LMFDB - Embedded newform 912.2.bo.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	912.289
Dual form			912.2.bo.c.385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{3} +(-2.97178 + 2.49362i) q^{5} +(0.613341 - 1.06234i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(-1.06031 - 1.83651i) q^{11} +(0.0851223 - 0.482753i) q^{13} +(2.97178 + 2.49362i) q^{15} +(5.19846 + 1.89209i) q^{17} +(-2.77719 - 3.35965i) q^{19} +(-1.15270 - 0.419550i) q^{21} +(6.85117 + 5.74881i) q^{23} +(1.74510 - 9.89695i) q^{25} +(0.500000 + 0.866025i) q^{27} +(7.96451 - 2.89884i) q^{29} +(1.20574 - 2.08840i) q^{31} +(-1.62449 + 1.36310i) q^{33} +(0.826352 + 4.68647i) q^{35} +1.69459 q^{37} -0.490200 q^{39} +(0.277189 + 1.57202i) q^{41} +(5.08512 - 4.26692i) q^{43} +(1.93969 - 3.35965i) q^{45} +(2.03936 - 0.742267i) q^{47} +(2.74763 + 4.75903i) q^{49} +(0.960637 - 5.44804i) q^{51} +(6.80793 + 5.71253i) q^{53} +(7.73055 + 2.81369i) q^{55} +(-2.82635 + 3.31839i) q^{57} +(-10.7306 - 3.90560i) q^{59} +(0.0320889 + 0.0269258i) q^{61} +(-0.213011 + 1.20805i) q^{63} +(0.950837 + 1.64690i) q^{65} +(4.20574 - 1.53076i) q^{67} +(4.47178 - 7.74535i) q^{69} +(-2.02094 + 1.69577i) q^{71} +(-2.66772 - 15.1294i) q^{73} -10.0496 q^{75} -2.60132 q^{77} +(0.809278 + 4.58964i) q^{79} +(0.766044 - 0.642788i) q^{81} +(6.24035 - 10.8086i) q^{83} +(-20.1668 + 7.34013i) q^{85} +(-4.23783 - 7.34013i) q^{87} +(1.46838 - 8.32759i) q^{89} +(-0.460637 - 0.386520i) q^{91} +(-2.26604 - 0.824773i) q^{93} +(16.6309 + 3.05888i) q^{95} +(13.5103 + 4.91734i) q^{97} +(1.62449 + 1.36310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 - 12 * q^11 - 21 * q^13 + 3 * q^15 + 3 * q^17 - 6 * q^19 - 9 * q^21 + 15 * q^23 + 9 * q^25 + 3 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 9 * q^43 + 6 * q^45 + 21 * q^47 - 3 * q^51 + 30 * q^53 + 9 * q^55 - 18 * q^57 - 27 * q^59 - 9 * q^61 - 9 * q^63 - 6 * q^65 + 15 * q^67 + 12 * q^69 - 9 * q^71 + 12 * q^73 - 6 * q^75 + 42 * q^77 - 15 * q^79 + 3 * q^83 - 36 * q^85 - 6 * q^87 - 48 * q^89 + 6 * q^91 - 9 * q^93 + 48 * q^95 + 18 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$		0			0
$5$	−2.97178	+	2.49362i	−1.32902	+	1.11518i	−0.344716	+	0.938707i	$0.612025\pi$
$5$	−2.97178	+	2.49362i	−1.32902	+	1.11518i	−0.984305	+	0.176474i	$0.943531\pi$
$6$		0			0
$7$	0.613341	−	1.06234i	0.231821	−	0.401526i	−0.726523	−	0.687142i	$-0.758865\pi$
$7$	0.613341	−	1.06234i	0.231821	−	0.401526i	0.958344	+	0.285616i	$0.0921983\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	−1.06031	−	1.83651i	−0.319695	−	0.553727i	0.660730	−	0.750624i	$-0.270247\pi$
$11$	−1.06031	−	1.83651i	−0.319695	−	0.553727i	−0.980424	+	0.196897i	$0.936914\pi$
$12$		0			0
$13$	0.0851223	−	0.482753i	0.0236087	−	0.133891i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	0.0851223	−	0.482753i	0.0236087	−	0.133891i	0.994334	+	0.106301i	$0.0339006\pi$
$14$		0			0
$15$	2.97178	+	2.49362i	0.767311	+	0.643850i
$16$		0			0
$17$	5.19846	+	1.89209i	1.26081	+	0.458898i	0.884042	−	0.467408i	$-0.154812\pi$
$17$	5.19846	+	1.89209i	1.26081	+	0.458898i	0.376771	+	0.926306i	$0.377034\pi$
$18$		0			0
$19$	−2.77719	−	3.35965i	−0.637131	−	0.770756i
$19$	−2.77719	−	3.35965i	−0.637131	−	0.770756i
$20$		0			0
$21$	−1.15270	−	0.419550i	−0.251541	−	0.0915533i
$22$		0			0
$23$	6.85117	+	5.74881i	1.42857	+	1.19871i	0.946554	+	0.322546i	$0.104539\pi$
$23$	6.85117	+	5.74881i	1.42857	+	1.19871i	0.482013	+	0.876164i	$0.339906\pi$
$24$		0			0
$25$	1.74510	−	9.89695i	0.349020	−	1.97939i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	7.96451	−	2.89884i	1.47897	−	0.538302i	0.528451	−	0.848964i	$-0.322773\pi$
$29$	7.96451	−	2.89884i	1.47897	−	0.538302i	0.950521	+	0.310662i	$0.100551\pi$
$30$		0			0
$31$	1.20574	−	2.08840i	0.216557	−	0.375087i	−0.737196	−	0.675679i	$-0.763851\pi$
$31$	1.20574	−	2.08840i	0.216557	−	0.375087i	0.953753	+	0.300591i	$0.0971840\pi$
$32$		0			0
$33$	−1.62449	+	1.36310i	−0.282787	+	0.237286i
$34$		0			0
$35$	0.826352	+	4.68647i	0.139679	+	0.792159i
$36$		0			0
$37$	1.69459			0.278589			0.139295	−	0.990251i	$-0.455516\pi$
$37$	1.69459			0.278589			0.139295	+	0.990251i	$0.455516\pi$
$38$		0			0
$39$	−0.490200			−0.0784948
$40$		0			0
$41$	0.277189	+	1.57202i	0.0432896	+	0.245508i	0.998772	−	0.0495401i	$-0.0157756\pi$
$41$	0.277189	+	1.57202i	0.0432896	+	0.245508i	−0.955483	+	0.295048i	$0.904664\pi$
$42$		0			0
$43$	5.08512	−	4.26692i	0.775474	−	0.650700i	−0.166631	−	0.986019i	$-0.553289\pi$
$43$	5.08512	−	4.26692i	0.775474	−	0.650700i	0.942104	+	0.335320i	$0.108844\pi$
$44$		0			0
$45$	1.93969	−	3.35965i	0.289152	−	0.500826i
$46$		0			0
$47$	2.03936	−	0.742267i	0.297472	−	0.108271i	−0.188973	−	0.981982i	$-0.560516\pi$
$47$	2.03936	−	0.742267i	0.297472	−	0.108271i	0.486444	+	0.873711i	$0.338294\pi$
$48$		0			0
$49$	2.74763	+	4.75903i	0.392518	+	0.679861i
$50$		0			0
$51$	0.960637	−	5.44804i	0.134516	−	0.762879i
$52$		0			0
$53$	6.80793	+	5.71253i	0.935142	+	0.784677i	0.976733	−	0.214458i	$-0.0687984\pi$
$53$	6.80793	+	5.71253i	0.935142	+	0.784677i	−0.0415917	+	0.999135i	$0.513243\pi$
$54$		0			0
$55$	7.73055	+	2.81369i	1.04239	+	0.379398i
$56$		0			0
$57$	−2.82635	+	3.31839i	−0.374359	+	0.439532i
$58$		0			0
$59$	−10.7306	−	3.90560i	−1.39700	−	0.508466i	−0.469713	−	0.882819i	$-0.655643\pi$
$59$	−10.7306	−	3.90560i	−1.39700	−	0.508466i	−0.927286	+	0.374353i	$0.877865\pi$
$60$		0			0
$61$	0.0320889	+	0.0269258i	0.00410856	+	0.00344749i	0.644840	−	0.764318i	$-0.276924\pi$
$61$	0.0320889	+	0.0269258i	0.00410856	+	0.00344749i	−0.640731	+	0.767765i	$0.721369\pi$
$62$		0			0
$63$	−0.213011	+	1.20805i	−0.0268369	+	0.152199i
$64$		0			0
$65$	0.950837	+	1.64690i	0.117937	+	0.204273i
$66$		0			0
$67$	4.20574	−	1.53076i	0.513813	−	0.187012i	−0.0720836	−	0.997399i	$-0.522965\pi$
$67$	4.20574	−	1.53076i	0.513813	−	0.187012i	0.585896	+	0.810386i	$0.300743\pi$
$68$		0			0
$69$	4.47178	−	7.74535i	0.538339	−	0.932431i
$70$		0			0
$71$	−2.02094	+	1.69577i	−0.239842	+	0.201251i	−0.754783	−	0.655974i	$-0.772258\pi$
$71$	−2.02094	+	1.69577i	−0.239842	+	0.201251i	0.514941	+	0.857225i	$0.327814\pi$
$72$		0			0
$73$	−2.66772	−	15.1294i	−0.312233	−	1.77076i	−0.587334	−	0.809345i	$-0.699822\pi$
$73$	−2.66772	−	15.1294i	−0.312233	−	1.77076i	0.275101	−	0.961415i	$-0.411289\pi$
$74$		0			0
$75$	−10.0496			−1.16043
$76$		0			0
$77$	−2.60132			−0.296448
$78$		0			0
$79$	0.809278	+	4.58964i	0.0910509	+	0.516375i	0.995886	+	0.0906133i	$0.0288827\pi$
$79$	0.809278	+	4.58964i	0.0910509	+	0.516375i	−0.904835	+	0.425762i	$0.860006\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	6.24035	−	10.8086i	0.684968	−	1.18640i	−0.288479	−	0.957486i	$-0.593150\pi$
$83$	6.24035	−	10.8086i	0.684968	−	1.18640i	0.973447	−	0.228913i	$-0.0735170\pi$
$84$		0			0
$85$	−20.1668	+	7.34013i	−2.18740	+	0.796149i
$86$		0			0
$87$	−4.23783	−	7.34013i	−0.454343	−	0.786945i
$88$		0			0
$89$	1.46838	−	8.32759i	0.155648	−	0.882722i	−0.802543	−	0.596594i	$-0.796520\pi$
$89$	1.46838	−	8.32759i	0.155648	−	0.882722i	0.958191	−	0.286129i	$-0.0923685\pi$
$90$		0			0
$91$	−0.460637	−	0.386520i	−0.0482879	−	0.0405184i
$92$		0			0
$93$	−2.26604	−	0.824773i	−0.234978	−	0.0855249i
$94$		0			0
$95$	16.6309	+	3.05888i	1.70629	+	0.313834i
$96$		0			0
$97$	13.5103	+	4.91734i	1.37176	+	0.499280i	0.919670	−	0.392693i	$-0.128456\pi$
$97$	13.5103	+	4.91734i	1.37176	+	0.499280i	0.452090	+	0.891972i	$0.350679\pi$
$98$		0			0
$99$	1.62449	+	1.36310i	0.163267	+	0.136997i
$100$		0			0
$101$	0.988856	−	5.60808i	0.0983948	−	0.558025i	−0.895259	−	0.445546i	$-0.853010\pi$
$101$	0.988856	−	5.60808i	0.0983948	−	0.558025i	0.993654	−	0.112479i	$-0.0358792\pi$
$102$		0			0
$103$	−0.156574	−	0.271194i	−0.0154277	−	0.0267216i	0.858208	−	0.513301i	$-0.171578\pi$
$103$	−0.156574	−	0.271194i	−0.0154277	−	0.0267216i	−0.873636	+	0.486580i	$0.838244\pi$
$104$		0			0
$105$	4.47178	−	1.62760i	0.436401	−	0.158837i
$106$		0			0
$107$	−8.41400	+	14.5735i	−0.813412	+	1.40887i	0.0970504	+	0.995279i	$0.469059\pi$
$107$	−8.41400	+	14.5735i	−0.813412	+	1.40887i	−0.910462	+	0.413592i	$0.864274\pi$
$108$		0			0
$109$	−7.97565	+	6.69237i	−0.763929	+	0.641012i	−0.939146	−	0.343517i	$-0.888382\pi$
$109$	−7.97565	+	6.69237i	−0.763929	+	0.641012i	0.175217	+	0.984530i	$0.443937\pi$
$110$		0			0
$111$	−0.294263	−	1.66885i	−0.0279302	−	0.158400i
$112$		0			0
$113$	−17.3824			−1.63520			−0.817598	−	0.575789i	$-0.804695\pi$
$113$	−17.3824			−1.63520			−0.817598	+	0.575789i	$0.804695\pi$
$114$		0			0
$115$	−34.6955			−3.23537
$116$		0			0
$117$	0.0851223	+	0.482753i	0.00786956	+	0.0446305i
$118$		0			0
$119$	5.19846	−	4.36203i	0.476542	−	0.399866i
$120$		0			0
$121$	3.25150	−	5.63176i	0.295591	−	0.511978i
$122$		0			0
$123$	1.50000	−	0.545955i	0.135250	−	0.0492271i
$124$		0			0
$125$	9.79473	+	16.9650i	0.876067	+	1.51739i
$126$		0			0
$127$	0.283119	−	1.60565i	0.0251227	−	0.142478i	−0.969666	−	0.244432i	$-0.921398\pi$
$127$	0.283119	−	1.60565i	0.0251227	−	0.142478i	0.994789	+	0.101954i	$0.0325095\pi$
$128$		0			0
$129$	−5.08512	−	4.26692i	−0.447720	−	0.375682i
$130$		0			0
$131$	5.60354	+	2.03952i	0.489584	+	0.178194i	0.575003	−	0.818151i	$-0.305001\pi$
$131$	5.60354	+	2.03952i	0.489584	+	0.178194i	−0.0854195	+	0.996345i	$0.527223\pi$
$132$		0			0
$133$	−5.27244	+	0.889704i	−0.457179	+	0.0771471i
$134$		0			0
$135$	−3.64543	−	1.32683i	−0.313749	−	0.114195i
$136$		0			0
$137$	−0.0150147	−	0.0125989i	−0.00128280	−	0.00107639i	0.642146	−	0.766582i	$-0.278044\pi$
$137$	−0.0150147	−	0.0125989i	−0.00128280	−	0.00107639i	−0.643429	+	0.765506i	$0.722489\pi$
$138$		0			0
$139$	−0.780592	+	4.42696i	−0.0662090	+	0.375490i	0.933642	+	0.358208i	$0.116612\pi$
$139$	−0.780592	+	4.42696i	−0.0662090	+	0.375490i	−0.999851	+	0.0172815i	$0.994499\pi$
$140$		0			0
$141$	−1.08512	−	1.87949i	−0.0913838	−	0.158281i
$142$		0			0
$143$	−0.976834	+	0.355538i	−0.0816870	+	0.0297316i
$144$		0			0
$145$	−16.4402	+	28.4752i	−1.36528	+	2.36474i
$146$		0			0
$147$	4.20961	−	3.53228i	0.347203	−	0.291338i
$148$		0			0
$149$	2.08899	+	11.8473i	0.171137	+	0.970566i	0.942509	+	0.334181i	$0.108460\pi$
$149$	2.08899	+	11.8473i	0.171137	+	0.970566i	−0.771372	+	0.636385i	$0.780429\pi$
$150$		0			0
$151$	−0.0591253			−0.00481155			−0.00240578	−	0.999997i	$-0.500766\pi$
$151$	−0.0591253			−0.00481155			−0.00240578	+	0.999997i	$0.500766\pi$
$152$		0			0
$153$	−5.53209			−0.447243
$154$		0			0
$155$	1.62449	+	9.21291i	0.130482	+	0.739999i
$156$		0			0
$157$	9.92649	−	8.32931i	0.792220	−	0.664752i	−0.154074	−	0.988059i	$-0.549239\pi$
$157$	9.92649	−	8.32931i	0.792220	−	0.664752i	0.946294	+	0.323308i	$0.104795\pi$
$158$		0			0
$159$	4.44356	−	7.69648i	0.352397	−	0.610370i
$160$		0			0
$161$	10.3093	−	3.75227i	0.812485	−	0.295720i
$162$		0			0
$163$	7.53596	+	13.0527i	0.590262	+	1.02236i	0.994197	+	0.107576i	$0.0343089\pi$
$163$	7.53596	+	13.0527i	0.590262	+	1.02236i	−0.403935	+	0.914788i	$0.632358\pi$
$164$		0			0
$165$	1.42855	−	8.10170i	0.111212	−	0.630716i
$166$		0			0
$167$	1.48680	+	1.24757i	0.115052	+	0.0965399i	0.698499	−	0.715612i	$-0.253852\pi$
$167$	1.48680	+	1.24757i	0.115052	+	0.0965399i	−0.583447	+	0.812151i	$0.698296\pi$
$168$		0			0
$169$	11.9902	+	4.36408i	0.922323	+	0.335698i
$170$		0			0
$171$	3.75877	+	2.20718i	0.287440	+	0.168787i
$172$		0			0
$173$	−15.1027	−	5.49692i	−1.14823	−	0.417923i	−0.303354	−	0.952878i	$-0.598106\pi$
$173$	−15.1027	−	5.49692i	−1.14823	−	0.417923i	−0.844881	+	0.534955i	$0.820329\pi$
$174$		0			0
$175$	−9.44356	−	7.92409i	−0.713866	−	0.599005i
$176$		0			0
$177$	−1.98293	+	11.2457i	−0.149046	+	0.845281i
$178$		0			0
$179$	7.38713	+	12.7949i	0.552140	+	0.956334i	0.998120	+	0.0612912i	$0.0195218\pi$
$179$	7.38713	+	12.7949i	0.552140	+	0.956334i	−0.445980	+	0.895043i	$0.647145\pi$
$180$		0			0
$181$	17.1275	−	6.23389i	1.27308	−	0.463362i	0.384939	−	0.922942i	$-0.374222\pi$
$181$	17.1275	−	6.23389i	1.27308	−	0.463362i	0.888136	+	0.459580i	$0.152000\pi$
$182$		0			0
$183$	0.0209445	−	0.0362770i	0.00154826	−	0.00268167i
$184$		0			0
$185$	−5.03596	+	4.22567i	−0.370251	+	0.310678i
$186$		0			0
$187$	−2.03714	−	11.5532i	−0.148971	−	0.844854i
$188$		0			0
$189$	1.22668			0.0892280
$190$		0			0
$191$	−1.29086			−0.0934033			−0.0467017	−	0.998909i	$-0.514871\pi$
$191$	−1.29086			−0.0934033			−0.0467017	+	0.998909i	$0.514871\pi$
$192$		0			0
$193$	−1.58378	−	8.98205i	−0.114003	−	0.646542i	−0.987239	−	0.159245i	$-0.949094\pi$
$193$	−1.58378	−	8.98205i	−0.114003	−	0.646542i	0.873236	−	0.487297i	$-0.162017\pi$
$194$		0			0
$195$	1.45677	−	1.22237i	0.104321	−	0.0875359i
$196$		0			0
$197$	−9.31180	+	16.1285i	−0.663439	+	1.14911i	0.316268	+	0.948670i	$0.397570\pi$
$197$	−9.31180	+	16.1285i	−0.663439	+	1.14911i	−0.979706	+	0.200439i	$0.935763\pi$
$198$		0			0
$199$	7.92262	−	2.88360i	0.561620	−	0.204413i	−0.0455821	−	0.998961i	$-0.514514\pi$
$199$	7.92262	−	2.88360i	0.561620	−	0.204413i	0.607202	+	0.794548i	$0.292292\pi$
$200$		0			0
$201$	−2.23783	−	3.87603i	−0.157844	−	0.273394i
$202$		0			0
$203$	1.80541	−	10.2390i	0.126715	−	0.718635i
$204$		0			0
$205$	−4.74376	−	3.98048i	−0.331318	−	0.278009i
$206$		0			0
$207$	−8.40420	−	3.05888i	−0.584132	−	0.212607i
$208$		0			0
$209$	−3.22534	+	8.66258i	−0.223101	+	0.599203i
$210$		0			0
$211$	−1.37939	−	0.502055i	−0.0949608	−	0.0345629i	0.294103	−	0.955774i	$-0.404979\pi$
$211$	−1.37939	−	0.502055i	−0.0949608	−	0.0345629i	−0.389064	+	0.921211i	$0.627201\pi$
$212$		0			0
$213$	2.02094	+	1.69577i	0.138473	+	0.116193i
$214$		0			0
$215$	−4.47178	+	25.3607i	−0.304973	+	1.72959i
$216$		0			0
$217$	−1.47906	−	2.56180i	−0.100405	−	0.173906i
$218$		0			0
$219$	−14.4363	+	5.25438i	−0.975514	+	0.355058i
$220$		0			0
$221$	1.35591	−	2.34851i	0.0912087	−	0.157978i
$222$		0			0
$223$	−20.1229	+	16.8851i	−1.34753	+	1.13071i	−0.367906	+	0.929863i	$0.619925\pi$
$223$	−20.1229	+	16.8851i	−1.34753	+	1.13071i	−0.979622	+	0.200848i	$0.935630\pi$
$224$		0			0
$225$	1.74510	+	9.89695i	0.116340	+	0.659797i
$226$		0			0
$227$	−18.3678			−1.21912			−0.609558	−	0.792742i	$-0.708653\pi$
$227$	−18.3678			−1.21912			−0.609558	+	0.792742i	$0.708653\pi$
$228$		0			0
$229$	3.87164			0.255845			0.127923	−	0.991784i	$-0.459169\pi$
$229$	3.87164			0.255845			0.127923	+	0.991784i	$0.459169\pi$
$230$		0			0
$231$	0.451714	+	2.56180i	0.0297206	+	0.168554i
$232$		0			0
$233$	12.5988	−	10.5716i	0.825374	−	0.692571i	−0.128850	−	0.991664i	$-0.541128\pi$
$233$	12.5988	−	10.5716i	0.825374	−	0.692571i	0.954224	+	0.299093i	$0.0966840\pi$
$234$		0			0
$235$	−4.20961	+	7.29125i	−0.274605	+	0.475629i
$236$		0			0
$237$	4.37939	−	1.59397i	0.284472	−	0.103539i
$238$		0			0
$239$	1.65270	+	2.86257i	0.106905	+	0.185164i	0.914515	−	0.404553i	$-0.132573\pi$
$239$	1.65270	+	2.86257i	0.106905	+	0.185164i	−0.807610	+	0.589717i	$0.799239\pi$
$240$		0			0
$241$	0.523633	−	2.96967i	0.0337302	−	0.191293i	−0.963287	−	0.268474i	$-0.913481\pi$
$241$	0.523633	−	2.96967i	0.0337302	−	0.191293i	0.997017	+	0.0771806i	$0.0245918\pi$
$242$		0			0
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$		0			0
$245$	−20.0326	−	7.29125i	−1.27983	−	0.465821i
$246$		0			0
$247$	−1.85828	+	1.05471i	−0.118239	+	0.0671099i
$248$		0			0
$249$	−11.7280	−	4.26865i	−0.743233	−	0.270515i
$250$		0			0
$251$	2.70780	+	2.27211i	0.170915	+	0.143414i	0.724233	−	0.689556i	$-0.242194\pi$
$251$	2.70780	+	2.27211i	0.170915	+	0.143414i	−0.553318	+	0.832970i	$0.686639\pi$
$252$		0			0
$253$	3.29339	−	18.6777i	0.207053	−	1.17426i
$254$		0			0
$255$	10.7306	+	18.5859i	0.671973	+	1.16389i
$256$		0			0
$257$	4.41875	−	1.60829i	0.275634	−	0.100323i	−0.200505	−	0.979693i	$-0.564258\pi$
$257$	4.41875	−	1.60829i	0.275634	−	0.100323i	0.476139	+	0.879370i	$0.342036\pi$
$258$		0			0
$259$	1.03936	−	1.80023i	0.0645829	−	0.111861i
$260$		0			0
$261$	−6.49273	+	5.44804i	−0.401890	+	0.337225i
$262$		0			0
$263$	−3.65745	−	20.7424i	−0.225528	−	1.27903i	−0.861673	−	0.507464i	$-0.830583\pi$
$263$	−3.65745	−	20.7424i	−0.225528	−	1.27903i	0.636145	−	0.771570i	$-0.280528\pi$
$264$		0			0
$265$	−34.4766			−2.11788
$266$		0			0
$267$	−8.45605			−0.517502
$268$		0			0
$269$	1.75015	+	9.92561i	0.106709	+	0.605175i	0.990524	+	0.137339i	$0.0438550\pi$
$269$	1.75015	+	9.92561i	0.106709	+	0.605175i	−0.883815	+	0.467836i	$0.845034\pi$
$270$		0			0
$271$	7.47952	−	6.27606i	0.454349	−	0.381244i	−0.386698	−	0.922206i	$-0.626384\pi$
$271$	7.47952	−	6.27606i	0.454349	−	0.381244i	0.841047	+	0.540963i	$0.181940\pi$
$272$		0			0
$273$	−0.300660	+	0.520758i	−0.0181967	+	0.0315177i
$274$		0			0
$275$	−20.0262	+	7.28893i	−1.20762	+	0.439539i
$276$		0			0
$277$	−8.42855	−	14.5987i	−0.506422	−	0.877149i	−0.999972	−	0.00743188i	$-0.997634\pi$
$277$	−8.42855	−	14.5987i	−0.506422	−	0.877149i	0.493550	−	0.869717i	$-0.335699\pi$
$278$		0			0
$279$	−0.418748	+	2.37484i	−0.0250698	+	0.142178i
$280$		0			0
$281$	−8.98158	−	7.53644i	−0.535796	−	0.449586i	0.334301	−	0.942466i	$-0.391500\pi$
$281$	−8.98158	−	7.53644i	−0.535796	−	0.449586i	−0.870097	+	0.492880i	$0.835944\pi$
$282$		0			0
$283$	−20.2456	−	7.36878i	−1.20347	−	0.438029i	−0.339039	−	0.940772i	$-0.610102\pi$
$283$	−20.2456	−	7.36878i	−1.20347	−	0.438029i	−0.864435	+	0.502744i	$0.832324\pi$
$284$		0			0
$285$	0.124485	−	16.9094i	0.00737386	−	1.00163i
$286$		0			0
$287$	1.84002	+	0.669713i	0.108613	+	0.0395319i
$288$		0			0
$289$	10.4213	+	8.74449i	0.613016	+	0.514382i
$290$		0			0
$291$	2.49660	−	14.1589i	0.146353	−	0.830010i
$292$		0			0
$293$	5.56031	+	9.63073i	0.324837	+	0.562634i	0.981479	−	0.191568i	$-0.0613573\pi$
$293$	5.56031	+	9.63073i	0.324837	+	0.562634i	−0.656643	+	0.754202i	$0.728024\pi$
$294$		0			0
$295$	41.6279	−	15.1513i	2.42367	−	0.882145i
$296$		0			0
$297$	1.06031	−	1.83651i	0.0615253	−	0.106565i
$298$		0			0
$299$	3.35844	−	2.81807i	0.194224	−	0.162973i
$300$		0			0
$301$	−1.41400	−	8.01919i	−0.0815016	−	0.462219i
$302$		0			0
$303$	−5.69459			−0.327146
$304$		0			0
$305$	−0.162504			−0.00930494
$306$		0			0
$307$	−4.34817	−	24.6597i	−0.248163	−	1.40740i	−0.813030	−	0.582222i	$-0.802183\pi$
$307$	−4.34817	−	24.6597i	−0.248163	−	1.40740i	0.564866	−	0.825182i	$-0.308928\pi$
$308$		0			0
$309$	−0.239885	+	0.201288i	−0.0136466	+	0.0114509i
$310$		0			0
$311$	0.0282185	−	0.0488759i	0.00160012	−	0.00277150i	−0.865224	−	0.501385i	$-0.832824\pi$
$311$	0.0282185	−	0.0488759i	0.00160012	−	0.00277150i	0.866824	+	0.498614i	$0.166157\pi$
$312$		0			0
$313$	−12.9338	+	4.70750i	−0.731059	+	0.266084i	−0.680613	−	0.732643i	$-0.738287\pi$
$313$	−12.9338	+	4.70750i	−0.731059	+	0.266084i	−0.0504462	+	0.998727i	$0.516064\pi$
$314$		0			0
$315$	−2.37939	−	4.12122i	−0.134063	−	0.232204i
$316$		0			0
$317$	1.89347	−	10.7384i	0.106348	−	0.603128i	−0.884326	−	0.466870i	$-0.845381\pi$
$317$	1.89347	−	10.7384i	0.106348	−	0.603128i	0.990673	−	0.136257i	$-0.0435074\pi$
$318$		0			0
$319$	−13.7686	−	11.5532i	−0.770892	−	0.646855i
$320$		0			0
$321$	15.8131	+	5.75552i	0.882604	+	0.321242i
$322$		0			0
$323$	−8.08037	−	22.7197i	−0.449604	−	1.26416i
$324$		0			0
$325$	−4.62923	−	1.68490i	−0.256784	−	0.0934616i
$326$		0			0
$327$	7.97565	+	6.69237i	0.441055	+	0.370089i
$328$		0			0
$329$	0.462286	−	2.62175i	0.0254867	−	0.144542i
$330$		0			0
$331$	4.29561	+	7.44021i	0.236108	+	0.408951i	0.959594	−	0.281388i	$-0.0907948\pi$
$331$	4.29561	+	7.44021i	0.236108	+	0.408951i	−0.723486	+	0.690339i	$0.757461\pi$
$332$		0			0
$333$	−1.59240	+	0.579585i	−0.0872628	+	0.0317611i
$334$		0			0
$335$	−8.68139	+	15.0366i	−0.474315	+	0.821538i
$336$		0			0
$337$	−1.76991	+	1.48513i	−0.0964134	+	0.0809005i	−0.689720	−	0.724076i	$-0.742267\pi$
$337$	−1.76991	+	1.48513i	−0.0964134	+	0.0809005i	0.593307	+	0.804976i	$0.297822\pi$
$338$		0			0
$339$	3.01842	+	17.1183i	0.163938	+	0.929738i
$340$		0			0
$341$	−5.11381			−0.276928
$342$		0			0
$343$	15.3277			0.827618
$344$		0			0
$345$	6.02481	+	34.1684i	0.324365	+	1.83957i
$346$		0			0
$347$	2.51707	−	2.11208i	0.135124	−	0.113382i	−0.572721	−	0.819750i	$-0.694112\pi$
$347$	2.51707	−	2.11208i	0.135124	−	0.113382i	0.707845	+	0.706368i	$0.249668\pi$
$348$		0			0
$349$	−14.6741	+	25.4163i	−0.785487	+	1.36050i	0.143220	+	0.989691i	$0.454254\pi$
$349$	−14.6741	+	25.4163i	−0.785487	+	1.36050i	−0.928707	+	0.370813i	$0.879079\pi$
$350$		0			0
$351$	0.460637	−	0.167658i	0.0245870	−	0.00894893i
$352$		0			0
$353$	3.86959	+	6.70232i	0.205957	+	0.356728i	0.950437	−	0.310916i	$-0.100636\pi$
$353$	3.86959	+	6.70232i	0.205957	+	0.356728i	−0.744480	+	0.667645i	$0.767303\pi$
$354$		0			0
$355$	1.77719	−	10.0789i	0.0943234	−	0.534935i
$356$		0			0
$357$	−5.19846	−	4.36203i	−0.275132	−	0.230863i
$358$		0			0
$359$	2.69459	+	0.980752i	0.142215	+	0.0517621i	0.412147	−	0.911117i	$-0.364779\pi$
$359$	2.69459	+	0.980752i	0.142215	+	0.0517621i	−0.269932	+	0.962879i	$0.587001\pi$
$360$		0			0
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$		0			0
$363$	−6.11081	−	2.22415i	−0.320735	−	0.116738i
$364$		0			0
$365$	45.6548	+	38.3089i	2.38968	+	2.00518i
$366$		0			0
$367$	3.98798	−	22.6169i	0.208171	−	1.18060i	−0.684201	−	0.729294i	$-0.739849\pi$
$367$	3.98798	−	22.6169i	0.208171	−	1.18060i	0.892372	−	0.451301i	$-0.149040\pi$
$368$		0			0
$369$	−0.798133	−	1.38241i	−0.0415492	−	0.0719653i
$370$		0			0
$371$	10.2442	−	3.72859i	0.531854	−	0.193579i
$372$		0			0
$373$	11.5954	−	20.0838i	0.600387	−	1.03990i	−0.392376	−	0.919805i	$-0.628347\pi$
$373$	11.5954	−	20.0838i	0.600387	−	1.03990i	0.992762	−	0.120095i	$-0.0383199\pi$
$374$		0			0
$375$	15.0064	−	12.5919i	0.774927	−	0.650241i
$376$		0			0
$377$	−0.721467	−	4.09164i	−0.0371574	−	0.210730i
$378$		0			0
$379$	33.5185			1.72173			0.860864	−	0.508835i	$-0.169924\pi$
$379$	33.5185			1.72173			0.860864	+	0.508835i	$0.169924\pi$
$380$		0			0
$381$	−1.63041			−0.0835287
$382$		0			0
$383$	−1.16860	−	6.62744i	−0.0597125	−	0.338646i	0.940286	−	0.340385i	$-0.110558\pi$
$383$	−1.16860	−	6.62744i	−0.0597125	−	0.338646i	−0.999998	+	0.00173918i	$0.999446\pi$
$384$		0			0
$385$	7.73055	−	6.48670i	0.393985	−	0.330593i
$386$		0			0
$387$	−3.31908	+	5.74881i	−0.168718	+	0.292229i
$388$		0			0
$389$	17.8751	−	6.50601i	0.906304	−	0.329868i	0.153528	−	0.988144i	$-0.450937\pi$
$389$	17.8751	−	6.50601i	0.906304	−	0.329868i	0.752776	+	0.658277i	$0.228714\pi$
$390$		0			0
$391$	24.7383	+	42.8480i	1.25107	+	2.16692i
$392$		0			0
$393$	1.03549	−	5.87257i	0.0522337	−	0.296232i
$394$		0			0
$395$	−13.8498	−	11.6214i	−0.696860	−	0.584735i
$396$		0			0
$397$	25.2913	+	9.20529i	1.26934	+	0.462000i	0.886891	−	0.461978i	$-0.152860\pi$
$397$	25.2913	+	9.20529i	1.26934	+	0.462000i	0.382444	+	0.923979i	$0.375082\pi$
$398$		0			0
$399$	1.79174	+	5.03785i	0.0896990	+	0.252208i
$400$		0			0
$401$	5.35756	+	1.94999i	0.267544	+	0.0973780i	0.472309	−	0.881433i	$-0.343421\pi$
$401$	5.35756	+	1.94999i	0.267544	+	0.0973780i	−0.204765	+	0.978811i	$0.565643\pi$
$402$		0			0
$403$	−0.905544	−	0.759842i	−0.0451084	−	0.0378504i
$404$		0			0
$405$	−0.673648	+	3.82045i	−0.0334738	+	0.189840i
$406$		0			0
$407$	−1.79679	−	3.11213i	−0.0890635	−	0.154263i
$408$		0			0
$409$	0.758770	−	0.276170i	0.0375188	−	0.0136557i	−0.323193	−	0.946333i	$-0.604756\pi$
$409$	0.758770	−	0.276170i	0.0375188	−	0.0136557i	0.360711	+	0.932677i	$0.382534\pi$
$410$		0			0
$411$	−0.00980018	+	0.0169744i	−0.000483407	+	0.000837286i
$412$		0			0
$413$	−10.7306	+	9.00400i	−0.528016	+	0.443058i
$414$		0			0
$415$	8.40760	+	47.6819i	0.412713	+	2.34061i
$416$		0			0
$417$	4.49525			0.220133
$418$		0			0
$419$	19.1215			0.934149			0.467074	−	0.884218i	$-0.345308\pi$
$419$	19.1215			0.934149			0.467074	+	0.884218i	$0.345308\pi$
$420$		0			0
$421$	−4.86618	−	27.5975i	−0.237163	−	1.34502i	−0.838010	−	0.545655i	$-0.816281\pi$
$421$	−4.86618	−	27.5975i	−0.237163	−	1.34502i	0.600847	−	0.799364i	$-0.294830\pi$
$422$		0			0
$423$	−1.66250	+	1.39501i	−0.0808337	+	0.0678275i
$424$		0			0
$425$	27.7977	−	48.1471i	1.34839	−	2.33548i
$426$		0			0
$427$	0.0482857	−	0.0175745i	0.00233671	−	0.000850492i
$428$		0			0
$429$	0.519762	+	0.900255i	0.0250944	+	0.0434647i
$430$		0			0
$431$	1.56923	−	8.89955i	0.0755872	−	0.428676i	−0.923406	−	0.383824i	$-0.874607\pi$
$431$	1.56923	−	8.89955i	0.0755872	−	0.428676i	0.998994	−	0.0448525i	$-0.0142818\pi$
$432$		0			0
$433$	1.12061	+	0.940307i	0.0538533	+	0.0451883i	0.669317	−	0.742977i	$-0.266587\pi$
$433$	1.12061	+	0.940307i	0.0538533	+	0.0451883i	−0.615464	+	0.788165i	$0.711031\pi$
$434$		0			0
$435$	30.8974	+	11.2457i	1.48142	+	0.539192i
$436$		0			0
$437$	0.286989	−	38.9830i	0.0137285	−	1.86481i
$438$		0			0
$439$	−5.08987	−	1.85256i	−0.242926	−	0.0884179i	0.217688	−	0.976018i	$-0.430149\pi$
$439$	−5.08987	−	1.85256i	−0.242926	−	0.0884179i	−0.460614	+	0.887601i	$0.652371\pi$
$440$		0			0
$441$	−4.20961	−	3.53228i	−0.200457	−	0.168204i
$442$		0			0
$443$	4.94310	−	28.0337i	0.234854	−	1.33192i	−0.608068	−	0.793885i	$-0.708055\pi$
$443$	4.94310	−	28.0337i	0.234854	−	1.33192i	0.842922	−	0.538036i	$-0.180834\pi$
$444$		0			0
$445$	16.4021	+	28.4093i	0.777536	+	1.34673i
$446$		0			0
$447$	11.3045	−	4.11451i	0.534686	−	0.194610i
$448$		0			0
$449$	11.3824	−	19.7149i	0.537168	−	0.930402i	−0.461887	−	0.886939i	$-0.652828\pi$
$449$	11.3824	−	19.7149i	0.537168	−	0.930402i	0.999055	−	0.0434631i	$-0.0138391\pi$
$450$		0			0
$451$	2.59311	−	2.17588i	0.122105	−	0.102458i
$452$		0			0
$453$	0.0102670	+	0.0582271i	0.000482386	+	0.00273575i
$454$		0			0
$455$	2.33275			0.109361
$456$		0			0
$457$	−1.13011			−0.0528643			−0.0264322	−	0.999651i	$-0.508415\pi$
$457$	−1.13011			−0.0528643			−0.0264322	+	0.999651i	$0.508415\pi$
$458$		0			0
$459$	0.960637	+	5.44804i	0.0448387	+	0.254293i
$460$		0			0
$461$	−9.94562	+	8.34537i	−0.463214	+	0.388683i	−0.844312	−	0.535852i	$-0.819990\pi$
$461$	−9.94562	+	8.34537i	−0.463214	+	0.388683i	0.381098	+	0.924535i	$0.375546\pi$
$462$		0			0
$463$	−15.3123	+	26.5216i	−0.711622	+	1.23256i	0.252627	+	0.967564i	$0.418706\pi$
$463$	−15.3123	+	26.5216i	−0.711622	+	1.23256i	−0.964248	+	0.265001i	$0.914628\pi$
$464$		0			0
$465$	8.79086	−	3.19961i	0.407666	−	0.148378i
$466$		0			0
$467$	5.52869	+	9.57596i	0.255837	+	0.443123i	0.965123	−	0.261799i	$-0.0843156\pi$
$467$	5.52869	+	9.57596i	0.255837	+	0.443123i	−0.709285	+	0.704921i	$0.750982\pi$
$468$		0			0
$469$	0.953363	−	5.40679i	0.0440222	−	0.249662i
$470$		0			0
$471$	−9.92649	−	8.32931i	−0.457388	−	0.383794i
$472$		0			0
$473$	−13.2280	−	4.81461i	−0.608225	−	0.221376i
$474$		0			0
$475$	−38.0967	+	21.6228i	−1.74800	+	0.992122i
$476$		0			0
$477$	−8.35117	−	3.03958i	−0.382374	−	0.139173i
$478$		0			0
$479$	13.5116	+	11.3376i	0.617361	+	0.518028i	0.896973	−	0.442086i	$-0.145761\pi$
$479$	13.5116	+	11.3376i	0.617361	+	0.518028i	−0.279612	+	0.960113i	$0.590206\pi$
$480$		0			0
$481$	0.144248	−	0.818069i	0.00657713	−	0.0373007i
$482$		0			0
$483$	−5.48545	−	9.50108i	−0.249597	−	0.432314i
$484$		0			0
$485$	−52.4115	+	19.0762i	−2.37989	+	0.866207i
$486$		0			0
$487$	−7.64677	+	13.2446i	−0.346508	+	0.600170i	−0.985627	−	0.168938i	$-0.945966\pi$
$487$	−7.64677	+	13.2446i	−0.346508	+	0.600170i	0.639118	+	0.769109i	$0.279299\pi$
$488$		0			0
$489$	11.5458	−	9.68804i	0.522117	−	0.438108i
$490$		0			0
$491$	0.308811	+	1.75135i	0.0139364	+	0.0790375i	0.990983	−	0.133990i	$-0.0427789\pi$
$491$	0.308811	+	1.75135i	0.0139364	+	0.0790375i	−0.977046	+	0.213027i	$0.931668\pi$
$492$		0			0
$493$	46.8881			2.11173
$494$		0			0
$495$	−8.22668			−0.369762
$496$		0			0
$497$	0.561956	+	3.18701i	0.0252072	+	0.142957i
$498$		0			0
$499$	0.0825961	−	0.0693063i	0.00369751	−	0.00310258i	−0.640937	−	0.767594i	$-0.721454\pi$
$499$	0.0825961	−	0.0693063i	0.00369751	−	0.00310258i	0.644634	+	0.764491i	$0.277010\pi$
$500$		0			0
$501$	0.970437	−	1.68085i	0.0433559	−	0.0750947i
$502$		0			0
$503$	−22.2615	+	8.10251i	−0.992589	+	0.361273i	−0.786722	−	0.617307i	$-0.788224\pi$
$503$	−22.2615	+	8.10251i	−0.992589	+	0.361273i	−0.205867	+	0.978580i	$0.566001\pi$
$504$		0			0
$505$	11.0458	+	19.1318i	0.491530	+	0.851355i
$506$		0			0
$507$	2.21570	−	12.5659i	0.0984027	−	0.558069i
$508$		0			0
$509$	−2.73783	−	2.29731i	−0.121352	−	0.101826i	0.580092	−	0.814551i	$-0.303017\pi$
$509$	−2.73783	−	2.29731i	−0.121352	−	0.101826i	−0.701444	+	0.712724i	$0.747461\pi$
$510$		0			0
$511$	−17.7087	−	6.44545i	−0.783388	−	0.285130i
$512$		0			0
$513$	1.52094	−	4.08494i	0.0671513	−	0.180354i
$514$		0			0
$515$	1.14156	+	0.415494i	0.0503031	+	0.0183088i
$516$		0			0
$517$	−3.52553	−	2.95827i	−0.155053	−	0.130105i
$518$		0			0
$519$	−2.79086	+	15.8278i	−0.122505	+	0.694761i
$520$		0			0
$521$	−17.0608	−	29.5501i	−0.747446	−	1.29461i	−0.949043	−	0.315146i	$-0.897946\pi$
$521$	−17.0608	−	29.5501i	−0.747446	−	1.29461i	0.201597	−	0.979469i	$-0.435387\pi$
$522$		0			0
$523$	16.0376	−	5.83721i	0.701276	−	0.255243i	0.0333202	−	0.999445i	$-0.489392\pi$
$523$	16.0376	−	5.83721i	0.701276	−	0.255243i	0.667955	+	0.744201i	$0.267170\pi$
$524$		0			0
$525$	−6.16385	+	10.6761i	−0.269012	+	0.465943i
$526$		0			0
$527$	10.2194	−	8.57510i	0.445164	−	0.373537i
$528$		0			0
$529$	9.89574	+	56.1216i	0.430250	+	2.44007i
$530$		0			0
$531$	11.4192			0.495552
$532$		0			0
$533$	0.782490			0.0338934
$534$		0			0
$535$	−11.3362	−	64.2905i	−0.490105	−	2.77952i
$536$		0			0
$537$	11.3177	−	9.49671i	0.488396	−	0.409813i
$538$		0			0
$539$	5.82666	−	10.0921i	0.250972	−	0.434696i
$540$		0			0
$541$	−24.7841	+	9.02066i	−1.06555	+	0.387828i	−0.814511	−	0.580149i	$-0.802994\pi$
$541$	−24.7841	+	9.02066i	−1.06555	+	0.387828i	−0.251039	+	0.967977i	$0.580772\pi$
$542$		0			0
$543$	−9.11334	−	15.7848i	−0.391091	−	0.677389i
$544$		0			0
$545$	7.01367	−	39.7765i	0.300433	−	1.70384i
$546$		0			0
$547$	26.7317	+	22.4306i	1.14297	+	0.959063i	0.999532	−	0.0305971i	$-0.00974088\pi$
$547$	26.7317	+	22.4306i	1.14297	+	0.959063i	0.143435	+	0.989660i	$0.454185\pi$
$548$		0			0
$549$	−0.0393628	−	0.0143269i	−0.00167997	−	0.000611457i
$550$		0			0
$551$	−31.8580	−	18.7073i	−1.35720	−	0.796957i
$552$		0			0
$553$	5.37211	+	1.95529i	0.228445	+	0.0831473i
$554$		0			0
$555$	5.03596	+	4.22567i	0.213765	+	0.179370i
$556$		0			0
$557$	−5.65957	+	32.0970i	−0.239804	+	1.35999i	0.592454	+	0.805604i	$0.298159\pi$
$557$	−5.65957	+	32.0970i	−0.239804	+	1.35999i	−0.832258	+	0.554389i	$0.812952\pi$
$558$		0			0
$559$	−1.62701	−	2.81807i	−0.0688152	−	0.119192i
$560$		0			0
$561$	−11.0239	+	4.01239i	−0.465431	+	0.169403i
$562$		0			0
$563$	−2.39780	+	4.15312i	−0.101055	+	0.175033i	−0.912120	−	0.409924i	$-0.865555\pi$
$563$	−2.39780	+	4.15312i	−0.101055	+	0.175033i	0.811064	+	0.584957i	$0.198889\pi$
$564$		0			0
$565$	51.6566	−	43.3451i	2.17321	−	1.82354i
$566$		0			0
$567$	−0.213011	−	1.20805i	−0.00894562	−	0.0507331i
$568$		0			0
$569$	−32.7006			−1.37088			−0.685440	−	0.728129i	$-0.740390\pi$
$569$	−32.7006			−1.37088			−0.685440	+	0.728129i	$0.740390\pi$
$570$		0			0
$571$	10.9531			0.458371			0.229186	−	0.973383i	$-0.426394\pi$
$571$	10.9531			0.458371			0.229186	+	0.973383i	$0.426394\pi$
$572$		0			0
$573$	0.224155	+	1.27125i	0.00936423	+	0.0531072i
$574$		0			0
$575$	68.8517	−	57.7734i	2.87131	−	2.40932i
$576$		0			0
$577$	9.15136	−	15.8506i	0.380976	−	0.659870i	−0.610226	−	0.792227i	$-0.708921\pi$
$577$	9.15136	−	15.8506i	0.380976	−	0.659870i	0.991202	+	0.132357i	$0.0422547\pi$
$578$		0			0
$579$	−8.57057	+	3.11943i	−0.356181	+	0.129639i
$580$		0			0
$581$	−7.65493	−	13.2587i	−0.317580	−	0.550064i
$582$		0			0
$583$	3.27260	−	18.5599i	0.135537	−	0.768671i
$584$		0			0
$585$	−1.45677	−	1.22237i	−0.0602299	−	0.0505389i
$586$		0			0
$587$	−5.34137	−	1.94410i	−0.220462	−	0.0802415i	0.229428	−	0.973326i	$-0.426314\pi$
$587$	−5.34137	−	1.94410i	−0.220462	−	0.0802415i	−0.449890	+	0.893084i	$0.648537\pi$
$588$		0			0
$589$	−10.3648	+	1.74903i	−0.427076	+	0.0720673i
$590$		0			0
$591$	17.5005	+	6.36965i	0.719873	+	0.262012i
$592$		0			0
$593$	−8.05097	−	6.75557i	−0.330614	−	0.277418i	0.462336	−	0.886705i	$-0.347011\pi$
$593$	−8.05097	−	6.75557i	−0.330614	−	0.277418i	−0.792950	+	0.609287i	$0.791456\pi$
$594$		0			0
$595$	−4.57145	+	25.9260i	−0.187411	+	1.06286i
$596$		0			0
$597$	−4.21554	−	7.30152i	−0.172530	−	0.298832i
$598$		0			0
$599$	−42.0146	+	15.2921i	−1.71667	+	0.624817i	−0.997543	−	0.0700613i	$-0.977681\pi$
$599$	−42.0146	+	15.2921i	−1.71667	+	0.624817i	−0.719128	+	0.694878i	$0.755458\pi$
$600$		0			0
$601$	−16.4363	+	28.4685i	−0.670450	+	1.16125i	0.307326	+	0.951604i	$0.400566\pi$
$601$	−16.4363	+	28.4685i	−0.670450	+	1.16125i	−0.977777	+	0.209650i	$0.932768\pi$
$602$		0			0
$603$	−3.42855	+	2.87689i	−0.139621	+	0.117156i
$604$		0			0
$605$	4.38073	+	24.8444i	0.178102	+	1.01007i
$606$		0			0
$607$	−29.9486			−1.21558			−0.607788	−	0.794099i	$-0.707943\pi$
$607$	−29.9486			−1.21558			−0.607788	+	0.794099i	$0.707943\pi$
$608$		0			0
$609$	−10.3969			−0.421305
$610$		0			0
$611$	−0.184736	−	1.04769i	−0.00747363	−	0.0423850i
$612$		0			0
$613$	4.47384	−	3.75400i	0.180697	−	0.151623i	−0.547953	−	0.836509i	$-0.684593\pi$
$613$	4.47384	−	3.75400i	0.180697	−	0.151623i	0.728650	+	0.684887i	$0.240148\pi$
$614$		0			0
$615$	−3.09627	+	5.36289i	−0.124854	+	0.216253i
$616$		0			0
$617$	11.8135	−	4.29975i	0.475592	−	0.173101i	−0.0930920	−	0.995658i	$-0.529675\pi$
$617$	11.8135	−	4.29975i	0.475592	−	0.173101i	0.568684	+	0.822556i	$0.307453\pi$
$618$		0			0
$619$	4.14290	+	7.17572i	0.166517	+	0.288417i	0.937193	−	0.348811i	$-0.113414\pi$
$619$	4.14290	+	7.17572i	0.166517	+	0.288417i	−0.770676	+	0.637228i	$0.780081\pi$
$620$		0			0
$621$	−1.55303	+	8.80769i	−0.0623211	+	0.353440i
$622$		0			0
$623$	−7.94609	−	6.66756i	−0.318353	−	0.267130i
$624$		0			0
$625$	−24.1942	−	8.80596i	−0.967767	−	0.352238i
$626$		0			0
$627$	9.09105	+	1.67210i	0.363062	+	0.0667771i
$628$		0			0
$629$	8.80928	+	3.20631i	0.351249	+	0.127844i
$630$		0			0
$631$	−5.23055	−	4.38895i	−0.208225	−	0.174722i	0.532711	−	0.846297i	$-0.321173\pi$
$631$	−5.23055	−	4.38895i	−0.208225	−	0.174722i	−0.740936	+	0.671576i	$0.765618\pi$
$632$		0			0
$633$	−0.254900	+	1.44561i	−0.0101314	+	0.0574578i
$634$		0			0
$635$	3.16250	+	5.47762i	0.125500	+	0.217373i
$636$		0			0
$637$	2.53132	−	0.921324i	0.100294	−	0.0365042i
$638$		0			0
$639$	1.31908	−	2.28471i	0.0521819	−	0.0903817i
$640$		0			0
$641$	29.6544	−	24.8830i	1.17128	−	0.982818i	0.171279	−	0.985222i	$-0.445210\pi$
$641$	29.6544	−	24.8830i	1.17128	−	0.982818i	0.999997	+	0.00240481i	$0.000765477\pi$
$642$		0			0
$643$	2.18820	+	12.4099i	0.0862940	+	0.489398i	0.997070	+	0.0764965i	$0.0243734\pi$
$643$	2.18820	+	12.4099i	0.0862940	+	0.489398i	−0.910776	+	0.412901i	$0.864515\pi$
$644$		0			0
$645$	25.7520			1.01398
$646$		0			0
$647$	−8.41241			−0.330726			−0.165363	−	0.986233i	$-0.552880\pi$
$647$	−8.41241			−0.330726			−0.165363	+	0.986233i	$0.552880\pi$
$648$		0			0
$649$	4.20502	+	23.8479i	0.165062	+	0.936111i
$650$		0			0
$651$	−2.26604	+	1.90144i	−0.0888133	+	0.0745232i
$652$		0			0
$653$	−13.1900	+	22.8458i	−0.516165	+	0.894024i	0.483659	+	0.875257i	$0.339307\pi$
$653$	−13.1900	+	22.8458i	−0.516165	+	0.894024i	−0.999824	+	0.0187673i	$0.994026\pi$
$654$		0			0
$655$	−21.7383	+	7.91209i	−0.849385	+	0.309151i
$656$		0			0
$657$	7.68139	+	13.3046i	0.299680	+	0.519060i
$658$		0			0
$659$	−5.55794	+	31.5207i	−0.216507	+	1.22787i	0.661766	+	0.749711i	$0.269807\pi$
$659$	−5.55794	+	31.5207i	−0.216507	+	1.22787i	−0.878273	+	0.478160i	$0.841304\pi$
$660$		0			0
$661$	−31.0462	−	26.0509i	−1.20756	−	1.01326i	−0.999381	−	0.0351705i	$-0.988803\pi$
$661$	−31.0462	−	26.0509i	−1.20756	−	1.01326i	−0.208177	−	0.978091i	$-0.566753\pi$
$662$		0			0
$663$	−2.54829	−	0.927500i	−0.0989672	−	0.0360211i
$664$		0			0
$665$	13.4500	−	15.7915i	0.521567	−	0.612367i
$666$		0			0
$667$	71.2311	+	25.9260i	2.75808	+	1.00386i
$668$		0			0
$669$	20.1229	+	16.8851i	0.777996	+	0.652816i
$670$		0			0
$671$	0.0154253	−	0.0874810i	0.000595486	−	0.00337717i
$672$		0			0
$673$	2.28059	+	3.95010i	0.0879104	+	0.152265i	0.906628	−	0.421932i	$-0.138648\pi$
$673$	2.28059	+	3.95010i	0.0879104	+	0.152265i	−0.818717	+	0.574197i	$0.805314\pi$
$674$		0			0
$675$	9.44356	−	3.43718i	0.363483	−	0.132297i
$676$		0			0
$677$	−16.7208	+	28.9612i	−0.642631	+	1.11307i	0.342213	+	0.939623i	$0.388824\pi$
$677$	−16.7208	+	28.9612i	−0.642631	+	1.11307i	−0.984843	+	0.173446i	$0.944510\pi$
$678$		0			0
$679$	13.5103	−	11.3365i	0.518476	−	0.435053i
$680$		0			0
$681$	3.18954	+	18.0888i	0.122223	+	0.693164i
$682$		0			0
$683$	26.4825			1.01332			0.506662	−	0.862145i	$-0.330879\pi$
$683$	26.4825			1.01332			0.506662	+	0.862145i	$0.330879\pi$
$684$		0			0
$685$	0.0760373			0.00290524
$686$		0			0
$687$	−0.672304	−	3.81283i	−0.0256500	−	0.145468i
$688$		0			0
$689$	3.33725	−	2.80028i	0.127139	−	0.106682i
$690$		0			0
$691$	16.7003	−	28.9257i	0.635308	−	1.10039i	−0.351141	−	0.936322i	$-0.614206\pi$
$691$	16.7003	−	28.9257i	0.635308	−	1.10039i	0.986450	−	0.164064i	$-0.0524603\pi$
$692$		0			0
$693$	2.44444	−	0.889704i	0.0928566	−	0.0337970i
$694$		0			0
$695$	−8.71941	−	15.1025i	−0.330746	−	0.572869i
$696$		0			0
$697$	−1.53343	+	8.69653i	−0.0580829	+	0.329405i
$698$		0			0
$699$	−12.5988	−	10.5716i	−0.476530	−	0.399856i
$700$		0			0
$701$	−17.7408	−	6.45713i	−0.670061	−	0.243882i	−0.0154871	−	0.999880i	$-0.504930\pi$
$701$	−17.7408	−	6.45713i	−0.670061	−	0.243882i	−0.654574	+	0.755998i	$0.727152\pi$
$702$		0			0
$703$	−4.70620	−	5.69323i	−0.177498	−	0.214724i
$704$		0			0
$705$	7.91147	+	2.87954i	0.297963	+	0.108450i
$706$		0			0
$707$	−5.35117	−	4.49016i	−0.201251	−	0.168870i
$708$		0			0
$709$	−0.0369988	+	0.209830i	−0.00138952	+	0.00788034i	−0.985495	−	0.169707i	$-0.945718\pi$
$709$	−0.0369988	+	0.209830i	−0.00138952	+	0.00788034i	0.984105	+	0.177587i	$0.0568291\pi$
$710$		0			0
$711$	−2.33022	−	4.03606i	−0.0873902	−	0.151364i
$712$		0			0
$713$	20.2665	−	7.37641i	0.758987	−	0.276249i
$714$		0			0
$715$	2.01636	−	3.49244i	0.0754075	−	0.130610i
$716$		0			0
$717$	2.53209	−	2.12467i	0.0945626	−	0.0793474i
$718$		0			0
$719$	2.25150	+	12.7689i	0.0839667	+	0.476199i	0.997575	+	0.0696027i	$0.0221732\pi$
$719$	2.25150	+	12.7689i	0.0839667	+	0.476199i	−0.913608	+	0.406596i	$0.866716\pi$
$720$		0			0
$721$	−0.384133			−0.0143059
$722$		0			0
$723$	−3.01548			−0.112147
$724$		0			0
$725$	−14.7909	−	83.8831i	−0.549319	−	3.11534i
$726$		0			0
$727$	−19.7062	+	16.5355i	−0.730863	+	0.613267i	−0.930367	−	0.366630i	$-0.880511\pi$
$727$	−19.7062	+	16.5355i	−0.730863	+	0.613267i	0.199504	+	0.979897i	$0.436067\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	34.5082	−	12.5600i	1.27633	−	0.464547i
$732$		0			0
$733$	−4.25995	−	7.37845i	−0.157345	−	0.272529i	0.776565	−	0.630037i	$-0.216960\pi$
$733$	−4.25995	−	7.37845i	−0.157345	−	0.272529i	−0.933910	+	0.357507i	$0.883627\pi$
$734$		0			0
$735$	−3.70187	+	20.9943i	−0.136545	+	0.774387i
$736$		0			0
$737$	−7.27063	−	6.10078i	−0.267817	−	0.224725i
$738$		0			0
$739$	−12.5030	−	4.55072i	−0.459930	−	0.167401i	0.101655	−	0.994820i	$-0.467586\pi$
$739$	−12.5030	−	4.55072i	−0.459930	−	0.167401i	−0.561585	+	0.827419i	$0.689808\pi$
$740$		0			0
$741$	1.36138	+	1.64690i	0.0500115	+	0.0605003i
$742$		0			0
$743$	−25.3307	−	9.21962i	−0.929293	−	0.338235i	−0.167364	−	0.985895i	$-0.553525\pi$
$743$	−25.3307	−	9.21962i	−0.929293	−	0.338235i	−0.761929	+	0.647660i	$0.775748\pi$
$744$		0			0
$745$	−35.7506	−	29.9983i	−1.30980	−	1.09905i
$746$		0			0
$747$	−2.16725	+	12.2911i	−0.0792956	+	0.449708i
$748$		0			0
$749$	10.3213	+	17.8770i	0.377132	+	0.653212i
$750$		0			0
$751$	17.3277	−	6.30677i	0.632297	−	0.230137i	−0.00593399	−	0.999982i	$-0.501889\pi$
$751$	17.3277	−	6.30677i	0.632297	−	0.230137i	0.638231	+	0.769845i	$0.279667\pi$
$752$		0			0
$753$	1.76739	−	3.06121i	0.0644072	−	0.111557i
$754$		0			0
$755$	0.175708	−	0.147436i	0.00639465	−	0.00536575i
$756$		0			0
$757$	5.19490	+	29.4617i	0.188812	+	1.07080i	0.920959	+	0.389659i	$0.127407\pi$
$757$	5.19490	+	29.4617i	0.188812	+	1.07080i	−0.732148	+	0.681146i	$0.761482\pi$
$758$		0			0
$759$	−18.9659			−0.688417
$760$		0			0
$761$	−28.6691			−1.03925			−0.519627	−	0.854393i	$-0.673929\pi$
$761$	−28.6691			−1.03925			−0.519627	+	0.854393i	$0.673929\pi$
$762$		0			0
$763$	2.21776	+	12.5775i	0.0802883	+	0.455337i
$764$		0			0
$765$	16.4402	−	13.7949i	0.594395	−	0.498757i
$766$		0			0
$767$	−2.79885	+	4.84775i	−0.101061	+	0.175042i
$768$		0			0
$769$	9.17277	−	3.33862i	0.330779	−	0.120394i	−0.171292	−	0.985220i	$-0.554794\pi$
$769$	9.17277	−	3.33862i	0.330779	−	0.120394i	0.502070	+	0.864827i	$0.332572\pi$
$770$		0			0
$771$	−2.35117	−	4.07234i	−0.0846752	−	0.146662i
$772$		0			0
$773$	−0.676641	+	3.83742i	−0.0243371	+	0.138023i	−0.994555	−	0.104210i	$-0.966769\pi$
$773$	−0.676641	+	3.83742i	−0.0243371	+	0.138023i	0.970218	+	0.242233i	$0.0778797\pi$
$774$		0			0
$775$	−18.5646	−	15.5776i	−0.666862	−	0.559563i
$776$		0			0
$777$	−1.95336	−	0.710966i	−0.0700765	−	0.0255058i
$778$		0			0
$779$	4.51161	−	5.29704i	0.161645	−	0.189786i
$780$		0			0
$781$	5.25712	+	1.91344i	0.188115	+	0.0684681i
$782$		0			0
$783$	6.49273	+	5.44804i	0.232031	+	0.194697i
$784$		0			0
$785$	−8.72921	+	49.5058i	−0.311559	+	1.76694i
$786$		0			0
$787$	−1.47044	−	2.54687i	−0.0524154	−	0.0907862i	0.838627	−	0.544706i	$-0.183359\pi$
$787$	−1.47044	−	2.54687i	−0.0524154	−	0.0907862i	−0.891043	+	0.453920i	$0.850025\pi$
$788$		0			0
$789$	−19.7922	+	7.20377i	−0.704621	+	0.256461i
$790$		0			0
$791$	−10.6613	+	18.4660i	−0.379073	+	0.656574i
$792$		0			0
$793$	0.0157300	−	0.0131990i	0.000558587	−	0.000468711i
$794$		0			0
$795$	5.98680	+	33.9528i	0.212330	+	1.20418i
$796$		0			0
$797$	8.26950			0.292921			0.146460	−	0.989217i	$-0.453212\pi$
$797$	8.26950			0.292921			0.146460	+	0.989217i	$0.453212\pi$
$798$		0			0
$799$	12.0060			0.424741
$800$		0			0
$801$	1.46838	+	8.32759i	0.0518826	+	0.294241i
$802$		0			0
$803$	−24.9566	+	20.9411i	−0.880699	+	0.738995i
$804$		0			0
$805$	−21.2802	+	36.8584i	−0.750028	+	1.29909i
$806$		0			0
$807$	9.47090	−	3.44713i	0.333392	−	0.121345i
$808$		0			0
$809$	1.04529	+	1.81050i	0.0367505	+	0.0636538i	0.883816	−	0.467835i	$-0.154966\pi$
$809$	1.04529	+	1.81050i	0.0367505	+	0.0636538i	−0.847065	+	0.531489i	$0.821633\pi$
$810$		0			0
$811$	−0.150177	+	0.851698i	−0.00527344	+	0.0299072i	−0.987331	−	0.158675i	$-0.949278\pi$
$811$	−0.150177	+	0.851698i	−0.00527344	+	0.0299072i	0.982057	+	0.188582i	$0.0603890\pi$
$812$		0			0
$813$	−7.47952	−	6.27606i	−0.262318	−	0.220111i
$814$		0			0
$815$	−54.9436	−	19.9978i	−1.92459	−	0.700494i
$816$		0			0
$817$	−28.4577	−	5.23416i	−0.995609	−	0.183120i
$818$		0			0
$819$	0.565055	+	0.205663i	0.0197446	+	0.00718646i
$820$		0			0
$821$	17.4394	+	14.6334i	0.608641	+	0.510710i	0.894210	−	0.447648i	$-0.147738\pi$
$821$	17.4394	+	14.6334i	0.608641	+	0.510710i	−0.285569	+	0.958358i	$0.592183\pi$
$822$		0			0
$823$	5.75056	−	32.6131i	0.200452	−	1.13682i	−0.703986	−	0.710214i	$-0.748598\pi$
$823$	5.75056	−	32.6131i	0.200452	−	1.13682i	0.904438	−	0.426606i	$-0.140291\pi$
$824$		0			0
$825$	10.6557	+	18.4562i	0.370984	+	0.642563i
$826$		0			0
$827$	−24.9158	+	9.06861i	−0.866408	+	0.315347i	−0.736712	−	0.676207i	$-0.763622\pi$
$827$	−24.9158	+	9.06861i	−0.866408	+	0.315347i	−0.129696	+	0.991554i	$0.541400\pi$
$828$		0			0
$829$	1.57873	−	2.73443i	0.0548314	−	0.0949708i	−0.837307	−	0.546733i	$-0.815871\pi$
$829$	1.57873	−	2.73443i	0.0548314	−	0.0949708i	0.892138	+	0.451762i	$0.149205\pi$
$830$		0			0
$831$	−12.9133	+	10.8355i	−0.447957	+	0.375880i
$832$		0			0
$833$	5.27894	+	29.9384i	0.182905	+	1.03730i
$834$		0			0
$835$	−7.52940			−0.260566
$836$		0			0
$837$	2.41147			0.0833527
$838$		0			0
$839$	7.31386	+	41.4790i	0.252503	+	1.43201i	0.802403	+	0.596783i	$0.203555\pi$
$839$	7.31386	+	41.4790i	0.252503	+	1.43201i	−0.549900	+	0.835230i	$0.685334\pi$
$840$		0			0
$841$	32.8148	−	27.5349i	1.13154	−	0.949479i
$842$		0			0
$843$	−5.86231	+	10.1538i	−0.201909	+	0.349716i
$844$		0			0
$845$	−46.5146	+	16.9299i	−1.60015	+	0.582407i
$846$		0			0
$847$	−3.98855	−	6.90837i	−0.137048	−	0.237375i
$848$		0			0
$849$	−3.74123	+	21.2176i	−0.128399	+	0.728185i
$850$		0			0
$851$	11.6099	+	9.74189i	0.397984	+	0.333948i
$852$		0			0
$853$	−53.1147	−	19.3322i	−1.81861	−	0.661921i	−0.995579	−	0.0939314i	$-0.970057\pi$
$853$	−53.1147	−	19.3322i	−1.81861	−	0.661921i	−0.823035	−	0.567990i	$-0.807721\pi$
$854$		0			0
$855$	−16.6741	+	2.81369i	−0.570243	+	0.0962262i
$856$		0			0
$857$	−12.3960	−	4.51179i	−0.423441	−	0.154120i	0.121505	−	0.992591i	$-0.461228\pi$
$857$	−12.3960	−	4.51179i	−0.423441	−	0.154120i	−0.544946	+	0.838471i	$0.683450\pi$
$858$		0			0
$859$	16.6623	+	13.9813i	0.568509	+	0.477036i	0.881151	−	0.472836i	$-0.156770\pi$
$859$	16.6623	+	13.9813i	0.568509	+	0.477036i	−0.312642	+	0.949871i	$0.601214\pi$
$860$		0			0
$861$	0.340022	−	1.92836i	0.0115879	−	0.0657184i
$862$		0			0
$863$	−23.4550	−	40.6253i	−0.798418	−	1.38290i	−0.920646	−	0.390398i	$-0.872337\pi$
$863$	−23.4550	−	40.6253i	−0.798418	−	1.38290i	0.122228	−	0.992502i	$-0.460996\pi$
$864$		0			0
$865$	58.5890	−	21.3247i	1.99209	−	0.725061i
$866$		0			0
$867$	6.80200	−	11.7814i	0.231008	−	0.400118i
$868$		0			0
$869$	7.57082	−	6.35267i	0.256823	−	0.215500i
$870$		0			0
$871$	−0.380978	−	2.16063i	−0.0129089	−	0.0732102i
$872$		0			0
$873$	−14.3773			−0.486599
$874$		0			0
$875$	24.0300			0.812363
$876$		0			0
$877$	−0.464451	−	2.63403i	−0.0156834	−	0.0889450i	0.975961	−	0.217944i	$-0.0699349\pi$
$877$	−0.464451	−	2.63403i	−0.0156834	−	0.0889450i	−0.991645	+	0.128999i	$0.958824\pi$
$878$		0			0
$879$	8.51889	−	7.14819i	0.287335	−	0.241103i
$880$		0			0
$881$	13.5548	−	23.4777i	0.456674	−	0.790983i	−0.542108	−	0.840309i	$-0.682374\pi$
$881$	13.5548	−	23.4777i	0.456674	−	0.790983i	0.998783	+	0.0493254i	$0.0157071\pi$
$882$		0			0
$883$	−40.8055	+	14.8520i	−1.37321	+	0.499809i	−0.920114	−	0.391651i	$-0.871904\pi$
$883$	−40.8055	+	14.8520i	−1.37321	+	0.499809i	−0.453099	+	0.891460i	$0.649682\pi$
$884$		0			0
$885$	−22.1498	−	38.3645i	−0.744556	−	1.28961i
$886$		0			0
$887$	3.72251	−	21.1114i	0.124990	−	0.708851i	−0.856325	−	0.516438i	$-0.827258\pi$
$887$	3.72251	−	21.1114i	0.124990	−	0.708851i	0.981314	−	0.192413i	$-0.0616313\pi$
$888$		0			0
$889$	−1.53209	−	1.28558i	−0.0513846	−	0.0431168i
$890$		0			0
$891$	−1.99273	−	0.725293i	−0.0667588	−	0.0242982i
$892$		0			0
$893$	−8.15745	−	4.79012i	−0.272979	−	0.160295i
$894$		0			0
$895$	−53.8585	−	19.6029i	−1.80029	−	0.655252i
$896$		0			0
$897$	−3.35844	−	2.81807i	−0.112135	−	0.0940925i
$898$		0			0
$899$	3.54916	−	20.1283i	0.118371	−	0.671317i
$900$		0			0
$901$	24.5822	+	42.5776i	0.818951	+	1.41847i
$902$		0			0
$903$	−7.65183	+	2.78504i	−0.254637	+	0.0926802i
$904$		0			0
$905$	−35.3542	+	61.2352i	−1.17521	+	2.03553i
$906$		0			0
$907$	12.5471	−	10.5283i	0.416620	−	0.349585i	−0.410256	−	0.911971i	$-0.634561\pi$
$907$	12.5471	−	10.5283i	0.416620	−	0.349585i	0.826875	+	0.562385i	$0.190116\pi$
$908$		0			0
$909$	0.988856	+	5.60808i	0.0327983	+	0.186008i
$910$		0			0
$911$	−28.4502			−0.942596			−0.471298	−	0.881974i	$-0.656214\pi$
$911$	−28.4502			−0.942596			−0.471298	+	0.881974i	$0.656214\pi$
$912$		0			0
$913$	−26.4668			−0.875922
$914$		0			0
$915$	0.0282185	+	0.160035i	0.000932875	+	0.00529059i
$916$		0			0
$917$	5.60354	−	4.70193i	0.185045	−	0.155271i
$918$		0			0
$919$	−25.6268	+	44.3869i	−0.845349	+	1.46419i	0.0399689	+	0.999201i	$0.487274\pi$
$919$	−25.6268	+	44.3869i	−0.845349	+	1.46419i	−0.885318	+	0.464986i	$0.846059\pi$
$920$		0			0
$921$	−23.5300	+	8.56423i	−0.775341	+	0.282201i
$922$		0			0
$923$	0.646612	+	1.11996i	0.0212835	+	0.0368641i
$924$		0			0
$925$	2.95723	−	16.7713i	0.0972332	−	0.551437i
$926$		0			0
$927$	0.239885	+	0.201288i	0.00787887	+	0.00661116i
$928$		0			0
$929$	−48.4445	−	17.6324i	−1.58941	−	0.578499i	−0.612189	−	0.790712i	$-0.709711\pi$
$929$	−48.4445	−	17.6324i	−1.58941	−	0.578499i	−0.977223	+	0.212213i	$0.931933\pi$
$930$		0			0
$931$	8.35797	−	22.4478i	0.273922	−	0.735696i
$932$		0			0
$933$	−0.0530334	−	0.0193026i	−0.00173624	−	0.000631938i
$934$		0			0
$935$	34.8632	+	29.2537i	1.14015	+	0.956699i
$936$		0			0
$937$	−2.51161	+	14.2441i	−0.0820508	+	0.465333i	0.915903	+	0.401399i	$0.131476\pi$
$937$	−2.51161	+	14.2441i	−0.0820508	+	0.465333i	−0.997954	+	0.0639341i	$0.979635\pi$
$938$		0			0
$939$	6.88191	+	11.9198i	0.224583	+	0.388989i
$940$		0			0
$941$	12.3855	−	4.50795i	0.403755	−	0.146955i	−0.132157	−	0.991229i	$-0.542190\pi$
$941$	12.3855	−	4.50795i	0.403755	−	0.146955i	0.535912	+	0.844274i	$0.319968\pi$
$942$		0			0
$943$	−7.13816	+	12.3636i	−0.232450	+	0.402616i
$944$		0			0
$945$	−3.64543	+	3.05888i	−0.118586	+	0.0995053i
$946$		0			0
$947$	7.43676	+	42.1759i	0.241662	+	1.37053i	0.828119	+	0.560553i	$0.189411\pi$
$947$	7.43676	+	42.1759i	0.241662	+	1.37053i	−0.586456	+	0.809981i	$0.699477\pi$
$948$		0			0
$949$	−7.53083			−0.244461
$950$		0			0
$951$	−10.9040			−0.353588
$952$		0			0
$953$	−5.59451	−	31.7281i	−0.181224	−	1.02777i	−0.930712	−	0.365754i	$-0.880811\pi$
$953$	−5.59451	−	31.7281i	−0.181224	−	1.02777i	0.749488	−	0.662018i	$-0.230300\pi$
$954$		0			0
$955$	3.83615	−	3.21891i	0.124135	−	0.104162i
$956$		0			0
$957$	−8.98680	+	15.5656i	−0.290502	+	0.503164i
$958$		0			0
$959$	−0.0225934	+	0.00822333i	−0.000729579	+	0.000265545i
$960$		0			0
$961$	12.5924	+	21.8107i	0.406206	+	0.703570i
$962$		0			0
$963$	2.92215	−	16.5723i	0.0941650	−	0.534036i
$964$		0			0
$965$	27.1045	+	22.7434i	0.872524	+	0.732134i
$966$		0			0
$967$	32.4650	+	11.8163i	1.04400	+	0.379986i	0.806396	−	0.591375i	$-0.201415\pi$
$967$	32.4650	+	11.8163i	1.04400	+	0.379986i	0.237607	+	0.971361i	$0.423637\pi$
$968$		0			0
$969$	−20.9714	+	11.9028i	−0.673697	+	0.382375i
$970$		0			0
$971$	−1.11556	−	0.406031i	−0.0358001	−	0.0130302i	0.324058	−	0.946037i	$-0.394953\pi$
$971$	−1.11556	−	0.406031i	−0.0358001	−	0.0130302i	−0.359858	+	0.933007i	$0.617175\pi$
$972$		0			0
$973$	4.22416	+	3.54449i	0.135420	+	0.113631i
$974$		0			0
$975$	−0.855448	+	4.85148i	−0.0273963	+	0.155372i
$976$		0			0
$977$	−10.4413	−	18.0849i	−0.334048	−	0.578588i	0.649253	−	0.760572i	$-0.275081\pi$
$977$	−10.4413	−	18.0849i	−0.334048	−	0.578588i	−0.983302	+	0.181984i	$0.941748\pi$
$978$		0			0
$979$	−16.8506	+	6.13311i	−0.538547	+	0.196015i
$980$		0			0
$981$	5.20574	−	9.01660i	0.166206	−	0.287878i
$982$		0			0
$983$	26.8855	−	22.5596i	0.857515	−	0.719541i	−0.103916	−	0.994586i	$-0.533137\pi$
$983$	26.8855	−	22.5596i	0.857515	−	0.719541i	0.961431	+	0.275045i	$0.0886928\pi$
$984$		0			0
$985$	−12.5458	−	71.1505i	−0.399741	−	2.26704i
$986$		0			0
$987$	−2.66220			−0.0847387
$988$		0			0
$989$	59.3688			1.88782
$990$		0			0
$991$	8.63651	+	48.9801i	0.274348	+	1.55590i	0.741026	+	0.671476i	$0.234339\pi$
$991$	8.63651	+	48.9801i	0.274348	+	1.55590i	−0.466679	+	0.884427i	$0.654550\pi$
$992$		0			0
$993$	6.58125	−	5.52233i	0.208850	−	0.175246i
$994$		0			0
$995$	−16.3537	+	28.3254i	−0.518447	+	0.897976i
$996$		0			0
$997$	−39.3105	+	14.3079i	−1.24498	+	0.453134i	−0.878701	−	0.477372i	$-0.841589\pi$
$997$	−39.3105	+	14.3079i	−1.24498	+	0.453134i	−0.366275	+	0.930507i	$0.619367\pi$
$998$		0			0
$999$	0.847296	+	1.46756i	0.0268073	+	0.0464316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.c.289.1		6
4.3	odd	2		114.2.i.b.61.1	yes	6
12.11	even	2		342.2.u.d.289.1		6
19.5	even	9	inner	912.2.bo.c.385.1		6
76.43	odd	18		114.2.i.b.43.1	✓	6
76.47	odd	18		2166.2.a.t.1.1		3
76.67	even	18		2166.2.a.n.1.1		3
228.47	even	18		6498.2.a.bo.1.3		3
228.119	even	18		342.2.u.d.271.1		6
228.143	odd	18		6498.2.a.bt.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.43.1	✓	6	76.43	odd	18
114.2.i.b.61.1	yes	6	4.3	odd	2
342.2.u.d.271.1		6	228.119	even	18
342.2.u.d.289.1		6	12.11	even	2
912.2.bo.c.289.1		6	1.1	even	1	trivial
912.2.bo.c.385.1		6	19.5	even	9	inner
2166.2.a.n.1.1		3	76.67	even	18
2166.2.a.t.1.1		3	76.47	odd	18
6498.2.a.bo.1.3		3	228.47	even	18
6498.2.a.bt.1.3		3	228.143	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{3} +(-2.97178 + 2.49362i) q^{5} +(0.613341 - 1.06234i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(-1.06031 - 1.83651i) q^{11} +(0.0851223 - 0.482753i) q^{13} +(2.97178 + 2.49362i) q^{15} +(5.19846 + 1.89209i) q^{17} +(-2.77719 - 3.35965i) q^{19} +(-1.15270 - 0.419550i) q^{21} +(6.85117 + 5.74881i) q^{23} +(1.74510 - 9.89695i) q^{25} +(0.500000 + 0.866025i) q^{27} +(7.96451 - 2.89884i) q^{29} +(1.20574 - 2.08840i) q^{31} +(-1.62449 + 1.36310i) q^{33} +(0.826352 + 4.68647i) q^{35} +1.69459 q^{37} -0.490200 q^{39} +(0.277189 + 1.57202i) q^{41} +(5.08512 - 4.26692i) q^{43} +(1.93969 - 3.35965i) q^{45} +(2.03936 - 0.742267i) q^{47} +(2.74763 + 4.75903i) q^{49} +(0.960637 - 5.44804i) q^{51} +(6.80793 + 5.71253i) q^{53} +(7.73055 + 2.81369i) q^{55} +(-2.82635 + 3.31839i) q^{57} +(-10.7306 - 3.90560i) q^{59} +(0.0320889 + 0.0269258i) q^{61} +(-0.213011 + 1.20805i) q^{63} +(0.950837 + 1.64690i) q^{65} +(4.20574 - 1.53076i) q^{67} +(4.47178 - 7.74535i) q^{69} +(-2.02094 + 1.69577i) q^{71} +(-2.66772 - 15.1294i) q^{73} -10.0496 q^{75} -2.60132 q^{77} +(0.809278 + 4.58964i) q^{79} +(0.766044 - 0.642788i) q^{81} +(6.24035 - 10.8086i) q^{83} +(-20.1668 + 7.34013i) q^{85} +(-4.23783 - 7.34013i) q^{87} +(1.46838 - 8.32759i) q^{89} +(-0.460637 - 0.386520i) q^{91} +(-2.26604 - 0.824773i) q^{93} +(16.6309 + 3.05888i) q^{95} +(13.5103 + 4.91734i) q^{97} +(1.62449 + 1.36310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 - 12 * q^11 - 21 * q^13 + 3 * q^15 + 3 * q^17 - 6 * q^19 - 9 * q^21 + 15 * q^23 + 9 * q^25 + 3 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 9 * q^43 + 6 * q^45 + 21 * q^47 - 3 * q^51 + 30 * q^53 + 9 * q^55 - 18 * q^57 - 27 * q^59 - 9 * q^61 - 9 * q^63 - 6 * q^65 + 15 * q^67 + 12 * q^69 - 9 * q^71 + 12 * q^73 - 6 * q^75 + 42 * q^77 - 15 * q^79 + 3 * q^83 - 36 * q^85 - 6 * q^87 - 48 * q^89 + 6 * q^91 - 9 * q^93 + 48 * q^95 + 18 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more