LMFDB - Embedded newform 900.2.bg.a.61.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(61,900)] 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("900.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 20, 24])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			61.1
Character	$\chi$	$=$	900.61
Dual form			900.2.bg.a.841.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67673 + 0.434241i) q^{3} +(-1.00789 + 1.99604i) q^{5} +(0.516228 - 0.894133i) q^{7} +(2.62287 - 1.45621i) q^{9} +(0.265072 + 2.52199i) q^{11} +(0.517761 - 4.92617i) q^{13} +(0.823198 - 3.78449i) q^{15} +(2.13525 + 6.57162i) q^{17} +(1.23138 + 3.78981i) q^{19} +(-0.477307 + 1.72339i) q^{21} +(3.24634 + 1.44536i) q^{23} +(-2.96832 - 4.02356i) q^{25} +(-3.76550 + 3.58064i) q^{27} +(-1.96071 - 2.17759i) q^{29} +(-6.90780 + 7.67189i) q^{31} +(-1.53961 - 4.11360i) q^{33} +(1.26442 + 1.93160i) q^{35} +(-8.89669 - 6.46382i) q^{37} +(1.27100 + 8.48471i) q^{39} +(0.372162 - 3.54088i) q^{41} +(-1.92102 + 3.32730i) q^{43} +(0.263097 + 6.70304i) q^{45} +(-8.95867 - 9.94962i) q^{47} +(2.96702 + 5.13902i) q^{49} +(-6.43391 - 10.0916i) q^{51} +(-1.62373 + 4.99732i) q^{53} +(-5.30115 - 2.01279i) q^{55} +(-3.71039 - 5.81978i) q^{57} +(-1.58376 + 15.0685i) q^{59} +(1.30272 + 12.3946i) q^{61} +(0.0519501 - 3.09693i) q^{63} +(9.31097 + 5.99850i) q^{65} +(-5.74991 + 6.38592i) q^{67} +(-6.07088 - 1.01380i) q^{69} +(-1.95303 + 6.01082i) q^{71} +(1.95559 - 1.42082i) q^{73} +(6.72429 + 5.45747i) q^{75} +(2.39184 + 1.06491i) q^{77} +(-2.95053 - 3.27689i) q^{79} +(4.75889 - 7.63891i) q^{81} +(7.40698 + 1.57440i) q^{83} +(-15.2693 - 2.36142i) q^{85} +(4.23319 + 2.79981i) q^{87} +(3.64661 - 2.64942i) q^{89} +(-4.13737 - 3.00598i) q^{91} +(8.25109 - 15.8634i) q^{93} +(-8.80569 - 1.36181i) q^{95} +(2.93440 + 3.25898i) q^{97} +(4.36781 + 6.22886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 2 q^{3} - 4 q^{5} - 2 q^{9} + 4 q^{11} + 33 q^{15} - 12 q^{17} + 12 q^{21} - 12 q^{23} - 12 q^{25} + 13 q^{27} + 12 q^{29} + 6 q^{31} + 31 q^{33} + 14 q^{35} - 12 q^{37} + 8 q^{39} + 16 q^{41} + 19 q^{45}+ \cdots - 66 q^{99}+O(q^{100}) $ 240 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 + 4 * q^11 + 33 * q^15 - 12 * q^17 + 12 * q^21 - 12 * q^23 - 12 * q^25 + 13 * q^27 + 12 * q^29 + 6 * q^31 + 31 * q^33 + 14 * q^35 - 12 * q^37 + 8 * q^39 + 16 * q^41 + 19 * q^45 - 19 * q^47 - 120 * q^49 + 2 * q^51 + 48 * q^53 - 18 * q^55 - 54 * q^57 + 9 * q^59 + 43 * q^63 + 37 * q^65 - 9 * q^67 + 40 * q^69 - 2 * q^71 + 70 * q^75 - 40 * q^77 + 12 * q^79 - 2 * q^81 + 22 * q^83 + 12 * q^85 + 101 * q^87 + 22 * q^89 - 66 * q^93 - 16 * q^95 + 30 * q^97 - 66 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−1.67673	+	0.434241i	−0.968062	+	0.250709i
$3$	−1.67673	+	0.434241i	−0.968062	+	0.250709i
$4$		0			0
$5$	−1.00789	+	1.99604i	−0.450741	+	0.892655i
$5$	−1.00789	+	1.99604i	−0.450741	+	0.892655i
$6$		0			0
$7$	0.516228	−	0.894133i	0.195116	−	0.337951i	−0.751823	−	0.659365i	$-0.770825\pi$
$7$	0.516228	−	0.894133i	0.195116	−	0.337951i	0.946939	+	0.321415i	$0.104158\pi$
$8$		0			0
$9$	2.62287	−	1.45621i	0.874290	−	0.485404i
$10$		0			0
$11$	0.265072	+	2.52199i	0.0799222	+	0.760409i	0.958938	+	0.283616i	$0.0915342\pi$
$11$	0.265072	+	2.52199i	0.0799222	+	0.760409i	−0.879016	+	0.476793i	$0.841799\pi$
$12$		0			0
$13$	0.517761	−	4.92617i	0.143601	−	1.36627i	−0.650970	−	0.759103i	$-0.725638\pi$
$13$	0.517761	−	4.92617i	0.143601	−	1.36627i	0.794571	−	0.607171i	$-0.207696\pi$
$14$		0			0
$15$	0.823198	−	3.78449i	0.212549	−	0.977150i
$16$		0			0
$17$	2.13525	+	6.57162i	0.517874	+	1.59385i	0.777991	+	0.628275i	$0.216239\pi$
$17$	2.13525	+	6.57162i	0.517874	+	1.59385i	−0.260118	+	0.965577i	$0.583761\pi$
$18$		0			0
$19$	1.23138	+	3.78981i	0.282499	+	0.869441i	0.987137	+	0.159875i	$0.0511091\pi$
$19$	1.23138	+	3.78981i	0.282499	+	0.869441i	−0.704639	+	0.709566i	$0.748891\pi$
$20$		0			0
$21$	−0.477307	+	1.72339i	−0.104157	+	0.376075i
$22$		0			0
$23$	3.24634	+	1.44536i	0.676909	+	0.301379i	0.716247	−	0.697847i	$-0.245858\pi$
$23$	3.24634	+	1.44536i	0.676909	+	0.301379i	−0.0393383	+	0.999226i	$0.512525\pi$
$24$		0			0
$25$	−2.96832	−	4.02356i	−0.593665	−	0.804712i
$26$		0			0
$27$	−3.76550	+	3.58064i	−0.724672	+	0.689094i
$28$		0			0
$29$	−1.96071	−	2.17759i	−0.364095	−	0.404368i	0.533065	−	0.846074i	$-0.321040\pi$
$29$	−1.96071	−	2.17759i	−0.364095	−	0.404368i	−0.897160	+	0.441706i	$0.854373\pi$
$30$		0			0
$31$	−6.90780	+	7.67189i	−1.24068	+	1.37791i	−0.341765	+	0.939785i	$0.611025\pi$
$31$	−6.90780	+	7.67189i	−1.24068	+	1.37791i	−0.898913	+	0.438127i	$0.855642\pi$
$32$		0			0
$33$	−1.53961	−	4.11360i	−0.268011	−	0.716087i
$34$		0			0
$35$	1.26442	+	1.93160i	0.213727	+	0.326499i
$36$		0			0
$37$	−8.89669	−	6.46382i	−1.46261	−	1.06265i	−0.982674	−	0.185341i	$-0.940661\pi$
$37$	−8.89669	−	6.46382i	−1.46261	−	1.06265i	−0.479933	−	0.877305i	$-0.659339\pi$
$38$		0			0
$39$	1.27100	+	8.48471i	0.203523	+	1.35864i
$40$		0			0
$41$	0.372162	−	3.54088i	0.0581219	−	0.552993i	−0.926252	−	0.376904i	$-0.876989\pi$
$41$	0.372162	−	3.54088i	0.0581219	−	0.552993i	0.984374	−	0.176089i	$-0.0563447\pi$
$42$		0			0
$43$	−1.92102	+	3.32730i	−0.292953	+	0.507409i	−0.974507	−	0.224359i	$-0.927971\pi$
$43$	−1.92102	+	3.32730i	−0.292953	+	0.507409i	0.681554	+	0.731768i	$0.261305\pi$
$44$		0			0
$45$	0.263097	+	6.70304i	0.0392202	+	0.999231i
$46$		0			0
$47$	−8.95867	−	9.94962i	−1.30676	−	1.45130i	−0.813678	−	0.581316i	$-0.802538\pi$
$47$	−8.95867	−	9.94962i	−1.30676	−	1.45130i	−0.493079	−	0.869984i	$-0.664129\pi$
$48$		0			0
$49$	2.96702	+	5.13902i	0.423860	+	0.734146i
$50$		0			0
$51$	−6.43391	−	10.0916i	−0.900928	−	1.41311i
$52$		0			0
$53$	−1.62373	+	4.99732i	−0.223036	+	0.686435i	0.775449	+	0.631410i	$0.217524\pi$
$53$	−1.62373	+	4.99732i	−0.223036	+	0.686435i	−0.998485	+	0.0550242i	$0.982476\pi$
$54$		0			0
$55$	−5.30115	−	2.01279i	−0.714807	−	0.271405i
$56$		0			0
$57$	−3.71039	−	5.81978i	−0.491453	−	0.770849i
$58$		0			0
$59$	−1.58376	+	15.0685i	−0.206188	+	1.96175i	0.0610897	+	0.998132i	$0.480542\pi$
$59$	−1.58376	+	15.0685i	−0.206188	+	1.96175i	−0.267278	+	0.963619i	$0.586124\pi$
$60$		0			0
$61$	1.30272	+	12.3946i	0.166796	+	1.58696i	0.682950	+	0.730465i	$0.260697\pi$
$61$	1.30272	+	12.3946i	0.166796	+	1.58696i	−0.516154	+	0.856496i	$0.672637\pi$
$62$		0			0
$63$	0.0519501	−	3.09693i	0.00654510	−	0.390177i
$64$		0			0
$65$	9.31097	+	5.99850i	1.15488	+	0.744022i
$66$		0			0
$67$	−5.74991	+	6.38592i	−0.702463	+	0.780164i	−0.983766	−	0.179455i	$-0.942567\pi$
$67$	−5.74991	+	6.38592i	−0.702463	+	0.780164i	0.281303	+	0.959619i	$0.409233\pi$
$68$		0			0
$69$	−6.07088	−	1.01380i	−0.730849	−	0.122047i
$70$		0			0
$71$	−1.95303	+	6.01082i	−0.231782	+	0.713353i	0.765750	+	0.643139i	$0.222368\pi$
$71$	−1.95303	+	6.01082i	−0.231782	+	0.713353i	−0.997532	+	0.0702138i	$0.977632\pi$
$72$		0			0
$73$	1.95559	−	1.42082i	0.228885	−	0.166294i	−0.467432	−	0.884029i	$-0.654821\pi$
$73$	1.95559	−	1.42082i	0.228885	−	0.166294i	0.696317	+	0.717734i	$0.254821\pi$
$74$		0			0
$75$	6.72429	+	5.45747i	0.776454	+	0.630174i
$76$		0			0
$77$	2.39184	+	1.06491i	0.272575	+	0.121358i
$78$		0			0
$79$	−2.95053	−	3.27689i	−0.331960	−	0.368679i	0.553939	−	0.832557i	$-0.313124\pi$
$79$	−2.95053	−	3.27689i	−0.331960	−	0.368679i	−0.885899	+	0.463878i	$0.846457\pi$
$80$		0			0
$81$	4.75889	−	7.63891i	0.528765	−	0.848768i
$82$		0			0
$83$	7.40698	+	1.57440i	0.813022	+	0.172813i	0.595617	−	0.803268i	$-0.296908\pi$
$83$	7.40698	+	1.57440i	0.813022	+	0.172813i	0.217405	+	0.976082i	$0.430241\pi$
$84$		0			0
$85$	−15.2693	−	2.36142i	−1.65619	−	0.256132i
$86$		0			0
$87$	4.23319	+	2.79981i	0.453845	+	0.300172i
$88$		0			0
$89$	3.64661	−	2.64942i	0.386540	−	0.280838i	−0.377496	−	0.926011i	$-0.623215\pi$
$89$	3.64661	−	2.64942i	0.386540	−	0.280838i	0.764036	+	0.645173i	$0.223215\pi$
$90$		0			0
$91$	−4.13737	−	3.00598i	−0.433714	−	0.315112i
$92$		0			0
$93$	8.25109	−	15.8634i	0.855598	−	1.64495i
$94$		0			0
$95$	−8.80569	−	1.36181i	−0.903445	−	0.139719i
$96$		0			0
$97$	2.93440	+	3.25898i	0.297943	+	0.330899i	0.873465	−	0.486887i	$-0.161868\pi$
$97$	2.93440	+	3.25898i	0.297943	+	0.330899i	−0.575522	+	0.817786i	$0.695201\pi$
$98$		0			0
$99$	4.36781	+	6.22886i	0.438981	+	0.626024i
$100$		0			0
$101$	−0.0675265	+	0.116959i	−0.00671914	+	0.0116379i	−0.869365	−	0.494170i	$-0.835472\pi$
$101$	−0.0675265	+	0.116959i	−0.00671914	+	0.0116379i	0.862646	+	0.505808i	$0.168805\pi$
$102$		0			0
$103$	17.3968	−	3.69780i	1.71416	−	0.364355i	0.756886	−	0.653547i	$-0.226720\pi$
$103$	17.3968	−	3.69780i	1.71416	−	0.364355i	0.957271	+	0.289191i	$0.0933863\pi$
$104$		0			0
$105$	−2.95888	−	2.68971i	−0.288757	−	0.262489i
$106$		0			0
$107$	−9.54635			−0.922880			−0.461440	−	0.887171i	$-0.652667\pi$
$107$	−9.54635			−0.922880			−0.461440	+	0.887171i	$0.652667\pi$
$108$		0			0
$109$	−8.88276	−	6.45370i	−0.850814	−	0.618152i	0.0745566	−	0.997217i	$-0.476246\pi$
$109$	−8.88276	−	6.45370i	−0.850814	−	0.618152i	−0.925370	+	0.379064i	$0.876246\pi$
$110$		0			0
$111$	17.7242	+	6.97480i	1.68231	+	0.662019i
$112$		0			0
$113$	0.264140	−	2.51312i	0.0248482	−	0.236415i	−0.975048	−	0.221995i	$-0.928743\pi$
$113$	0.264140	−	2.51312i	0.0248482	−	0.236415i	0.999896	−	0.0144199i	$-0.00459015\pi$
$114$		0			0
$115$	−6.15695	+	5.02305i	−0.574138	+	0.468402i
$116$		0			0
$117$	−5.81553	−	13.6747i	−0.537646	−	1.26422i
$118$		0			0
$119$	6.97818	+	1.48326i	0.639689	+	0.135970i
$120$		0			0
$121$	4.46944	−	0.950009i	0.406313	−	0.0863644i
$122$		0			0
$123$	0.913581	+	6.09873i	0.0823749	+	0.549904i
$124$		0			0
$125$	11.0229	−	1.86959i	0.985919	−	0.167221i
$126$		0			0
$127$	2.41188	−	1.75233i	0.214020	−	0.155495i	−0.475611	−	0.879656i	$-0.657773\pi$
$127$	2.41188	−	1.75233i	0.214020	−	0.155495i	0.689631	+	0.724161i	$0.257773\pi$
$128$		0			0
$129$	1.77619	−	6.41319i	0.156384	−	0.564649i
$130$		0			0
$131$	−7.77938	+	8.63988i	−0.679688	+	0.754870i	−0.980006	−	0.198969i	$-0.936241\pi$
$131$	−7.77938	+	8.63988i	−0.679688	+	0.754870i	0.300318	+	0.953839i	$0.402907\pi$
$132$		0			0
$133$	4.02427	+	0.855385i	0.348948	+	0.0741712i
$134$		0			0
$135$	−3.35188	−	11.1250i	−0.288484	−	0.957485i
$136$		0			0
$137$	5.83300	−	2.59702i	0.498347	−	0.221878i	−0.142141	−	0.989846i	$-0.545399\pi$
$137$	5.83300	−	2.59702i	0.498347	−	0.221878i	0.640488	+	0.767968i	$0.278732\pi$
$138$		0			0
$139$	−8.06933	−	3.59270i	−0.684431	−	0.304728i	0.0349048	−	0.999391i	$-0.488887\pi$
$139$	−8.06933	−	3.59270i	−0.684431	−	0.304728i	−0.719336	+	0.694662i	$0.755554\pi$
$140$		0			0
$141$	19.3418	+	12.7926i	1.62888	+	1.07733i
$142$		0			0
$143$	12.5610			1.05040
$144$		0			0
$145$	6.32272	−	1.71888i	0.525073	−	0.142745i
$146$		0			0
$147$	−7.20647	−	7.32837i	−0.594380	−	0.604434i
$148$		0			0
$149$	8.83610	+	15.3046i	0.723881	+	1.25380i	0.959433	+	0.281937i	$0.0909770\pi$
$149$	8.83610	+	15.3046i	0.723881	+	1.25380i	−0.235552	+	0.971862i	$0.575690\pi$
$150$		0			0
$151$	−2.74498	+	4.75445i	−0.223383	+	0.386911i	−0.955833	−	0.293910i	$-0.905044\pi$
$151$	−2.74498	+	4.75445i	−0.223383	+	0.386911i	0.732450	+	0.680821i	$0.238377\pi$
$152$		0			0
$153$	15.1702	+	14.1271i	1.22643	+	1.14211i
$154$		0			0
$155$	−8.35109	−	21.5206i	−0.670776	−	1.72858i
$156$		0			0
$157$	4.05191	+	7.01811i	0.323377	+	0.560106i	0.981183	−	0.193082i	$-0.0618484\pi$
$157$	4.05191	+	7.01811i	0.323377	+	0.560106i	−0.657805	+	0.753188i	$0.728515\pi$
$158$		0			0
$159$	0.552516	−	9.08426i	0.0438174	−	0.720429i
$160$		0			0
$161$	2.96820	−	2.15652i	0.233927	−	0.169958i
$162$		0			0
$163$	−10.7669	−	7.82263i	−0.843331	−	0.612716i	0.0799684	−	0.996797i	$-0.474518\pi$
$163$	−10.7669	−	7.82263i	−0.843331	−	0.612716i	−0.923299	+	0.384082i	$0.874518\pi$
$164$		0			0
$165$	9.76266	+	1.07294i	0.760022	+	0.0835280i
$166$		0			0
$167$	−8.31897	+	9.23915i	−0.643741	+	0.714947i	−0.973390	−	0.229157i	$-0.926403\pi$
$167$	−8.31897	+	9.23915i	−0.643741	+	0.714947i	0.329648	+	0.944104i	$0.393070\pi$
$168$		0			0
$169$	−11.2832	−	2.39831i	−0.867935	−	0.184485i
$170$		0			0
$171$	8.74852	+	8.14701i	0.669016	+	0.623018i
$172$		0			0
$173$	−1.91971	−	18.2648i	−0.145953	−	1.38865i	−0.785008	−	0.619486i	$-0.787341\pi$
$173$	−1.91971	−	18.2648i	−0.145953	−	1.38865i	0.639055	−	0.769161i	$-0.279326\pi$
$174$		0			0
$175$	−5.12993	+	0.577003i	−0.387787	+	0.0436173i
$176$		0			0
$177$	−3.88781	−	25.9536i	−0.292226	−	1.95079i
$178$		0			0
$179$	2.43586	−	7.49682i	0.182065	−	0.560339i	−0.817820	−	0.575474i	$-0.804818\pi$
$179$	2.43586	−	7.49682i	0.182065	−	0.560339i	0.999885	+	0.0151349i	$0.00481778\pi$
$180$		0			0
$181$	−5.48395	−	16.8779i	−0.407619	−	1.25452i	−0.918689	−	0.394982i	$-0.870751\pi$
$181$	−5.48395	−	16.8779i	−0.407619	−	1.25452i	0.511070	−	0.859539i	$-0.329249\pi$
$182$		0			0
$183$	−7.56654	−	20.2167i	−0.559335	−	1.49446i
$184$		0			0
$185$	21.8689	−	11.2433i	1.60783	−	0.826625i
$186$		0			0
$187$	−16.0076	+	7.12703i	−1.17059	+	0.521180i
$188$		0			0
$189$	1.25771	+	5.21529i	0.0914849	+	0.379357i
$190$		0			0
$191$	−1.19632	+	0.532635i	−0.0865625	+	0.0385401i	−0.449561	−	0.893250i	$-0.648420\pi$
$191$	−1.19632	+	0.532635i	−0.0865625	+	0.0385401i	0.362999	+	0.931790i	$0.381753\pi$
$192$		0			0
$193$	−9.11434	−	15.7865i	−0.656064	−	1.13634i	−0.981626	−	0.190816i	$-0.938887\pi$
$193$	−9.11434	−	15.7865i	−0.656064	−	1.13634i	0.325561	−	0.945521i	$-0.394447\pi$
$194$		0			0
$195$	−18.2168	−	6.01467i	−1.30453	−	0.430720i
$196$		0			0
$197$	−7.41217	+	22.8123i	−0.528095	+	1.62531i	0.230017	+	0.973187i	$0.426122\pi$
$197$	−7.41217	+	22.8123i	−0.528095	+	1.62531i	−0.758112	+	0.652124i	$0.773878\pi$
$198$		0			0
$199$	7.94265			0.563040			0.281520	−	0.959555i	$-0.409161\pi$
$199$	7.94265			0.563040			0.281520	+	0.959555i	$0.409161\pi$
$200$		0			0
$201$	6.86803	−	13.2043i	0.484434	−	0.931361i
$202$		0			0
$203$	−2.95923	+	0.629003i	−0.207697	+	0.0441474i
$204$		0			0
$205$	6.69264	+	4.31166i	0.467434	+	0.301140i
$206$		0			0
$207$	10.6195	−	0.936363i	0.738105	−	0.0650818i
$208$		0			0
$209$	−9.23146	+	4.11011i	−0.638553	+	0.284302i
$210$		0			0
$211$	20.9570	+	9.33067i	1.44274	+	0.642350i	0.970933	−	0.239351i	$-0.0769348\pi$
$211$	20.9570	+	9.33067i	1.44274	+	0.642350i	0.471808	+	0.881701i	$0.343601\pi$
$212$		0			0
$213$	0.664571	−	10.9266i	0.0455357	−	0.748680i
$214$		0			0
$215$	−4.70525	−	7.18797i	−0.320895	−	0.490216i
$216$		0			0
$217$	3.29369	+	10.1369i	0.223590	+	0.688141i
$218$		0			0
$219$	−2.66203	+	3.23153i	−0.179883	+	0.218367i
$220$		0			0
$221$	33.4785	−	7.11607i	2.25201	−	0.478678i
$222$		0			0
$223$	−0.692154	−	6.58541i	−0.0463501	−	0.440992i	−0.992946	−	0.118569i	$-0.962169\pi$
$223$	−0.692154	−	6.58541i	−0.0463501	−	0.440992i	0.946596	−	0.322423i	$-0.104497\pi$
$224$		0			0
$225$	−13.6447	−	6.23076i	−0.909646	−	0.415384i
$226$		0			0
$227$	0.947851	+	9.01820i	0.0629111	+	0.598559i	0.979878	+	0.199596i	$0.0639630\pi$
$227$	0.947851	+	9.01820i	0.0629111	+	0.598559i	−0.916967	+	0.398963i	$0.869370\pi$
$228$		0			0
$229$	9.75075	−	2.07259i	0.644348	−	0.136960i	0.125864	−	0.992048i	$-0.459830\pi$
$229$	9.75075	−	2.07259i	0.644348	−	0.136960i	0.518484	+	0.855087i	$0.326497\pi$
$230$		0			0
$231$	−4.47290	−	0.746943i	−0.294295	−	0.0491452i
$232$		0			0
$233$	3.02332	+	9.30481i	0.198064	+	0.609578i	0.999927	+	0.0120706i	$0.00384228\pi$
$233$	3.02332	+	9.30481i	0.198064	+	0.609578i	−0.801863	+	0.597508i	$0.796158\pi$
$234$		0			0
$235$	28.8891	−	7.85375i	1.88452	−	0.512322i
$236$		0			0
$237$	6.37021	+	4.21323i	0.413789	+	0.273679i
$238$		0			0
$239$	21.4560	+	9.55281i	1.38787	+	0.617920i	0.958470	−	0.285194i	$-0.0920582\pi$
$239$	21.4560	+	9.55281i	1.38787	+	0.617920i	0.429401	+	0.903114i	$0.358725\pi$
$240$		0			0
$241$	−7.81553	+	3.47970i	−0.503443	+	0.224147i	−0.642713	−	0.766107i	$-0.722191\pi$
$241$	−7.81553	+	3.47970i	−0.503443	+	0.224147i	0.139270	+	0.990254i	$0.455524\pi$
$242$		0			0
$243$	−4.66225	+	14.8749i	−0.299084	+	0.954227i
$244$		0			0
$245$	−13.2481	+	0.742716i	−0.846390	+	0.0474504i
$246$		0			0
$247$	19.3068	−	4.10379i	1.22846	−	0.261118i
$248$		0			0
$249$	−13.1032	+	0.576563i	−0.830382	+	0.0365382i
$250$		0			0
$251$	−8.87229			−0.560014			−0.280007	−	0.959998i	$-0.590337\pi$
$251$	−8.87229			−0.560014			−0.280007	+	0.959998i	$0.590337\pi$
$252$		0			0
$253$	−2.78468	+	8.57037i	−0.175072	+	0.538815i
$254$		0			0
$255$	26.6279	−	2.67108i	1.66751	−	0.167270i
$256$		0			0
$257$	1.81236	+	3.13910i	0.113052	+	0.195812i	0.916999	−	0.398889i	$-0.130604\pi$
$257$	1.81236	+	3.13910i	0.113052	+	0.195812i	−0.803947	+	0.594700i	$0.797271\pi$
$258$		0			0
$259$	−10.3722	+	4.61802i	−0.644500	+	0.286950i
$260$		0			0
$261$	−8.31372	−	2.85632i	−0.514606	−	0.176802i
$262$		0			0
$263$	4.32082	−	1.92375i	0.266433	−	0.118624i	−0.269172	−	0.963092i	$-0.586750\pi$
$263$	4.32082	−	1.92375i	0.266433	−	0.118624i	0.535605	+	0.844468i	$0.320083\pi$
$264$		0			0
$265$	−8.33830	−	8.27775i	−0.512217	−	0.508498i
$266$		0			0
$267$	−4.96391	+	6.02588i	−0.303786	+	0.368778i
$268$		0			0
$269$	6.55220	+	20.1656i	0.399495	+	1.22952i	0.925406	+	0.378978i	$0.123725\pi$
$269$	6.55220	+	20.1656i	0.399495	+	1.22952i	−0.525911	+	0.850540i	$0.676275\pi$
$270$		0			0
$271$	−0.798540	+	2.45765i	−0.0485079	+	0.149292i	−0.972377	−	0.233418i	$-0.925009\pi$
$271$	−0.798540	+	2.45765i	−0.0485079	+	0.149292i	0.923869	+	0.382710i	$0.125009\pi$
$272$		0			0
$273$	8.24258	+	3.24360i	0.498864	+	0.196312i
$274$		0			0
$275$	9.36057	−	8.55263i	0.564464	−	0.515743i
$276$		0			0
$277$	−2.01328	−	19.1551i	−0.120966	−	1.15092i	−0.871607	−	0.490206i	$-0.836921\pi$
$277$	−2.01328	−	19.1551i	−0.120966	−	1.15092i	0.750640	−	0.660711i	$-0.229745\pi$
$278$		0			0
$279$	−6.94635	+	30.1816i	−0.415867	+	1.80693i
$280$		0			0
$281$	3.53990	+	0.752429i	0.211173	+	0.0448862i	0.312283	−	0.949989i	$-0.398906\pi$
$281$	3.53990	+	0.752429i	0.211173	+	0.0448862i	−0.101110	+	0.994875i	$0.532240\pi$
$282$		0			0
$283$	−0.295108	+	0.327751i	−0.0175424	+	0.0194828i	−0.751852	−	0.659332i	$-0.770839\pi$
$283$	−0.295108	+	0.327751i	−0.0175424	+	0.0194828i	0.734310	+	0.678815i	$0.237506\pi$
$284$		0			0
$285$	15.3561	−	1.54039i	0.909620	−	0.0912450i
$286$		0			0
$287$	−2.97390	−	2.16067i	−0.175544	−	0.127540i
$288$		0			0
$289$	−24.8736	+	18.0717i	−1.46315	+	1.06304i
$290$		0			0
$291$	−6.33539	−	4.19020i	−0.371387	−	0.245634i
$292$		0			0
$293$	11.2936	+	19.5611i	0.659780	+	1.14277i	0.980672	+	0.195657i	$0.0626839\pi$
$293$	11.2936	+	19.5611i	0.659780	+	1.14277i	−0.320892	+	0.947116i	$0.603983\pi$
$294$		0			0
$295$	−28.4810	−	18.3486i	−1.65823	−	1.06830i
$296$		0			0
$297$	−10.0285	−	8.54745i	−0.581911	−	0.495973i
$298$		0			0
$299$	8.80094	−	15.2437i	0.508971	−	0.881564i
$300$		0			0
$301$	1.98337	+	3.43530i	0.114319	+	0.198007i
$302$		0			0
$303$	0.0624354	−	0.225432i	0.00358682	−	0.0129508i
$304$		0			0
$305$	−26.0530	−	9.89205i	−1.49179	−	0.566417i
$306$		0			0
$307$	12.4948			0.713114			0.356557	−	0.934274i	$-0.383951\pi$
$307$	12.4948			0.713114			0.356557	+	0.934274i	$0.383951\pi$
$308$		0			0
$309$	−27.5641	+	13.7546i	−1.56806	+	0.782474i
$310$		0			0
$311$	0.570474	+	0.253991i	0.0323486	+	0.0144025i	0.422847	−	0.906201i	$-0.361031\pi$
$311$	0.570474	+	0.253991i	0.0323486	+	0.0144025i	−0.390499	+	0.920604i	$0.627697\pi$
$312$		0			0
$313$	24.3683	−	10.8495i	1.37738	−	0.613248i	0.421450	−	0.906852i	$-0.361521\pi$
$313$	24.3683	−	10.8495i	1.37738	−	0.613248i	0.955927	+	0.293604i	$0.0948546\pi$
$314$		0			0
$315$	6.12923	+	3.22506i	0.345343	+	0.181711i
$316$		0			0
$317$	−26.5870	−	5.65124i	−1.49327	−	0.317405i	−0.612321	−	0.790610i	$-0.709764\pi$
$317$	−26.5870	−	5.65124i	−1.49327	−	0.317405i	−0.880953	+	0.473204i	$0.843097\pi$
$318$		0			0
$319$	4.97213	−	5.52211i	0.278386	−	0.309179i
$320$		0			0
$321$	16.0067	−	4.14542i	0.893406	−	0.231375i
$322$		0			0
$323$	−22.2759	+	16.1844i	−1.23946	+	0.900522i
$324$		0			0
$325$	−21.3576	+	12.5392i	−1.18471	+	0.695551i
$326$		0			0
$327$	17.6965	+	6.96388i	0.978617	+	0.385103i
$328$		0			0
$329$	−13.5210	+	2.87398i	−0.745437	+	0.158448i
$330$		0			0
$331$	15.5228	+	3.29948i	0.853212	+	0.181356i	0.613702	−	0.789538i	$-0.289680\pi$
$331$	15.5228	+	3.29948i	0.853212	+	0.181356i	0.239510	+	0.970894i	$0.423013\pi$
$332$		0			0
$333$	−32.7476	−	3.99829i	−1.79456	−	0.219105i
$334$		0			0
$335$	−6.95127	−	17.9133i	−0.379788	−	0.978709i
$336$		0			0
$337$	0.522482	−	4.97108i	0.0284614	−	0.270792i	−0.971032	−	0.238951i	$-0.923196\pi$
$337$	0.522482	−	4.97108i	0.0284614	−	0.270792i	0.999493	−	0.0318408i	$-0.0101369\pi$
$338$		0			0
$339$	0.648409	+	4.32854i	0.0352168	+	0.235094i
$340$		0			0
$341$	−21.1795	−	15.3878i	−1.14694	−	0.833297i
$342$		0			0
$343$	13.3538			0.721039
$344$		0			0
$345$	8.14234	−	11.0959i	0.438369	−	0.597384i
$346$		0			0
$347$	−7.30276	+	1.55225i	−0.392033	+	0.0833291i	−0.399711	−	0.916641i	$-0.630889\pi$
$347$	−7.30276	+	1.55225i	−0.392033	+	0.0833291i	0.00767789	+	0.999971i	$0.497556\pi$
$348$		0			0
$349$	17.0088	−	29.4601i	0.910461	−	1.57697i	0.0970477	−	0.995280i	$-0.469060\pi$
$349$	17.0088	−	29.4601i	0.910461	−	1.57697i	0.813414	−	0.581686i	$-0.197607\pi$
$350$		0			0
$351$	15.6892	+	20.4034i	0.837428	+	1.08905i
$352$		0			0
$353$	15.8791	+	17.6355i	0.845157	+	0.938642i	0.998775	−	0.0494880i	$-0.0157590\pi$
$353$	15.8791	+	17.6355i	0.845157	+	0.938642i	−0.153617	+	0.988130i	$0.549092\pi$
$354$		0			0
$355$	−10.0294	−	9.95655i	−0.532304	−	0.528439i
$356$		0			0
$357$	−12.3446	+	0.543185i	−0.653347	+	0.0287484i
$358$		0			0
$359$	5.80041	+	4.21424i	0.306134	+	0.222419i	0.730236	−	0.683195i	$-0.239410\pi$
$359$	5.80041	+	4.21424i	0.306134	+	0.222419i	−0.424102	+	0.905614i	$0.639410\pi$
$360$		0			0
$361$	2.52499	−	1.83451i	0.132894	−	0.0965532i
$362$		0			0
$363$	−7.08153	+	3.53373i	−0.371684	+	0.185473i
$364$		0			0
$365$	0.864993	+	5.33546i	0.0452758	+	0.279271i
$366$		0			0
$367$	−1.02096	−	0.217012i	−0.0532938	−	0.0113279i	0.181188	−	0.983449i	$-0.442006\pi$
$367$	−1.02096	−	0.217012i	−0.0532938	−	0.0113279i	−0.234481	+	0.972121i	$0.575339\pi$
$368$		0			0
$369$	−4.18015	−	9.82922i	−0.217610	−	0.511689i
$370$		0			0
$371$	3.63006	+	4.03159i	0.188463	+	0.209309i
$372$		0			0
$373$	−6.65500	−	2.96300i	−0.344583	−	0.153418i	0.227146	−	0.973861i	$-0.427061\pi$
$373$	−6.65500	−	2.96300i	−0.344583	−	0.153418i	−0.571729	+	0.820442i	$0.693727\pi$
$374$		0			0
$375$	−17.6706	+	7.92140i	−0.912508	+	0.409059i
$376$		0			0
$377$	−11.7424	+	8.53132i	−0.604762	+	0.439385i
$378$		0			0
$379$	2.43513	−	7.49455i	0.125084	−	0.384969i	−0.868832	−	0.495106i	$-0.835129\pi$
$379$	2.43513	−	7.49455i	0.125084	−	0.384969i	0.993916	+	0.110137i	$0.0351291\pi$
$380$		0			0
$381$	−3.28315	+	3.98554i	−0.168201	+	0.204185i
$382$		0			0
$383$	−5.79208	+	6.43276i	−0.295962	+	0.328699i	−0.872725	−	0.488213i	$-0.837649\pi$
$383$	−5.79208	+	6.43276i	−0.295962	+	0.328699i	0.576763	+	0.816912i	$0.304316\pi$
$384$		0			0
$385$	−4.53631	+	3.70088i	−0.231192	+	0.188614i
$386$		0			0
$387$	−0.193320	+	11.5245i	−0.00982700	+	0.585823i
$388$		0			0
$389$	0.348118	+	3.31213i	0.0176503	+	0.167931i	0.999796	−	0.0201895i	$-0.00642696\pi$
$389$	0.348118	+	3.31213i	0.0176503	+	0.167931i	−0.982146	+	0.188121i	$0.939760\pi$
$390$		0			0
$391$	−2.56664	+	24.4199i	−0.129800	+	1.23497i
$392$		0			0
$393$	9.29216	−	17.8649i	0.468727	−	0.901165i
$394$		0			0
$395$	9.51459	−	2.58662i	0.478731	−	0.130147i
$396$		0			0
$397$	−4.45570	+	13.7132i	−0.223625	+	0.688247i	0.774803	+	0.632203i	$0.217849\pi$
$397$	−4.45570	+	13.7132i	−0.223625	+	0.688247i	−0.998428	+	0.0560447i	$0.982151\pi$
$398$		0			0
$399$	−7.11907	+	0.313251i	−0.356399	+	0.0156822i
$400$		0			0
$401$	−5.84707	−	10.1274i	−0.291989	−	0.505739i	0.682291	−	0.731080i	$-0.260984\pi$
$401$	−5.84707	−	10.1274i	−0.291989	−	0.505739i	−0.974280	+	0.225341i	$0.927650\pi$
$402$		0			0
$403$	34.2165	+	38.0012i	1.70444	+	1.89298i
$404$		0			0
$405$	10.4511	+	17.1981i	0.519321	+	0.854579i
$406$		0			0
$407$	13.9435	−	24.1508i	0.691151	−	1.19711i
$408$		0			0
$409$	−1.92914	+	18.3545i	−0.0953897	+	0.907572i	0.837264	+	0.546799i	$0.184154\pi$
$409$	−1.92914	+	18.3545i	−0.0953897	+	0.907572i	−0.932654	+	0.360773i	$0.882513\pi$
$410$		0			0
$411$	−8.65265	+	6.88744i	−0.426804	+	0.339732i
$412$		0			0
$413$	12.6557	+	9.19488i	0.622745	+	0.452450i
$414$		0			0
$415$	−10.6080	+	13.1978i	−0.520725	+	0.647854i
$416$		0			0
$417$	15.0902	+	2.51996i	0.738971	+	0.123403i
$418$		0			0
$419$	16.2215	−	18.0158i	0.792470	−	0.880127i	−0.202604	−	0.979261i	$-0.564940\pi$
$419$	16.2215	−	18.0158i	0.792470	−	0.880127i	0.995074	+	0.0991336i	$0.0316071\pi$
$420$		0			0
$421$	3.02600	+	3.36071i	0.147478	+	0.163791i	0.812358	−	0.583160i	$-0.198184\pi$
$421$	3.02600	+	3.36071i	0.147478	+	0.163791i	−0.664879	+	0.746951i	$0.731517\pi$
$422$		0			0
$423$	−37.9862	−	13.0508i	−1.84695	−	0.634552i
$424$		0			0
$425$	20.1032	−	28.0980i	0.975149	−	1.36295i
$426$		0			0
$427$	11.7549	+	5.23362i	0.568859	+	0.253272i
$428$		0			0
$429$	−21.0615	+	5.45451i	−1.01686	+	0.263346i
$430$		0			0
$431$	−9.29000	−	28.5917i	−0.447483	−	1.37721i	−0.879737	−	0.475460i	$-0.842282\pi$
$431$	−9.29000	−	28.5917i	−0.447483	−	1.37721i	0.432254	−	0.901752i	$-0.357718\pi$
$432$		0			0
$433$	0.782062	+	2.40694i	0.0375835	+	0.115670i	0.968088	−	0.250610i	$-0.0806312\pi$
$433$	0.782062	+	2.40694i	0.0375835	+	0.115670i	−0.930505	+	0.366280i	$0.880631\pi$
$434$		0			0
$435$	−9.85511	+	5.62769i	−0.472516	+	0.269827i
$436$		0			0
$437$	−1.48016	+	14.0828i	−0.0708058	+	0.673672i
$438$		0			0
$439$	−2.04084	−	19.4173i	−0.0974041	−	0.926738i	−0.928681	−	0.370879i	$-0.879056\pi$
$439$	−2.04084	−	19.4173i	−0.0974041	−	0.926738i	0.831277	−	0.555858i	$-0.187610\pi$
$440$		0			0
$441$	15.2656	+	9.15838i	0.726934	+	0.436113i
$442$		0			0
$443$	1.72679	−	2.99088i	0.0820421	−	0.142101i	−0.822085	−	0.569365i	$-0.807189\pi$
$443$	1.72679	−	2.99088i	0.0820421	−	0.142101i	0.904127	+	0.427264i	$0.140522\pi$
$444$		0			0
$445$	1.61296	+	9.94909i	0.0764617	+	0.471632i
$446$		0			0
$447$	−21.4617	−	21.8247i	−1.01510	−	1.03227i
$448$		0			0
$449$	−9.51272			−0.448933			−0.224467	−	0.974482i	$-0.572064\pi$
$449$	−9.51272			−0.448933			−0.224467	+	0.974482i	$0.572064\pi$
$450$		0			0
$451$	9.02873			0.425146
$452$		0			0
$453$	2.53803	−	9.16392i	0.119247	−	0.430559i
$454$		0			0
$455$	10.1700	−	5.22866i	0.476779	−	0.245123i
$456$		0			0
$457$	−19.9378	+	34.5332i	−0.932650	+	1.61540i	−0.153878	+	0.988090i	$0.549176\pi$
$457$	−19.9378	+	34.5332i	−0.932650	+	1.61540i	−0.778772	+	0.627307i	$0.784157\pi$
$458$		0			0
$459$	−31.5709	−	17.0999i	−1.47360	−	0.798155i
$460$		0			0
$461$	−0.166682	−	1.58587i	−0.00776314	−	0.0738613i	0.989954	−	0.141387i	$-0.0451562\pi$
$461$	−0.166682	−	1.58587i	−0.00776314	−	0.0738613i	−0.997718	+	0.0675257i	$0.978490\pi$
$462$		0			0
$463$	2.10939	−	20.0695i	0.0980317	−	0.932710i	−0.829384	−	0.558678i	$-0.811309\pi$
$463$	2.10939	−	20.0695i	0.0980317	−	0.932710i	0.927416	−	0.374031i	$-0.122025\pi$
$464$		0			0
$465$	23.3477	+	32.4580i	1.08272	+	1.50520i
$466$		0			0
$467$	3.15387	+	9.70663i	0.145944	+	0.449169i	0.997131	−	0.0756929i	$-0.0241169\pi$
$467$	3.15387	+	9.70663i	0.145944	+	0.449169i	−0.851187	+	0.524862i	$0.824117\pi$
$468$		0			0
$469$	2.74160	+	8.43777i	0.126595	+	0.389620i
$470$		0			0
$471$	−9.84152	−	10.0080i	−0.453473	−	0.461144i
$472$		0			0
$473$	−8.90064	−	3.96282i	−0.409252	−	0.182211i
$474$		0			0
$475$	11.5934	−	16.2039i	0.531941	−	0.743487i
$476$		0			0
$477$	3.01834	+	15.4718i	0.138200	+	0.708405i
$478$		0			0
$479$	−16.8091	−	18.6684i	−0.768030	−	0.852983i	0.224565	−	0.974459i	$-0.427904\pi$
$479$	−16.8091	−	18.6684i	−0.768030	−	0.852983i	−0.992594	+	0.121476i	$0.961237\pi$
$480$		0			0
$481$	−36.4483	+	40.4799i	−1.66190	+	1.84572i
$482$		0			0
$483$	−4.04043	+	4.90483i	−0.183846	+	0.223178i
$484$		0			0
$485$	−9.46259	+	2.57248i	−0.429674	+	0.116810i
$486$		0			0
$487$	18.2553	+	13.2632i	0.827225	+	0.601014i	0.918773	−	0.394787i	$-0.129181\pi$
$487$	18.2553	+	13.2632i	0.827225	+	0.601014i	−0.0915479	+	0.995801i	$0.529181\pi$
$488$		0			0
$489$	21.4502	+	8.44102i	0.970010	+	0.381716i
$490$		0			0
$491$	2.30514	−	21.9320i	0.104030	−	0.989775i	−0.810632	−	0.585555i	$-0.800876\pi$
$491$	2.30514	−	21.9320i	0.104030	−	0.989775i	0.914662	−	0.404220i	$-0.132457\pi$
$492$		0			0
$493$	10.1237	−	17.5347i	0.455948	−	0.789724i
$494$		0			0
$495$	−16.8353	+	2.44032i	−0.756690	+	0.109684i
$496$		0			0
$497$	4.36626	+	4.84922i	0.195854	+	0.217517i
$498$		0			0
$499$	−10.0199	−	17.3550i	−0.448552	−	0.776915i	0.549740	−	0.835336i	$-0.314727\pi$
$499$	−10.0199	−	17.3550i	−0.448552	−	0.776915i	−0.998292	+	0.0584210i	$0.981393\pi$
$500$		0			0
$501$	9.93667	−	19.1040i	0.443938	−	0.853505i
$502$		0			0
$503$	−8.52785	+	26.2460i	−0.380238	+	1.17025i	0.559638	+	0.828737i	$0.310940\pi$
$503$	−8.52785	+	26.2460i	−0.380238	+	1.17025i	−0.939876	+	0.341515i	$0.889060\pi$
$504$		0			0
$505$	−0.165396	−	0.252667i	−0.00736003	−	0.0112435i
$506$		0			0
$507$	19.9603	−	0.878286i	0.886468	−	0.0390061i
$508$		0			0
$509$	1.79352	−	17.0642i	0.0794964	−	0.756358i	−0.880064	−	0.474855i	$-0.842500\pi$
$509$	1.79352	−	17.0642i	0.0794964	−	0.756358i	0.959560	−	0.281503i	$-0.0908329\pi$
$510$		0			0
$511$	−0.260871	−	2.48203i	−0.0115403	−	0.109798i
$512$		0			0
$513$	−18.2067	−	9.86140i	−0.803846	−	0.435391i
$514$		0			0
$515$	−10.1531	+	38.4516i	−0.447398	+	1.69438i
$516$		0			0
$517$	22.7182	−	25.2311i	0.999144	−	1.10966i
$518$		0			0
$519$	11.1502	+	29.7916i	0.489438	+	1.30771i
$520$		0			0
$521$	−0.601691	+	1.85182i	−0.0263606	+	0.0811295i	−0.963371	−	0.268171i	$-0.913581\pi$
$521$	−0.601691	+	1.85182i	−0.0263606	+	0.0811295i	0.937011	+	0.349301i	$0.113581\pi$
$522$		0			0
$523$	9.12129	−	6.62701i	0.398846	−	0.289779i	−0.370225	−	0.928942i	$-0.620719\pi$
$523$	9.12129	−	6.62701i	0.398846	−	0.289779i	0.769071	+	0.639164i	$0.220719\pi$
$524$		0			0
$525$	8.35097	−	3.19511i	0.364466	−	0.139446i
$526$		0			0
$527$	−65.1666	−	29.0141i	−2.83870	−	1.26387i
$528$		0			0
$529$	−6.94035	−	7.70804i	−0.301754	−	0.335132i
$530$		0			0
$531$	17.7889	+	41.8290i	0.771974	+	1.81522i
$532$		0			0
$533$	−17.2503	−	3.66667i	−0.747194	−	0.158821i
$534$		0			0
$535$	9.62165	−	19.0549i	0.415980	−	0.823814i
$536$		0			0
$537$	−0.828867	+	13.6279i	−0.0357683	+	0.588088i
$538$		0			0
$539$	−12.1741	+	8.84501i	−0.524376	+	0.380981i
$540$		0			0
$541$	18.5958	+	13.5107i	0.799498	+	0.580869i	0.910767	−	0.412921i	$-0.135492\pi$
$541$	18.5958	+	13.5107i	0.799498	+	0.580869i	−0.111269	+	0.993790i	$0.535492\pi$
$542$		0			0
$543$	16.5242	+	25.9183i	0.709121	+	1.11226i
$544$		0			0
$545$	21.8346	−	11.2257i	0.935293	−	0.480856i
$546$		0			0
$547$	15.2414	+	16.9273i	0.651676	+	0.723760i	0.974920	−	0.222556i	$-0.0714400\pi$
$547$	15.2414	+	16.9273i	0.651676	+	0.723760i	−0.323244	+	0.946316i	$0.604773\pi$
$548$		0			0
$549$	21.4660	+	30.6123i	0.916146	+	1.30650i
$550$		0			0
$551$	5.83826	−	10.1122i	0.248718	−	0.430792i
$552$		0			0
$553$	−4.45312	+	0.946540i	−0.189366	+	0.0402510i
$554$		0			0
$555$	−31.7860	+	28.3484i	−1.34924	+	1.20332i
$556$		0			0
$557$	−26.3367			−1.11592			−0.557962	−	0.829867i	$-0.688416\pi$
$557$	−26.3367			−1.11592			−0.557962	+	0.829867i	$0.688416\pi$
$558$		0			0
$559$	15.3962	+	11.1860i	0.651191	+	0.473118i
$560$		0			0
$561$	23.7456	−	18.9013i	1.00254	−	0.798013i
$562$		0			0
$563$	−1.23170	+	11.7189i	−0.0519102	+	0.493892i	0.937420	+	0.348201i	$0.113207\pi$
$563$	−1.23170	+	11.7189i	−0.0519102	+	0.493892i	−0.989330	+	0.145691i	$0.953459\pi$
$564$		0			0
$565$	4.75006	+	3.06018i	0.199837	+	0.128743i
$566$		0			0
$567$	−4.37354	−	8.19850i	−0.183671	−	0.344305i
$568$		0			0
$569$	−23.2266	−	4.93696i	−0.973708	−	0.206968i	−0.306526	−	0.951862i	$-0.599166\pi$
$569$	−23.2266	−	4.93696i	−0.973708	−	0.206968i	−0.667182	+	0.744894i	$0.732500\pi$
$570$		0			0
$571$	9.56343	−	2.03277i	0.400217	−	0.0850687i	−0.00340593	−	0.999994i	$-0.501084\pi$
$571$	9.56343	−	2.03277i	0.400217	−	0.0850687i	0.403623	+	0.914925i	$0.367751\pi$
$572$		0			0
$573$	1.77461	−	1.41258i	0.0741355	−	0.0590112i
$574$		0			0
$575$	−3.82068	−	17.3522i	−0.159333	−	0.723635i
$576$		0			0
$577$	−22.3174	+	16.2145i	−0.929085	+	0.675019i	−0.945769	−	0.324841i	$-0.894689\pi$
$577$	−22.3174	+	16.2145i	−0.929085	+	0.675019i	0.0166839	+	0.999861i	$0.494689\pi$
$578$		0			0
$579$	22.1375	+	22.5119i	0.920001	+	0.935564i
$580$		0			0
$581$	5.23142	−	5.81008i	0.217036	−	0.241043i
$582$		0			0
$583$	−13.0336	−	2.77038i	−0.539797	−	0.114737i
$584$		0			0
$585$	33.1566	+	2.17451i	1.37085	+	0.0899051i
$586$		0			0
$587$	6.99043	−	3.11234i	0.288526	−	0.128460i	−0.257370	−	0.966313i	$-0.582856\pi$
$587$	6.99043	−	3.11234i	0.288526	−	0.128460i	0.545896	+	0.837853i	$0.316189\pi$
$588$		0			0
$589$	−37.5811	−	16.7322i	−1.54850	−	0.689438i
$590$		0			0
$591$	2.52219	−	41.4689i	0.103749	−	1.70580i
$592$		0			0
$593$	23.4962			0.964873			0.482436	−	0.875931i	$-0.339752\pi$
$593$	23.4962			0.964873			0.482436	+	0.875931i	$0.339752\pi$
$594$		0			0
$595$	−9.99386	+	12.4337i	−0.409708	+	0.509734i
$596$		0			0
$597$	−13.3177	+	3.44903i	−0.545058	+	0.141159i
$598$		0			0
$599$	10.4090	+	18.0289i	0.425300	+	0.736641i	0.996448	−	0.0842056i	$-0.0268353\pi$
$599$	10.4090	+	18.0289i	0.425300	+	0.736641i	−0.571148	+	0.820847i	$0.693502\pi$
$600$		0			0
$601$	0.539117	−	0.933777i	0.0219910	−	0.0380896i	−0.854820	−	0.518924i	$-0.826333\pi$
$601$	0.539117	−	0.933777i	0.0219910	−	0.0380896i	0.876811	+	0.480834i	$0.159666\pi$
$602$		0			0
$603$	−5.78199	+	25.1225i	−0.235461	+	1.02307i
$604$		0			0
$605$	−2.60844	+	9.87867i	−0.106048	+	0.401625i
$606$		0			0
$607$	1.86892	+	3.23706i	0.0758570	+	0.131388i	0.901459	−	0.432865i	$-0.142497\pi$
$607$	1.86892	+	3.23706i	0.0758570	+	0.131388i	−0.825602	+	0.564253i	$0.809164\pi$
$608$		0			0
$609$	4.68870	−	2.33969i	0.189996	−	0.0948090i
$610$		0			0
$611$	−53.6520	+	38.9804i	−2.17053	+	1.57698i
$612$		0			0
$613$	4.53158	+	3.29239i	0.183029	+	0.132978i	0.675527	−	0.737335i	$-0.263916\pi$
$613$	4.53158	+	3.29239i	0.183029	+	0.132978i	−0.492498	+	0.870314i	$0.663916\pi$
$614$		0			0
$615$	−13.0941	−	4.32329i	−0.528004	−	0.174332i
$616$		0			0
$617$	19.1113	−	21.2252i	0.769391	−	0.854495i	−0.223354	−	0.974737i	$-0.571701\pi$
$617$	19.1113	−	21.2252i	0.769391	−	0.854495i	0.992745	+	0.120243i	$0.0383672\pi$
$618$		0			0
$619$	44.7860	+	9.51956i	1.80010	+	0.382623i	0.981458	−	0.191678i	$-0.0613929\pi$
$619$	44.7860	+	9.51956i	1.80010	+	0.382623i	0.818644	+	0.574301i	$0.194726\pi$
$620$		0			0
$621$	−17.3994	+	6.18145i	−0.698215	+	0.248053i
$622$		0			0
$623$	−0.486450	−	4.62826i	−0.0194892	−	0.185427i
$624$		0			0
$625$	−7.37810	+	23.8865i	−0.295124	+	0.955459i
$626$		0			0
$627$	13.6939	−	10.9002i	0.546882	−	0.435314i
$628$		0			0
$629$	23.4811	−	72.2675i	0.936255	−	2.88150i
$630$		0			0
$631$	−3.04564	−	9.37351i	−0.121245	−	0.373153i	0.871953	−	0.489589i	$-0.162853\pi$
$631$	−3.04564	−	9.37351i	−0.121245	−	0.373153i	−0.993198	+	0.116436i	$0.962853\pi$
$632$		0			0
$633$	−39.1911	−	6.54464i	−1.55771	−	0.260126i
$634$		0			0
$635$	1.06682	+	6.58036i	0.0423354	+	0.261134i
$636$		0			0
$637$	26.8519	−	11.9552i	1.06391	−	0.473684i
$638$		0			0
$639$	3.63048	+	18.6096i	0.143620	+	0.736185i
$640$		0			0
$641$	1.05656	−	0.470413i	0.0417318	−	0.0185802i	−0.385765	−	0.922597i	$-0.626062\pi$
$641$	1.05656	−	0.470413i	0.0417318	−	0.0185802i	0.427496	+	0.904017i	$0.359396\pi$
$642$		0			0
$643$	−9.28843	−	16.0880i	−0.366300	−	0.634450i	0.622684	−	0.782473i	$-0.286042\pi$
$643$	−9.28843	−	16.0880i	−0.366300	−	0.634450i	−0.988984	+	0.148023i	$0.952709\pi$
$644$		0			0
$645$	11.0108	+	10.0091i	0.433548	+	0.394108i
$646$		0			0
$647$	8.31884	−	25.6028i	0.327047	−	1.00655i	−0.643461	−	0.765479i	$-0.722502\pi$
$647$	8.31884	−	25.6028i	0.327047	−	1.00655i	0.970508	−	0.241069i	$-0.0774980\pi$
$648$		0			0
$649$	−38.4225			−1.50821
$650$		0			0
$651$	−9.92452	−	15.5667i	−0.388973	−	0.610107i
$652$		0			0
$653$	3.13381	−	0.666112i	0.122635	−	0.0260670i	−0.146185	−	0.989257i	$-0.546699\pi$
$653$	3.13381	−	0.666112i	0.122635	−	0.0260670i	0.268820	+	0.963190i	$0.413366\pi$
$654$		0			0
$655$	−9.40477	−	24.2360i	−0.367475	−	0.946977i
$656$		0			0
$657$	3.06024	−	6.57438i	0.119391	−	0.256491i
$658$		0			0
$659$	17.6179	−	7.84399i	0.686296	−	0.305559i	−0.0338047	−	0.999428i	$-0.510762\pi$
$659$	17.6179	−	7.84399i	0.686296	−	0.305559i	0.720100	+	0.693870i	$0.244096\pi$
$660$		0			0
$661$	−0.130950	−	0.0583029i	−0.00509338	−	0.00226772i	0.404188	−	0.914676i	$-0.367554\pi$
$661$	−0.130950	−	0.0583029i	−0.00509338	−	0.00226772i	−0.409282	+	0.912408i	$0.634221\pi$
$662$		0			0
$663$	−53.0444	+	26.4695i	−2.06007	+	1.02799i
$664$		0			0
$665$	−5.76339	+	7.17045i	−0.223495	+	0.278058i
$666$		0			0
$667$	−3.21772	−	9.90313i	−0.124591	−	0.383451i
$668$		0			0
$669$	4.02021	+	10.7414i	0.155430	+	0.415287i
$670$		0			0
$671$	−30.9137	+	6.57091i	−1.19341	+	0.253667i
$672$		0			0
$673$	2.31481	+	22.0239i	0.0892293	+	0.848960i	0.943998	+	0.329951i	$0.107032\pi$
$673$	2.31481	+	22.0239i	0.0892293	+	0.848960i	−0.854769	+	0.519009i	$0.826301\pi$
$674$		0			0
$675$	25.5842	+	4.52224i	0.984735	+	0.174061i
$676$		0			0
$677$	3.28623	+	31.2664i	0.126300	+	1.20167i	0.855661	+	0.517536i	$0.173151\pi$
$677$	3.28623	+	31.2664i	0.126300	+	1.20167i	−0.729361	+	0.684129i	$0.760183\pi$
$678$		0			0
$679$	4.42878	−	0.941367i	0.169961	−	0.0361263i
$680$		0			0
$681$	−5.50537	−	14.7095i	−0.210966	−	0.563670i
$682$		0			0
$683$	−12.7893	−	39.3613i	−0.489367	−	1.50612i	−0.825554	−	0.564323i	$-0.809137\pi$
$683$	−12.7893	−	39.3613i	−0.489367	−	1.50612i	0.336187	−	0.941795i	$-0.390863\pi$
$684$		0			0
$685$	−0.695264	+	14.2604i	−0.0265647	+	0.544861i
$686$		0			0
$687$	−15.4494	+	7.70935i	−0.589432	+	0.294130i
$688$		0			0
$689$	23.7769	+	10.5862i	0.905829	+	0.403301i
$690$		0			0
$691$	−11.9928	+	5.33955i	−0.456229	+	0.203126i	−0.621967	−	0.783044i	$-0.713666\pi$
$691$	−11.9928	+	5.33955i	−0.456229	+	0.203126i	0.165738	+	0.986170i	$0.446999\pi$
$692$		0			0
$693$	7.82421	−	0.689893i	0.297217	−	0.0262069i
$694$		0			0
$695$	15.3041	−	12.4856i	0.580519	−	0.473607i
$696$		0			0
$697$	24.0640	−	5.11496i	0.911489	−	0.193743i
$698$		0			0
$699$	−9.10983	−	14.2888i	−0.344565	−	0.540453i
$700$		0			0
$701$	−23.3219			−0.880855			−0.440427	−	0.897788i	$-0.645173\pi$
$701$	−23.3219			−0.880855			−0.440427	+	0.897788i	$0.645173\pi$
$702$		0			0
$703$	13.5414	−	41.6762i	0.510724	−	1.57185i
$704$		0			0
$705$	−45.0290	+	25.7135i	−1.69589	+	0.968426i
$706$		0			0
$707$	0.0697182	+	0.120755i	0.00262202	+	0.00454148i
$708$		0			0
$709$	16.8897	−	7.51977i	0.634306	−	0.282411i	−0.0642862	−	0.997932i	$-0.520477\pi$
$709$	16.8897	−	7.51977i	0.634306	−	0.282411i	0.698592	+	0.715520i	$0.253810\pi$
$710$		0			0
$711$	−12.5107	−	4.29826i	−0.469188	−	0.161197i
$712$		0			0
$713$	−33.5138	+	14.9213i	−1.25510	+	0.558807i
$714$		0			0
$715$	−12.6601	+	25.0722i	−0.473460	+	0.937648i
$716$		0			0
$717$	−40.1241	−	6.70045i	−1.49846	−	0.250233i
$718$		0			0
$719$	9.29188	+	28.5975i	0.346528	+	1.06651i	0.960760	+	0.277379i	$0.0894659\pi$
$719$	9.29188	+	28.5975i	0.346528	+	1.06651i	−0.614232	+	0.789126i	$0.710534\pi$
$720$		0			0
$721$	5.67439	−	17.4640i	0.211325	−	0.650392i
$722$		0			0
$723$	11.5935	−	9.22835i	0.431168	−	0.343206i
$724$		0			0
$725$	−2.94164	+	14.3528i	−0.109250	+	0.533051i
$726$		0			0
$727$	2.85913	+	27.2028i	0.106039	+	1.00889i	0.910112	+	0.414363i	$0.135996\pi$
$727$	2.85913	+	27.2028i	0.106039	+	1.00889i	−0.804072	+	0.594531i	$0.797338\pi$
$728$		0			0
$729$	1.35805	−	26.9658i	0.0502981	−	0.998734i
$730$		0			0
$731$	−25.9676	−	5.51959i	−0.960447	−	0.204149i
$732$		0			0
$733$	26.0874	−	28.9730i	0.963559	−	1.07014i	−0.0339371	−	0.999424i	$-0.510805\pi$
$733$	26.0874	−	28.9730i	0.963559	−	1.07014i	0.997496	−	0.0707171i	$-0.0225288\pi$
$734$		0			0
$735$	21.8910	−	6.99821i	0.807462	−	0.258133i
$736$		0			0
$737$	−17.6294	−	12.8085i	−0.649386	−	0.471807i
$738$		0			0
$739$	5.14414	−	3.73744i	0.189230	−	0.137484i	−0.489137	−	0.872207i	$-0.662688\pi$
$739$	5.14414	−	3.73744i	0.189230	−	0.137484i	0.678367	+	0.734723i	$0.262688\pi$
$740$		0			0
$741$	−30.5903	+	15.2648i	−1.12376	+	0.560765i
$742$		0			0
$743$	−12.7656	−	22.1107i	−0.468325	−	0.811163i	0.531019	−	0.847360i	$-0.321809\pi$
$743$	−12.7656	−	22.1107i	−0.468325	−	0.811163i	−0.999345	+	0.0361965i	$0.988476\pi$
$744$		0			0
$745$	−39.4543	+	2.21189i	−1.44549	+	0.0810373i
$746$		0			0
$747$	21.7202	−	6.65669i	0.794701	−	0.243556i
$748$		0			0
$749$	−4.92809	+	8.53571i	−0.180069	+	0.311888i
$750$		0			0
$751$	4.49880	+	7.79215i	0.164164	+	0.284340i	0.936358	−	0.351047i	$-0.114174\pi$
$751$	4.49880	+	7.79215i	0.164164	+	0.284340i	−0.772194	+	0.635386i	$0.780841\pi$
$752$		0			0
$753$	14.8765	−	3.85271i	0.542128	−	0.140401i
$754$		0			0
$755$	−6.72342	−	10.2710i	−0.244690	−	0.373801i
$756$		0			0
$757$	35.7243			1.29842			0.649211	−	0.760608i	$-0.275099\pi$
$757$	35.7243			1.29842			0.649211	+	0.760608i	$0.275099\pi$
$758$		0			0
$759$	0.947562	−	15.5795i	0.0343943	−	0.565498i
$760$		0			0
$761$	23.5105	+	10.4675i	0.852253	+	0.379448i	0.785904	−	0.618349i	$-0.212198\pi$
$761$	23.5105	+	10.4675i	0.852253	+	0.379448i	0.0663496	+	0.997796i	$0.478865\pi$
$762$		0			0
$763$	−10.3560	+	4.61079i	−0.374912	+	0.166922i
$764$		0			0
$765$	−43.4881	+	16.0416i	−1.57231	+	0.579987i
$766$		0			0
$767$	73.4100	+	15.6038i	2.65068	+	0.563420i
$768$		0			0
$769$	−1.57325	+	1.74727i	−0.0567329	+	0.0630083i	−0.770843	−	0.637025i	$-0.780165\pi$
$769$	−1.57325	+	1.74727i	−0.0567329	+	0.0630083i	0.714110	+	0.700033i	$0.246831\pi$
$770$		0			0
$771$	−4.40197	−	4.47643i	−0.158533	−	0.161215i
$772$		0			0
$773$	13.4494	−	9.77156i	0.483741	−	0.351458i	−0.319031	−	0.947744i	$-0.603357\pi$
$773$	13.4494	−	9.77156i	0.483741	−	0.351458i	0.802772	+	0.596286i	$0.203357\pi$
$774$		0			0
$775$	51.3729	+	5.02130i	1.84537	+	0.180370i
$776$		0			0
$777$	15.3862	−	12.2472i	0.551975	−	0.439367i
$778$		0			0
$779$	13.8775	−	2.94976i	0.497215	−	0.105686i
$780$		0			0
$781$	−15.6769	−	3.33223i	−0.560965	−	0.119237i
$782$		0			0
$783$	15.1802	+	1.17913i	0.542497	+	0.0421385i
$784$		0			0
$785$	−18.0923	+	1.01429i	−0.645741	+	0.0362015i
$786$		0			0
$787$	2.65624	−	25.2725i	0.0946848	−	0.900866i	−0.839328	−	0.543626i	$-0.817051\pi$
$787$	2.65624	−	25.2725i	0.0946848	−	0.900866i	0.934013	−	0.357240i	$-0.116282\pi$
$788$		0			0
$789$	−6.40949	+	5.10190i	−0.228184	+	0.181632i
$790$		0			0
$791$	−2.11071	−	1.53352i	−0.0750482	−	0.0545257i
$792$		0			0
$793$	61.7322			2.19218
$794$		0			0
$795$	17.5756	+	10.2588i	0.623344	+	0.363841i
$796$		0			0
$797$	29.2504	−	6.21737i	1.03610	−	0.220230i	0.341694	−	0.939811i	$-0.388999\pi$
$797$	29.2504	−	6.21737i	1.03610	−	0.220230i	0.694409	+	0.719581i	$0.255666\pi$
$798$		0			0
$799$	46.2561	−	80.1179i	1.63642	−	2.83437i
$800$		0			0
$801$	5.70647	−	12.2593i	0.201628	−	0.433162i
$802$		0			0
$803$	4.10167	+	4.55537i	0.144745	+	0.160755i
$804$		0			0
$805$	1.31289	+	8.09817i	0.0462732	+	0.285423i
$806$		0			0
$807$	−19.7430	−	30.9671i	−0.694987	−	1.09009i
$808$		0			0
$809$	31.0093	+	22.5296i	1.09023	+	0.792097i	0.979438	−	0.201746i	$-0.0646616\pi$
$809$	31.0093	+	22.5296i	1.09023	+	0.792097i	0.110791	+	0.993844i	$0.464662\pi$
$810$		0			0
$811$	−26.1494	+	18.9987i	−0.918230	+	0.667133i	−0.943083	−	0.332558i	$-0.892088\pi$
$811$	−26.1494	+	18.9987i	−0.918230	+	0.667133i	0.0248525	+	0.999691i	$0.492088\pi$
$812$		0			0
$813$	0.271725	−	4.46759i	0.00952980	−	0.156685i
$814$		0			0
$815$	26.4661	−	13.6068i	0.927067	−	0.476627i
$816$		0			0
$817$	−14.9753	−	3.18311i	−0.523921	−	0.111363i
$818$		0			0
$819$	−15.2291	−	1.85939i	−0.532149	−	0.0649723i
$820$		0			0
$821$	−16.3837	−	18.1959i	−0.571795	−	0.635043i	0.385999	−	0.922499i	$-0.373857\pi$
$821$	−16.3837	−	18.1959i	−0.571795	−	0.635043i	−0.957794	+	0.287457i	$0.907190\pi$
$822$		0			0
$823$	8.05367	+	3.58572i	0.280733	+	0.124990i	0.542273	−	0.840202i	$-0.317564\pi$
$823$	8.05367	+	3.58572i	0.280733	+	0.124990i	−0.261540	+	0.965193i	$0.584230\pi$
$824$		0			0
$825$	−11.9813	+	18.4052i	−0.417135	+	0.640788i
$826$		0			0
$827$	−5.67002	+	4.11951i	−0.197166	+	0.143249i	−0.681988	−	0.731363i	$-0.738884\pi$
$827$	−5.67002	+	4.11951i	−0.197166	+	0.143249i	0.484822	+	0.874613i	$0.338884\pi$
$828$		0			0
$829$	6.88192	−	21.1804i	0.239019	−	0.735624i	−0.757544	−	0.652784i	$-0.773601\pi$
$829$	6.88192	−	21.1804i	0.239019	−	0.735624i	0.996563	−	0.0828402i	$-0.0263991\pi$
$830$		0			0
$831$	11.6937	+	31.2437i	0.405649	+	1.08383i
$832$		0			0
$833$	−27.4364	+	30.4712i	−0.950615	+	1.05576i
$834$		0			0
$835$	−10.0571	−	25.9170i	−0.348040	−	0.896895i
$836$		0			0
$837$	−1.45891	−	53.6229i	−0.0504274	−	1.85348i
$838$		0			0
$839$	3.08006	+	29.3048i	0.106336	+	1.01172i	0.909428	+	0.415861i	$0.136520\pi$
$839$	3.08006	+	29.3048i	0.106336	+	1.01172i	−0.803093	+	0.595854i	$0.796814\pi$
$840$		0			0
$841$	2.13382	−	20.3019i	0.0735798	−	0.700065i
$842$		0			0
$843$	−6.26221	+	0.275548i	−0.215682	+	0.00949036i
$844$		0			0
$845$	16.1593	−	20.1044i	0.555896	−	0.691611i
$846$		0			0
$847$	1.45782	−	4.48670i	0.0500912	−	0.154165i
$848$		0			0
$849$	0.352495	−	0.677699i	0.0120976	−	0.0232586i
$850$		0			0
$851$	−19.5391	−	33.8427i	−0.669792	−	1.16011i
$852$		0			0
$853$	36.2183	+	40.2245i	1.24009	+	1.37726i	0.899425	+	0.437076i	$0.143986\pi$
$853$	36.2183	+	40.2245i	1.24009	+	1.37726i	0.340666	+	0.940184i	$0.389347\pi$
$854$		0			0
$855$	−25.0793	+	9.25110i	−0.857693	+	0.316381i
$856$		0			0
$857$	−4.76848	+	8.25926i	−0.162888	+	0.282131i	−0.935903	−	0.352257i	$-0.885414\pi$
$857$	−4.76848	+	8.25926i	−0.162888	+	0.282131i	0.773015	+	0.634388i	$0.218748\pi$
$858$		0			0
$859$	−0.734255	+	6.98597i	−0.0250525	+	0.238358i	0.974829	+	0.222954i	$0.0715701\pi$
$859$	−0.734255	+	6.98597i	−0.0250525	+	0.238358i	−0.999881	+	0.0154039i	$0.995097\pi$
$860$		0			0
$861$	5.92469	+	2.33147i	0.201913	+	0.0794563i
$862$		0			0
$863$	−5.21720	−	3.79052i	−0.177596	−	0.129031i	0.495436	−	0.868644i	$-0.335008\pi$
$863$	−5.21720	−	3.79052i	−0.177596	−	0.129031i	−0.673032	+	0.739614i	$0.735008\pi$
$864$		0			0
$865$	38.3921	+	14.5771i	1.30537	+	0.495635i
$866$		0			0
$867$	33.8589	−	41.1026i	1.14991	−	1.39592i
$868$		0			0
$869$	7.48219	−	8.30982i	0.253816	−	0.281891i
$870$		0			0
$871$	28.4810	+	31.6314i	0.965043	+	1.07179i
$872$		0			0
$873$	12.4423	+	4.27477i	0.421109	+	0.144679i
$874$		0			0
$875$	4.01868	−	10.8211i	0.135856	−	0.365820i
$876$		0			0
$877$	45.4609	+	20.2405i	1.53510	+	0.683472i	0.988122	−	0.153672i	$-0.0491098\pi$
$877$	45.4609	+	20.2405i	1.53510	+	0.683472i	0.546982	+	0.837144i	$0.315777\pi$
$878$		0			0
$879$	−27.4306	−	27.8946i	−0.925212	−	0.940862i
$880$		0			0
$881$	7.67445	+	23.6195i	0.258559	+	0.795762i	0.993108	+	0.117206i	$0.0373938\pi$
$881$	7.67445	+	23.6195i	0.258559	+	0.795762i	−0.734549	+	0.678556i	$0.762606\pi$
$882$		0			0
$883$	−10.8333	−	33.3414i	−0.364568	−	1.12203i	−0.950251	−	0.311485i	$-0.899173\pi$
$883$	−10.8333	−	33.3414i	−0.364568	−	1.12203i	0.585683	−	0.810540i	$-0.300827\pi$
$884$		0			0
$885$	55.7228	+	18.3981i	1.87310	+	0.618445i
$886$		0			0
$887$	−0.128329	+	1.22097i	−0.00430887	+	0.0409961i	−0.996465	−	0.0840082i	$-0.973228\pi$
$887$	−0.128329	+	1.22097i	−0.00430887	+	0.0409961i	0.992156	+	0.125004i	$0.0398945\pi$
$888$		0			0
$889$	−0.321740	−	3.06115i	−0.0107908	−	0.102668i
$890$		0			0
$891$	20.5267	+	9.97701i	0.687671	+	0.334243i
$892$		0			0
$893$	26.6756	−	46.2034i	0.892664	−	1.54614i
$894$		0			0
$895$	12.5088	+	12.4180i	0.418125	+	0.415089i
$896$		0			0
$897$	−8.13740	+	29.3813i	−0.271700	+	0.981013i
$898$		0			0
$899$	30.2504			1.00891
$900$		0			0
$901$	−36.3075			−1.20958
$902$		0			0
$903$	−4.81733	−	4.89881i	−0.160311	−	0.163022i
$904$		0			0
$905$	39.2160	+	6.06482i	1.30359	+	0.201602i
$906$		0			0
$907$	6.73122	−	11.6588i	0.223506	−	0.387125i	−0.732364	−	0.680914i	$-0.761583\pi$
$907$	6.73122	−	11.6588i	0.223506	−	0.387125i	0.955870	+	0.293789i	$0.0949163\pi$
$908$		0			0
$909$	−0.00679546	+	0.405102i	−0.000225391	+	0.0134364i
$910$		0			0
$911$	−2.67531	−	25.4539i	−0.0886371	−	0.843326i	−0.945026	−	0.326995i	$-0.893964\pi$
$911$	−2.67531	−	25.4539i	−0.0886371	−	0.843326i	0.856389	−	0.516331i	$-0.172703\pi$
$912$		0			0
$913$	−2.00725	+	19.0977i	−0.0664302	+	0.632041i
$914$		0			0
$915$	47.9795	+	5.27304i	1.58615	+	0.174321i
$916$		0			0
$917$	3.70927	+	11.4160i	0.122491	+	0.376988i
$918$		0			0
$919$	−6.79831	−	20.9231i	−0.224256	−	0.690188i	−0.998366	−	0.0571377i	$-0.981803\pi$
$919$	−6.79831	−	20.9231i	−0.224256	−	0.690188i	0.774111	−	0.633050i	$-0.218197\pi$
$920$		0			0
$921$	−20.9504	+	5.42574i	−0.690339	+	0.178784i
$922$		0			0
$923$	28.5991	+	12.7331i	0.941351	+	0.419116i
$924$		0			0
$925$	0.400674	+	54.9831i	0.0131741	+	1.80783i
$926$		0			0
$927$	40.2447	−	35.0323i	1.32181	−	1.15061i
$928$		0			0
$929$	−3.56786	−	3.96252i	−0.117058	−	0.130006i	0.681768	−	0.731569i	$-0.261212\pi$
$929$	−3.56786	−	3.96252i	−0.117058	−	0.130006i	−0.798825	+	0.601563i	$0.794545\pi$
$930$		0			0
$931$	−15.8224	+	17.5725i	−0.518557	+	0.575916i
$932$		0			0
$933$	−1.06683	−	0.178152i	−0.0349263	−	0.00583245i
$934$		0			0
$935$	1.90802	−	39.1350i	0.0623990	−	1.27985i
$936$		0			0
$937$	2.24688	+	1.63246i	0.0734025	+	0.0533300i	0.623881	−	0.781519i	$-0.285555\pi$
$937$	2.24688	+	1.63246i	0.0734025	+	0.0533300i	−0.550479	+	0.834849i	$0.685555\pi$
$938$		0			0
$939$	−36.1478	+	28.7734i	−1.17964	+	0.938983i
$940$		0			0
$941$	1.63238	−	15.5311i	0.0532142	−	0.506299i	−0.935156	−	0.354235i	$-0.884741\pi$
$941$	1.63238	−	15.5311i	0.0532142	−	0.506299i	0.988371	−	0.152064i	$-0.0485920\pi$
$942$		0			0
$943$	6.32603	−	10.9570i	0.206004	−	0.356809i
$944$		0			0
$945$	−11.6775	−	2.74599i	−0.379870	−	0.0893271i
$946$		0			0
$947$	−28.7049	−	31.8800i	−0.932782	−	1.03596i	−0.999271	−	0.0381727i	$-0.987846\pi$
$947$	−28.7049	−	31.8800i	−0.932782	−	1.03596i	0.0664887	−	0.997787i	$-0.478820\pi$
$948$		0			0
$949$	−5.98667	−	10.3692i	−0.194336	−	0.336599i
$950$		0			0
$951$	47.0333	−	2.06954i	1.52516	−	0.0671095i
$952$		0			0
$953$	−14.1054	+	43.4120i	−0.456919	+	1.40625i	0.411948	+	0.911207i	$0.364848\pi$
$953$	−14.1054	+	43.4120i	−0.456919	+	1.40625i	−0.868867	+	0.495045i	$0.835152\pi$
$954$		0			0
$955$	0.142595	−	2.92473i	0.00461426	−	0.0946420i
$956$		0			0
$957$	−5.93901	+	11.4182i	−0.191981	+	0.369098i
$958$		0			0
$959$	0.689077	−	6.55613i	0.0222515	−	0.211709i
$960$		0			0
$961$	−7.89981	−	75.1617i	−0.254833	−	2.42457i
$962$		0			0
$963$	−25.0388	+	13.9015i	−0.806865	+	0.447970i
$964$		0			0
$965$	40.6967	−	2.28154i	1.31007	−	0.0734453i
$966$		0			0
$967$	−8.56048	+	9.50738i	−0.275287	+	0.305737i	−0.864895	−	0.501952i	$-0.832615\pi$
$967$	−8.56048	+	9.50738i	−0.275287	+	0.305737i	0.589609	+	0.807689i	$0.299282\pi$
$968$		0			0
$969$	30.3228	−	36.8100i	0.974107	−	1.18251i
$970$		0			0
$971$	15.1024	−	46.4804i	0.484659	−	1.49163i	−0.347816	−	0.937563i	$-0.613077\pi$
$971$	15.1024	−	46.4804i	0.484659	−	1.49163i	0.832475	−	0.554063i	$-0.186923\pi$
$972$		0			0
$973$	−7.37796	+	5.36040i	−0.236527	+	0.171847i
$974$		0			0
$975$	30.3660	−	30.2993i	0.972490	−	0.970354i
$976$		0			0
$977$	15.7250	+	7.00121i	0.503087	+	0.223989i	0.642557	−	0.766238i	$-0.277873\pi$
$977$	15.7250	+	7.00121i	0.503087	+	0.223989i	−0.139471	+	0.990226i	$0.544540\pi$
$978$		0			0
$979$	7.64843	+	8.49444i	0.244445	+	0.271484i
$980$		0			0
$981$	−32.6963	−	3.99202i	−1.04391	−	0.127456i
$982$		0			0
$983$	−30.5727	−	6.49843i	−0.975119	−	0.207268i	−0.307317	−	0.951607i	$-0.599431\pi$
$983$	−30.5727	−	6.49843i	−0.975119	−	0.207268i	−0.667802	+	0.744339i	$0.732765\pi$
$984$		0			0
$985$	−38.0636	−	37.7872i	−1.21281	−	1.20400i
$986$		0			0
$987$	21.4231	−	10.6903i	0.681905	−	0.340275i
$988$		0			0
$989$	−11.0454	+	8.02499i	−0.351225	+	0.255180i
$990$		0			0
$991$	12.6807	+	9.21307i	0.402816	+	0.292663i	0.770687	−	0.637214i	$-0.219913\pi$
$991$	12.6807	+	9.21307i	0.402816	+	0.292663i	−0.367871	+	0.929877i	$0.619913\pi$
$992$		0			0
$993$	−27.4604	+	1.20830i	−0.871430	+	0.0383444i
$994$		0			0
$995$	−8.00530	+	15.8538i	−0.253785	+	0.502600i
$996$		0			0
$997$	−7.58379	−	8.42266i	−0.240181	−	0.266748i	0.610988	−	0.791640i	$-0.290772\pi$
$997$	−7.58379	−	8.42266i	−0.240181	−	0.266748i	−0.851169	+	0.524892i	$0.824106\pi$
$998$		0			0
$999$	56.6452	−	7.51628i	1.79217	−	0.237805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bg.a.61.1	✓	240
9.4	even	3	inner	900.2.bg.a.661.22	yes	240
25.16	even	5	inner	900.2.bg.a.241.22	yes	240
225.166	even	15	inner	900.2.bg.a.841.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.bg.a.61.1	✓	240	1.1	even	1	trivial
900.2.bg.a.241.22	yes	240	25.16	even	5	inner
900.2.bg.a.661.22	yes	240	9.4	even	3	inner
900.2.bg.a.841.1	yes	240	225.166	even	15	inner

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67673 + 0.434241i) q^{3} +(-1.00789 + 1.99604i) q^{5} +(0.516228 - 0.894133i) q^{7} +(2.62287 - 1.45621i) q^{9} +(0.265072 + 2.52199i) q^{11} +(0.517761 - 4.92617i) q^{13} +(0.823198 - 3.78449i) q^{15} +(2.13525 + 6.57162i) q^{17} +(1.23138 + 3.78981i) q^{19} +(-0.477307 + 1.72339i) q^{21} +(3.24634 + 1.44536i) q^{23} +(-2.96832 - 4.02356i) q^{25} +(-3.76550 + 3.58064i) q^{27} +(-1.96071 - 2.17759i) q^{29} +(-6.90780 + 7.67189i) q^{31} +(-1.53961 - 4.11360i) q^{33} +(1.26442 + 1.93160i) q^{35} +(-8.89669 - 6.46382i) q^{37} +(1.27100 + 8.48471i) q^{39} +(0.372162 - 3.54088i) q^{41} +(-1.92102 + 3.32730i) q^{43} +(0.263097 + 6.70304i) q^{45} +(-8.95867 - 9.94962i) q^{47} +(2.96702 + 5.13902i) q^{49} +(-6.43391 - 10.0916i) q^{51} +(-1.62373 + 4.99732i) q^{53} +(-5.30115 - 2.01279i) q^{55} +(-3.71039 - 5.81978i) q^{57} +(-1.58376 + 15.0685i) q^{59} +(1.30272 + 12.3946i) q^{61} +(0.0519501 - 3.09693i) q^{63} +(9.31097 + 5.99850i) q^{65} +(-5.74991 + 6.38592i) q^{67} +(-6.07088 - 1.01380i) q^{69} +(-1.95303 + 6.01082i) q^{71} +(1.95559 - 1.42082i) q^{73} +(6.72429 + 5.45747i) q^{75} +(2.39184 + 1.06491i) q^{77} +(-2.95053 - 3.27689i) q^{79} +(4.75889 - 7.63891i) q^{81} +(7.40698 + 1.57440i) q^{83} +(-15.2693 - 2.36142i) q^{85} +(4.23319 + 2.79981i) q^{87} +(3.64661 - 2.64942i) q^{89} +(-4.13737 - 3.00598i) q^{91} +(8.25109 - 15.8634i) q^{93} +(-8.80569 - 1.36181i) q^{95} +(2.93440 + 3.25898i) q^{97} +(4.36781 + 6.22886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 2 q^{3} - 4 q^{5} - 2 q^{9} + 4 q^{11} + 33 q^{15} - 12 q^{17} + 12 q^{21} - 12 q^{23} - 12 q^{25} + 13 q^{27} + 12 q^{29} + 6 q^{31} + 31 q^{33} + 14 q^{35} - 12 q^{37} + 8 q^{39} + 16 q^{41} + 19 q^{45}+ \cdots - 66 q^{99}+O(q^{100}) \) 240 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 + 4 * q^11 + 33 * q^15 - 12 * q^17 + 12 * q^21 - 12 * q^23 - 12 * q^25 + 13 * q^27 + 12 * q^29 + 6 * q^31 + 31 * q^33 + 14 * q^35 - 12 * q^37 + 8 * q^39 + 16 * q^41 + 19 * q^45 - 19 * q^47 - 120 * q^49 + 2 * q^51 + 48 * q^53 - 18 * q^55 - 54 * q^57 + 9 * q^59 + 43 * q^63 + 37 * q^65 - 9 * q^67 + 40 * q^69 - 2 * q^71 + 70 * q^75 - 40 * q^77 + 12 * q^79 - 2 * q^81 + 22 * q^83 + 12 * q^85 + 101 * q^87 + 22 * q^89 - 66 * q^93 - 16 * q^95 + 30 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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