	0.0941415	+	0.0543526i	−0.452190	+	0.891922i	$0.649357\pi$
$678$	−12.0000	−	16.9706i	−0.460857	−	0.651751i
$679$		0			0
$680$	−6.92820	−	8.48528i	−0.265684	−	0.325396i
$681$	0.449490	+	4.87832i	0.0172245	+	0.186937i
$682$	24.0000	+	41.5692i	0.919007	+	1.59177i
$683$	−5.19615	−	9.00000i	−0.198825	−	0.344375i	0.749323	−	0.662205i	$-0.230379\pi$
$683$	−5.19615	−	9.00000i	−0.198825	−	0.344375i	−0.948148	+	0.317830i	$0.897046\pi$
$684$		0			0
$685$	−12.0000	+	9.79796i	−0.458496	+	0.374361i
$686$		0			0
$687$	−27.7128	+	19.5959i	−1.05731	+	0.747631i
$688$	21.2132	+	12.2474i	0.808746	+	0.466930i
$689$		0			0
$690$	−5.81670	−	22.4981i	−0.221438	−	0.856489i
$691$	−8.48528	−	4.89898i	−0.322795	−	0.186366i	0.329843	−	0.944036i	$-0.393004\pi$
$691$	−8.48528	−	4.89898i	−0.322795	−	0.186366i	−0.652638	+	0.757670i	$0.726338\pi$
$692$		−	19.7990i		−	0.752645i
$693$		0			0
$694$	−30.0000			−1.13878
$695$	21.6251	−	3.51472i	0.820288	−	0.133321i
$696$	−15.4135	−	7.10102i	−0.584247	−	0.269163i
$697$	−8.48528	+	4.89898i	−0.321403	+	0.185562i
$698$	−29.3939	−	16.9706i	−1.11257	−	0.642345i
$699$	−20.7846	−	29.3939i	−0.786146	−	1.11178i
$700$		0			0
$701$		−	22.6274i		−	0.854626i	−0.904104	−	0.427313i	$-0.859460\pi$
$701$		−	22.6274i		−	0.854626i	0.904104	−	0.427313i	$-0.140540\pi$
$702$	−8.83523	+	34.8990i	−0.333464	+	1.31718i
$703$		0			0
$704$	2.44949	−	1.41421i	0.0923186	−	0.0533002i
$705$	7.67752	+	7.81382i	0.289152	+	0.294285i
$706$		−	53.8888i		−	2.02813i
$707$		0			0
$708$	−6.92820	−	9.79796i	−0.260378	−	0.368230i
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	−3.88437	+	10.2426i	−0.145778	+	0.384399i
$711$	23.5959	−	4.38551i	0.884916	−	0.164469i
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$			33.9411i			1.27111i
$714$		0			0
$715$	16.0000	+	19.5959i	0.598366	+	0.732846i
$716$	−2.44949	−	1.41421i	−0.0915417	−	0.0528516i
$717$	4.44949	+	2.04989i	0.166169	+	0.0765545i
$718$	46.6690	−	26.9444i	1.74167	−	1.00556i
$719$	−20.7846	+	36.0000i	−0.775135	+	1.34257i	0.159583	+	0.987184i	$0.448985\pi$
$719$	−20.7846	+	36.0000i	−0.775135	+	1.34257i	−0.934718	+	0.355389i	$0.884348\pi$
$720$	−11.3397	−	31.5660i	−0.422607	−	1.17639i
$721$		0			0
$722$	−32.9090			−1.22474
$723$	−1.55708	−	16.8990i	−0.0579084	−	0.628480i
$724$		0			0
$725$	8.95743	+	26.8284i	0.332670	+	0.996383i
$726$	8.96204	−	0.825765i	0.332612	−	0.0306470i
$727$	10.0000			0.370879			0.185440	−	0.982656i	$-0.440629\pi$
$727$	10.0000			0.370879			0.185440	+	0.982656i	$0.440629\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	4.97056	+	30.5826i	0.183969	+	1.13191i
$731$	−6.92820	−	12.0000i	−0.256249	−	0.443836i
$732$	15.4135	+	7.10102i	0.569699	+	0.262461i
$733$	−14.0000	+	24.2487i	−0.517102	+	0.895647i	0.482701	+	0.875785i	$0.339656\pi$
$733$	−14.0000	+	24.2487i	−0.517102	+	0.895647i	−0.999803	+	0.0198613i	$0.993678\pi$
$734$	−17.3205			−0.639312
$735$		0			0
$736$	−18.0000			−0.663489
$737$	−6.92820	+	12.0000i	−0.255204	+	0.442026i
$738$	−17.6969	+	3.28913i	−0.651433	+	0.121075i
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.2487			−0.889599			−0.444799	−	0.895630i	$-0.646725\pi$
$743$	−24.2487			−0.889599			−0.444799	+	0.895630i	$0.646725\pi$
$744$	2.69694	+	29.2699i	0.0988746	+	1.07309i
$745$	8.97056	−	23.6544i	0.328656	−	0.866629i
$746$	−14.6969	+	8.48528i	−0.538093	+	0.310668i
$747$	−6.44949	+	5.51399i	−0.235974	+	0.201746i
$748$	8.00000			0.292509
$749$		0			0
$750$	−15.2487	+	29.8744i	−0.556804	+	1.09086i
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$	12.2474	−	7.07107i	0.446619	−	0.257855i
$753$	−15.0635	+	32.6969i	−0.548946	+	1.19154i
$754$	−33.9411	−	19.5959i	−1.23606	−	0.713641i
$755$	13.8564	−	11.3137i	0.504286	−	0.411748i
$756$		0			0
$757$		−	29.3939i		−	1.06834i	−0.845378	−	0.534169i	$-0.820624\pi$
$757$		−	29.3939i		−	1.06834i	0.845378	−	0.534169i	$-0.179376\pi$
$758$	−24.2487	+	42.0000i	−0.880753	+	1.52551i
$759$	−15.4135	−	7.10102i	−0.559474	−	0.257751i
$760$		0			0
$761$	19.0526	−	33.0000i	0.690655	−	1.19625i	−0.280969	−	0.959717i	$-0.590656\pi$
$761$	19.0526	−	33.0000i	0.690655	−	1.19625i	0.971624	−	0.236532i	$-0.0760109\pi$
$762$	36.0000	−	25.4558i	1.30414	−	0.922168i
$763$		0			0
$764$			19.7990i			0.716302i
$765$	−3.37288	+	18.6715i	−0.121947	+	0.675068i
$766$	−21.2132	+	12.2474i	−0.766464	+	0.442518i
$767$	13.8564	+	24.0000i	0.500326	+	0.866590i
$768$	−32.7702	+	3.01945i	−1.18249	+	0.108955i
$769$			19.5959i			0.706647i	0.935501	+	0.353323i	$0.114948\pi$
$769$			19.5959i			0.706647i	−0.935501	+	0.353323i	$0.885052\pi$
$770$		0			0
$771$	−20.0000	+	14.1421i	−0.720282	+	0.509317i
$772$	−8.48528	−	4.89898i	−0.305392	−	0.176318i
$773$	−2.44949	+	1.41421i	−0.0881020	+	0.0508657i	−0.543404	−	0.839471i	$-0.682865\pi$
$773$	−2.44949	+	1.41421i	−0.0881020	+	0.0508657i	0.455302	+	0.890337i	$0.349531\pi$
$774$	−4.65153	−	25.0273i	−0.167196	−	0.899586i
$775$	32.4853	−	36.6702i	1.16691	−	1.31723i
$776$	−13.8564			−0.497416
$777$		0			0
$778$			39.1918i			1.40510i
$779$		0			0
$780$	−3.87780	−	14.9988i	−0.138848	−	0.537042i
$781$	4.00000	+	6.92820i	0.143131	+	0.247911i
$782$	14.6969	+	8.48528i	0.525561	+	0.303433i
$783$	8.00000	+	28.2843i	0.285897	+	1.01080i
$784$		0			0
$785$	6.92820	−	5.65685i	0.247278	−	0.201902i
$786$	−20.6969	+	1.90702i	−0.738235	+	0.0680213i
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	0.963394	−	0.268091i	$-0.0863928\pi$
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	−0.713871	+	0.700278i	$0.753059\pi$
$788$		0			0
$789$	−5.97469	+	0.550510i	−0.212705	+	0.0195987i
$790$	−24.0000	+	19.5959i	−0.853882	+	0.697191i
$791$		0			0
$792$	−13.8564	−	4.89898i	−0.492366	−	0.174078i
$793$	−33.9411	−	19.5959i	−1.20528	−	0.695871i
$794$	−17.3205	−	30.0000i	−0.614682	−	1.06466i
$795$		0			0
$796$		0			0
$797$		−	36.7696i		−	1.30244i	−0.758887	−	0.651222i	$-0.774257\pi$
$797$		−	36.7696i		−	1.30244i	0.758887	−	0.651222i	$-0.225743\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	19.4473	+	17.2279i	0.687567	+	0.609099i
$801$	−30.6520	+	5.69694i	−1.08304	+	0.201291i
$802$	33.9411	−	19.5959i	1.19850	−	0.691956i
$803$	19.5959	+	11.3137i	0.691525	+	0.399252i
$804$	6.92820	−	4.89898i	0.244339	−	0.172774i
$805$		0			0
$806$			67.8823i			2.39105i
$807$	−17.9241	+	1.65153i	−0.630957	+	0.0581366i
$808$	−15.0000	−	25.9808i	−0.527698	−	0.914000i
$809$	−19.5959	+	11.3137i	−0.688956	+	0.397769i	−0.803221	−	0.595682i	$-0.796882\pi$
$809$	−19.5959	+	11.3137i	−0.688956	+	0.397769i	0.114265	+	0.993450i	$0.463549\pi$
$810$	−17.2759	+	30.2745i	−0.607013	+	1.06374i
$811$		−	29.3939i		−	1.03216i	−0.856541	−	0.516079i	$-0.827391\pi$
$811$		−	29.3939i		−	1.03216i	0.856541	−	0.516079i	$-0.172609\pi$
$812$		0			0
$813$	41.5692	−	29.3939i	1.45790	−	1.03089i
$814$		0			0
$815$	−11.6531	+	30.7279i	−0.408190	+	1.07635i
$816$	22.2474	+	10.2494i	0.778816	+	0.358802i
$817$		0			0
$818$			16.9706i			0.593362i
$819$		0			0
$820$	6.00000	−	4.89898i	0.209529	−	0.171080i
$821$	19.5959	+	11.3137i	0.683902	+	0.394851i	0.801324	−	0.598231i	$-0.204129\pi$
$821$	19.5959	+	11.3137i	0.683902	+	0.394851i	−0.117421	+	0.993082i	$0.537463\pi$
$822$	8.69694	−	18.8776i	0.303341	−	0.658431i
$823$	−4.24264	+	2.44949i	−0.147889	+	0.0853838i	−0.572119	−	0.820171i	$-0.693878\pi$
$823$	−4.24264	+	2.44949i	−0.147889	+	0.0853838i	0.424229	+	0.905555i	$0.360545\pi$
$824$	−8.66025	+	15.0000i	−0.301694	+	0.522550i
$825$	9.85641	+	22.4243i	0.343156	+	0.780715i
$826$		0			0
$827$	10.3923			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$827$	10.3923			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$828$	6.75323	+	7.89898i	0.234691	+	0.274509i
$829$	25.4558	−	14.6969i	0.884118	−	0.510446i	0.0121040	−	0.999927i	$-0.496147\pi$
$829$	25.4558	−	14.6969i	0.884118	−	0.510446i	0.872014	+	0.489481i	$0.162814\pi$
$830$	3.88437	−	10.2426i	0.134828	−	0.355527i
$831$	−3.11416	−	33.7980i	−0.108029	−	1.17244i
$832$	4.00000			0.138675
$833$		0			0
$834$	−24.0000	+	16.9706i	−0.831052	+	0.587643i
$835$	−31.2132	+	5.07306i	−1.08018	+	0.175560i
$836$		0			0
$837$	35.4982	−	36.4949i	1.22700	−	1.26145i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	27.7128			0.956753			0.478376	−	0.878155i	$-0.341226\pi$
$839$	27.7128			0.956753			0.478376	+	0.878155i	$0.341226\pi$
$840$		0			0
$841$	−3.00000			−0.103448
$842$	22.5167	−	39.0000i	0.775975	−	1.34403i
$843$	44.4949	+	20.4989i	1.53249	+	0.706019i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	1.07616	+	6.62132i	0.0370210	+	0.227780i
$846$	−13.8564	−	4.89898i	−0.476393	−	0.168430i
$847$		0			0
$848$		0			0
$849$	24.1464	−	2.22486i	0.828703	−	0.0763570i
$850$	−7.75736	−	23.2341i	−0.266075	−	0.796923i
$851$		0			0
$852$	−0.449490	−	4.87832i	−0.0153993	−	0.167128i
$853$	−20.0000			−0.684787			−0.342393	−	0.939557i	$-0.611238\pi$
$853$	−20.0000			−0.684787			−0.342393	+	0.939557i	$0.611238\pi$
$854$		0			0
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	41.6413	−	24.0416i	1.42244	−	0.821246i	0.425933	−	0.904754i	$-0.359946\pi$
$857$	41.6413	−	24.0416i	1.42244	−	0.821246i	0.996507	+	0.0835080i	$0.0266124\pi$
$858$	−30.8270	−	14.2020i	−1.05242	−	0.484850i
$859$	33.9411	+	19.5959i	1.15806	+	0.668604i	0.950837	−	0.309691i	$-0.100225\pi$
$859$	33.9411	+	19.5959i	1.15806	+	0.668604i	0.207219	+	0.978295i	$0.433559\pi$
$860$	6.92820	+	8.48528i	0.236250	+	0.289346i
$861$		0			0
$862$		−	4.89898i		−	0.166860i
$863$	−5.19615	+	9.00000i	−0.176879	+	0.306364i	−0.940810	−	0.338935i	$-0.889933\pi$
$863$	−5.19615	+	9.00000i	−0.176879	+	0.306364i	0.763931	+	0.645298i	$0.223267\pi$
$864$	19.3543	+	18.8258i	0.658448	+	0.640466i
$865$	−15.6985	+	41.3951i	−0.533764	+	1.40748i
$866$	13.8564	−	24.0000i	0.470860	−	0.815553i
$867$	9.00000	+	12.7279i	0.305656	+	0.432263i
$868$		0			0
$869$			22.6274i			0.767583i
$870$	−26.5957	−	27.0679i	−0.901679	−	0.917686i
$871$	−16.9706	+	9.79796i	−0.575026	+	0.331991i
$872$	8.66025	+	15.0000i	0.293273	+	0.507964i
$873$	15.5959	+	18.2419i	0.527842	+	0.617395i
$874$		0			0
$875$		0			0
$876$	−8.00000	−	11.3137i	−0.270295	−	0.382255i
$877$	42.4264	+	24.4949i	1.43264	+	0.827134i	0.997321	−	0.0731435i	$-0.0233031\pi$
$877$	42.4264	+	24.4949i	1.43264	+	0.827134i	0.435317	+	0.900277i	$0.356636\pi$
$878$	−58.7878	+	33.9411i	−1.98399	+	1.14546i
$879$	−4.44949	−	2.04989i	−0.150078	−	0.0691410i
$880$	31.2132	−	5.07306i	1.05220	−	0.171013i
$881$	10.3923			0.350126			0.175063	−	0.984557i	$-0.443987\pi$
$881$	10.3923			0.350126			0.175063	+	0.984557i	$0.443987\pi$
$882$		0			0
$883$			14.6969i			0.494591i	0.968940	+	0.247296i	$0.0795419\pi$
$883$			14.6969i			0.494591i	−0.968940	+	0.247296i	$0.920458\pi$
$884$	9.79796	+	5.65685i	0.329541	+	0.190261i
$885$	6.71655	+	25.9786i	0.225774	+	0.873261i
$886$	−15.0000	−	25.9808i	−0.503935	−	0.872841i
$887$	2.44949	+	1.41421i	0.0822458	+	0.0474846i	0.540559	−	0.841306i	$-0.318213\pi$
$887$	2.44949	+	1.41421i	0.0822458	+	0.0474846i	−0.458313	+	0.888791i	$0.651546\pi$
$888$		0			0
$889$		0			0
$890$	31.1769	−	25.4558i	1.04505	−	0.853282i
$891$	9.14643	+	23.7559i	0.306417	+	0.795853i
$892$	13.0000	+	22.5167i	0.435272	+	0.753914i
$893$		0			0
$894$	3.11416	+	33.7980i	0.104153	+	1.13037i
$895$	4.00000	+	4.89898i	0.133705	+	0.163755i
$896$		0			0
$897$	−13.8564	−	19.5959i	−0.462652	−	0.654289i
$898$	−8.48528	−	4.89898i	−0.283158	−	0.163481i
$899$	27.7128	+	48.0000i	0.924274	+	1.60089i
$900$	0.263927	−	14.9977i	0.00879757	−	0.499923i
$901$		0			0
$902$		−	16.9706i		−	0.565058i
$903$		0			0
$904$	12.0000			0.399114
$905$		0			0
$906$	−10.0424	+	21.7980i	−0.333635	+	0.724189i
$907$	−21.2132	+	12.2474i	−0.704373	+	0.406670i	−0.808974	−	0.587844i	$-0.799977\pi$
$907$	−21.2132	+	12.2474i	−0.704373	+	0.406670i	0.104601	+	0.994514i	$0.466643\pi$
$908$	2.44949	+	1.41421i	0.0812892	+	0.0469323i
$909$	−17.3205	+	48.9898i	−0.574485	+	1.62489i
$910$		0			0
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$		0			0
$913$	−4.00000	−	6.92820i	−0.132381	−	0.229290i
$914$	−29.3939	+	16.9706i	−0.972263	+	0.561336i
$915$	−26.5957	−	27.0679i	−0.879227	−	0.894836i
$916$			19.5959i			0.647467i
$917$		0			0
$918$	−6.92820	−	24.4949i	−0.228665	−	0.808452i
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	12.5446	+	4.75736i	0.413584	+	0.156845i
$921$	7.24745	−	15.7313i	0.238812	−	0.518365i
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$			11.3137i			0.372395i
$924$		0			0
$925$		0			0
$926$	−7.34847	−	4.24264i	−0.241486	−	0.139422i
$927$	29.4949	−	5.48188i	0.968740	−	0.180049i
$928$	−25.4558	+	14.6969i	−0.835629	+	0.482451i
$929$	22.5167	−	39.0000i	0.738748	−	1.27955i	−0.214312	−	0.976765i	$-0.568751\pi$
$929$	22.5167	−	39.0000i	0.738748	−	1.27955i	0.953059	−	0.302783i	$-0.0979158\pi$
$930$	−17.5692	+	63.3350i	−0.576117	+	2.07684i
$931$		0			0
$932$	−20.7846			−0.680823
$933$	47.7975	−	4.40408i	1.56482	−	0.144183i
$934$	4.24264	−	2.44949i	0.138823	−	0.0801498i
$935$	−16.7262	−	6.34315i	−0.547004	−	0.207443i
$936$	−13.5065	−	15.7980i	−0.441472	−	0.516372i
$937$	−8.00000			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$938$		0			0
$939$	16.0000	+	22.6274i	0.522140	+	0.738418i
$940$	6.24264	−	1.01461i	0.203612	−	0.0330930i
$941$	−12.1244	−	21.0000i	−0.395243	−	0.684580i	0.597889	−	0.801579i	$-0.296006\pi$
$941$	−12.1244	−	21.0000i	−0.395243	−	0.684580i	−0.993132	+	0.116998i	$0.962673\pi$
$942$	−5.02118	+	10.8990i	−0.163599	+	0.355108i
$943$	6.00000	−	10.3923i	0.195387	−	0.338420i
$944$	34.6410			1.12747
$945$		0			0
$946$	24.0000			0.780307
$947$	−1.73205	+	3.00000i	−0.0562841	+	0.0974869i	−0.892795	−	0.450464i	$-0.851259\pi$
$947$	−1.73205	+	3.00000i	−0.0562841	+	0.0974869i	0.836511	+	0.547951i	$0.184592\pi$
$948$	5.79796	−	12.5851i	0.188309	−	0.408744i
$949$	16.0000	+	27.7128i	0.519382	+	0.899596i
$950$		0			0
$951$	13.8564	+	19.5959i	0.449325	+	0.635441i
$952$		0			0
$953$	−20.7846			−0.673280			−0.336640	−	0.941634i	$-0.609290\pi$
$953$	−20.7846			−0.673280			−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$	15.6985	−	41.3951i	0.507991	−	1.33952i
$956$	2.44949	−	1.41421i	0.0792222	−	0.0457389i
$957$	−27.5959	+	2.54270i	−0.892049	+	0.0821938i
$958$	−48.0000			−1.55081
$959$		0			0
$960$	3.73205	+	1.03528i	0.120451	+	0.0334134i
$961$	32.5000	−	56.2917i	1.04839	−	1.81586i
$962$		0			0
$963$	30.6520	−	5.69694i	0.987747	−	0.183581i
$964$	−8.48528	−	4.89898i	−0.273293	−	0.157786i
$965$	13.8564	+	16.9706i	0.446054	+	0.546302i
$966$		0			0
$967$		−	34.2929i		−	1.10278i	−0.834246	−	0.551392i	$-0.814097\pi$
$967$		−	34.2929i		−	1.10278i	0.834246	−	0.551392i	$-0.185903\pi$
$968$	−2.59808	+	4.50000i	−0.0835053	+	0.144635i
$969$		0			0
$970$	−28.9706	−	10.9867i	−0.930189	−	0.352760i
$971$	−10.3923	+	18.0000i	−0.333505	+	0.577647i	−0.983196	−	0.182550i	$-0.941565\pi$
$971$	−10.3923	+	18.0000i	−0.333505	+	0.577647i	0.649692	+	0.760198i	$0.274898\pi$
$972$	1.00000	−	15.5563i	0.0320750	−	0.498970i
$973$		0			0
$974$		−	25.4558i		−	0.815658i
$975$	−3.78482	+	34.4336i	−0.121211	+	1.10276i
$976$	−42.4264	+	24.4949i	−1.35804	+	0.784063i
$977$	−24.2487	−	42.0000i	−0.775785	−	1.34370i	−0.934352	−	0.356351i	$-0.884021\pi$
$977$	−24.2487	−	42.0000i	−0.775785	−	1.34370i	0.158567	−	0.987348i	$-0.449313\pi$
$978$	−4.04541	−	43.9048i	−0.129358	−	1.40392i
$979$		−	29.3939i		−	0.939432i
$980$		0			0
$981$	10.0000	−	28.2843i	0.319275	−	0.903047i
$982$	−21.2132	−	12.2474i	−0.676941	−	0.390832i
$983$	−2.44949	+	1.41421i	−0.0781266	+	0.0451064i	−0.538554	−	0.842591i	$-0.681029\pi$
$983$	−2.44949	+	1.41421i	−0.0781266	+	0.0451064i	0.460428	+	0.887697i	$0.347696\pi$
$984$	4.34847	−	9.43879i	0.138624	−	0.300898i
$985$		0			0
$986$	27.7128			0.882556
$987$		0			0
$988$		0			0
$989$	14.6969	+	8.48528i	0.467335	+	0.269816i
$990$	−25.0862	−	21.2293i	−0.797292	−	0.674711i
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	44.0908	+	25.4558i	1.39988	+	0.808224i
$993$	−28.0000	−	39.5980i	−0.888553	−	1.25660i
$994$		0			0
$995$		0			0
$996$	0.449490	+	4.87832i	0.0142426	+	0.154575i
$997$	−26.0000	−	45.0333i	−0.823428	−	1.42622i	−0.903115	−	0.429400i	$-0.858725\pi$
$997$	−26.0000	−	45.0333i	−0.823428	−	1.42622i	0.0796863	−	0.996820i	$-0.474608\pi$
$998$	−3.46410	−	6.00000i	−0.109654	−	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.a.509.4		8
3.2	odd	2	inner	735.2.p.a.509.1		8
5.4	even	2		735.2.p.c.509.1		8
7.2	even	3		105.2.g.c.104.2	yes	4
7.3	odd	6		735.2.p.c.374.4		8
7.4	even	3	inner	735.2.p.a.374.3		8
7.5	odd	6		105.2.g.a.104.1	✓	4
7.6	odd	2		735.2.p.c.509.3		8
15.14	odd	2		735.2.p.c.509.4		8
21.2	odd	6		105.2.g.c.104.3	yes	4
21.5	even	6		105.2.g.a.104.4	yes	4
21.11	odd	6	inner	735.2.p.a.374.2		8
21.17	even	6		735.2.p.c.374.1		8
21.20	even	2		735.2.p.c.509.2		8
28.19	even	6		1680.2.k.c.209.3		4
28.23	odd	6		1680.2.k.a.209.2		4
35.2	odd	12		525.2.b.j.251.3		8
35.4	even	6		735.2.p.c.374.2		8
35.9	even	6		105.2.g.a.104.3	yes	4
35.12	even	12		525.2.b.j.251.2		8
35.19	odd	6		105.2.g.c.104.4	yes	4
35.23	odd	12		525.2.b.j.251.6		8
35.24	odd	6	inner	735.2.p.a.374.1		8
35.33	even	12		525.2.b.j.251.7		8
35.34	odd	2	inner	735.2.p.a.509.2		8
84.23	even	6		1680.2.k.a.209.3		4
84.47	odd	6		1680.2.k.c.209.2		4
105.2	even	12		525.2.b.j.251.5		8
105.23	even	12		525.2.b.j.251.4		8
105.44	odd	6		105.2.g.a.104.2	yes	4
105.47	odd	12		525.2.b.j.251.8		8
105.59	even	6	inner	735.2.p.a.374.4		8
105.68	odd	12		525.2.b.j.251.1		8
105.74	odd	6		735.2.p.c.374.3		8
105.89	even	6		105.2.g.c.104.1	yes	4
105.104	even	2	inner	735.2.p.a.509.3		8
140.19	even	6		1680.2.k.a.209.1		4
140.79	odd	6		1680.2.k.c.209.4		4
420.299	odd	6		1680.2.k.a.209.4		4
420.359	even	6		1680.2.k.c.209.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.g.a.104.1	✓	4	7.5	odd	6
105.2.g.a.104.2	yes	4	105.44	odd	6
105.2.g.a.104.3	yes	4	35.9	even	6
105.2.g.a.104.4	yes	4	21.5	even	6
105.2.g.c.104.1	yes	4	105.89	even	6
105.2.g.c.104.2	yes	4	7.2	even	3
105.2.g.c.104.3	yes	4	21.2	odd	6
105.2.g.c.104.4	yes	4	35.19	odd	6
525.2.b.j.251.1		8	105.68	odd	12
525.2.b.j.251.2		8	35.12	even	12
525.2.b.j.251.3		8	35.2	odd	12
525.2.b.j.251.4		8	105.23	even	12
525.2.b.j.251.5		8	105.2	even	12
525.2.b.j.251.6		8	35.23	odd	12
525.2.b.j.251.7		8	35.33	even	12
525.2.b.j.251.8		8	105.47	odd	12
735.2.p.a.374.1		8	35.24	odd	6	inner
735.2.p.a.374.2		8	21.11	odd	6	inner
735.2.p.a.374.3		8	7.4	even	3	inner
735.2.p.a.374.4		8	105.59	even	6	inner
735.2.p.a.509.1		8	3.2	odd	2	inner
735.2.p.a.509.2		8	35.34	odd	2	inner
735.2.p.a.509.3		8	105.104	even	2	inner
735.2.p.a.509.4		8	1.1	even	1	trivial
735.2.p.c.374.1		8	21.17	even	6
735.2.p.c.374.2		8	35.4	even	6
735.2.p.c.374.3		8	105.74	odd	6
735.2.p.c.374.4		8	7.3	odd	6
735.2.p.c.509.1		8	5.4	even	2
735.2.p.c.509.2		8	21.20	even	2
735.2.p.c.509.3		8	7.6	odd	2
735.2.p.c.509.4		8	15.14	odd	2
1680.2.k.a.209.1		4	140.19	even	6
1680.2.k.a.209.2		4	28.23	odd	6
1680.2.k.a.209.3		4	84.23	even	6
1680.2.k.a.209.4		4	420.299	odd	6
1680.2.k.c.209.1		4	420.359	even	6
1680.2.k.c.209.2		4	84.47	odd	6
1680.2.k.c.209.3		4	28.19	even	6
1680.2.k.c.209.4		4	140.79	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.358719 + 2.20711i) q^{5} +(-1.73205 - 2.44949i) q^{6} +1.73205 q^{8} +(-1.94949 - 2.28024i) q^{9} +(3.62132 + 1.37333i) q^{10} +(2.44949 - 1.41421i) q^{11} +(-1.72474 + 0.158919i) q^{12} +4.00000 q^{13} +(3.73205 + 1.03528i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.44949 + 1.41421i) q^{17} +(-5.10867 + 0.949490i) q^{18} +(1.73205 - 1.41421i) q^{20} -4.89898i q^{22} +(1.73205 - 3.00000i) q^{23} +(1.25529 - 2.72474i) q^{24} +(-4.74264 + 1.58346i) q^{25} +(3.46410 - 6.00000i) q^{26} +(-5.00000 + 1.41421i) q^{27} -5.65685i q^{29} +(4.78497 - 4.70150i) q^{30} +(-8.48528 + 4.89898i) q^{31} +(-2.59808 - 4.50000i) q^{32} +(-0.449490 - 4.87832i) q^{33} +4.89898i q^{34} +(-1.00000 + 2.82843i) q^{36} +(2.89898 - 6.29253i) q^{39} +(0.621320 + 3.82282i) q^{40} +3.46410 q^{41} +4.89898i q^{43} +(-2.44949 - 1.41421i) q^{44} +(4.33341 - 5.12070i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(2.44949 + 1.41421i) q^{47} +(-5.00000 - 7.07107i) q^{48} +(-1.73205 + 8.48528i) q^{50} +(0.449490 + 4.87832i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-2.20881 + 8.72474i) q^{54} +(4.00000 + 4.89898i) q^{55} +(-8.48528 - 4.89898i) q^{58} +(3.46410 + 6.00000i) q^{59} +(-0.969450 - 3.74969i) q^{60} +(-8.48528 - 4.89898i) q^{61} +16.9706i q^{62} +1.00000 q^{64} +(1.43488 + 8.82843i) q^{65} +(-7.70674 - 3.55051i) q^{66} +(-4.24264 + 2.44949i) q^{67} +(2.44949 + 1.41421i) q^{68} +(-3.46410 - 4.89898i) q^{69} +2.82843i q^{71} +(-3.37662 - 3.94949i) q^{72} +(4.00000 + 6.92820i) q^{73} +(-0.946206 + 8.60841i) q^{75} +(-6.92820 - 9.79796i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(10.4539 + 3.96447i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(3.00000 - 5.19615i) q^{82} -2.82843i q^{83} +(-4.00000 - 4.89898i) q^{85} +(7.34847 + 4.24264i) q^{86} +(-8.89898 - 4.09978i) q^{87} +(4.24264 - 2.44949i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-3.92820 - 10.9348i) q^{90} -3.46410 q^{92} +(1.55708 + 16.8990i) q^{93} +(4.24264 - 2.44949i) q^{94} +(-8.96204 + 0.825765i) q^{96} -8.00000 q^{97} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{4} + 4 q^{9} + 12 q^{10} - 4 q^{12} + 32 q^{13} + 16 q^{15} + 20 q^{16} - 4 q^{25} - 40 q^{27} + 12 q^{30} + 16 q^{33} - 8 q^{36} - 16 q^{39} - 12 q^{40} - 16 q^{45} - 24 q^{46} - 40 q^{48}+ \cdots - 64 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^4 + 4 * q^9 + 12 * q^10 - 4 * q^12 + 32 * q^13 + 16 * q^15 + 20 * q^16 - 4 * q^25 - 40 * q^27 + 12 * q^30 + 16 * q^33 - 8 * q^36 - 16 * q^39 - 12 * q^40 - 16 * q^45 - 24 * q^46 - 40 * q^48 - 16 * q^51 - 16 * q^52 + 32 * q^55 - 8 * q^60 + 8 * q^64 + 32 * q^73 - 4 * q^75 - 32 * q^79 + 28 * q^81 + 24 * q^82 - 32 * q^85 - 32 * q^87 + 24 * q^90 - 64 * q^97 - 64 * q^99

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