LMFDB - Embedded newform 308.2.j.a.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	308.113
Dual form			308.2.j.a.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 3.07768i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-6.04508 + 4.39201i) q^{9} +O(q^{10})$	\(q+(1.00000 + 3.07768i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-6.04508 + 4.39201i) q^{9} +(2.19098 + 2.48990i) q^{11} +(-2.61803 + 1.90211i) q^{13} +(2.00000 - 6.15537i) q^{15} +(3.23607 + 2.35114i) q^{17} +(-0.618034 - 1.90211i) q^{19} -3.23607 q^{21} +0.618034 q^{23} +(-0.309017 - 0.951057i) q^{25} +(-11.7082 - 8.50651i) q^{27} +(-0.263932 + 0.812299i) q^{29} +(3.61803 - 2.62866i) q^{31} +(-5.47214 + 9.23305i) q^{33} +(1.61803 - 1.17557i) q^{35} +(3.04508 - 9.37181i) q^{37} +(-8.47214 - 6.15537i) q^{39} +(3.61803 + 11.1352i) q^{41} +10.8541 q^{43} +14.9443 q^{45} +(3.09017 + 9.51057i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-4.00000 + 12.3107i) q^{51} +(7.78115 - 5.65334i) q^{53} +(-0.618034 - 6.60440i) q^{55} +(5.23607 - 3.80423i) q^{57} +(-1.14590 + 3.52671i) q^{59} +(-0.381966 - 0.277515i) q^{61} +(-2.30902 - 7.10642i) q^{63} +6.47214 q^{65} +0.381966 q^{67} +(0.618034 + 1.90211i) q^{69} +(-1.54508 - 1.12257i) q^{71} +(-4.52786 + 13.9353i) q^{73} +(2.61803 - 1.90211i) q^{75} +(-3.04508 + 1.31433i) q^{77} +(4.92705 - 3.57971i) q^{79} +(7.54508 - 23.2214i) q^{81} +(-12.0902 - 8.78402i) q^{83} +(-2.47214 - 7.60845i) q^{85} -2.76393 q^{87} -6.76393 q^{89} +(-1.00000 - 3.07768i) q^{91} +(11.7082 + 8.50651i) q^{93} +(-1.23607 + 3.80423i) q^{95} +(12.4721 - 9.06154i) q^{97} +(-24.1803 - 5.42882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9	$ 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9} + 11 q^{11} - 6 q^{13} + 8 q^{15} + 4 q^{17} + 2 q^{19} - 4 q^{21} - 2 q^{23} + q^{25} - 20 q^{27} - 10 q^{29} + 10 q^{31} - 4 q^{33} + 2 q^{35} + q^{37} - 16 q^{39} + 10 q^{41} + 30 q^{43} + 24 q^{45} - 10 q^{47} - q^{49} - 16 q^{51} + 11 q^{53} + 2 q^{55} + 12 q^{57} - 18 q^{59} - 6 q^{61} - 7 q^{63} + 8 q^{65} + 6 q^{67} - 2 q^{69} + 5 q^{71} - 36 q^{73} + 6 q^{75} - q^{77} + 13 q^{79} + 19 q^{81} - 26 q^{83} + 8 q^{85} - 20 q^{87} - 36 q^{89} - 4 q^{91} + 20 q^{93} + 4 q^{95} + 32 q^{97} - 52 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9 + 11 * q^11 - 6 * q^13 + 8 * q^15 + 4 * q^17 + 2 * q^19 - 4 * q^21 - 2 * q^23 + q^25 - 20 * q^27 - 10 * q^29 + 10 * q^31 - 4 * q^33 + 2 * q^35 + q^37 - 16 * q^39 + 10 * q^41 + 30 * q^43 + 24 * q^45 - 10 * q^47 - q^49 - 16 * q^51 + 11 * q^53 + 2 * q^55 + 12 * q^57 - 18 * q^59 - 6 * q^61 - 7 * q^63 + 8 * q^65 + 6 * q^67 - 2 * q^69 + 5 * q^71 - 36 * q^73 + 6 * q^75 - q^77 + 13 * q^79 + 19 * q^81 - 26 * q^83 + 8 * q^85 - 20 * q^87 - 36 * q^89 - 4 * q^91 + 20 * q^93 + 4 * q^95 + 32 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	1.00000	+	3.07768i	0.577350	+	1.77690i	0.628033	+	0.778187i	$0.283860\pi$
$3$	1.00000	+	3.07768i	0.577350	+	1.77690i	−0.0506828	+	0.998715i	$0.516140\pi$
$4$		0			0
$5$	−1.61803	−	1.17557i	−0.723607	−	0.525731i	0.163928	−	0.986472i	$-0.447584\pi$
$5$	−1.61803	−	1.17557i	−0.723607	−	0.525731i	−0.887535	+	0.460741i	$0.847584\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	−6.04508	+	4.39201i	−2.01503	+	1.46400i
$10$		0			0
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$12$		0			0
$13$	−2.61803	+	1.90211i	−0.726112	+	0.527551i	−0.888331	−	0.459204i	$-0.848135\pi$
$13$	−2.61803	+	1.90211i	−0.726112	+	0.527551i	0.162219	+	0.986755i	$0.448135\pi$
$14$		0			0
$15$	2.00000	−	6.15537i	0.516398	−	1.58931i
$16$		0			0
$17$	3.23607	+	2.35114i	0.784862	+	0.570235i	0.906434	−	0.422347i	$-0.138794\pi$
$17$	3.23607	+	2.35114i	0.784862	+	0.570235i	−0.121572	+	0.992583i	$0.538794\pi$
$18$		0			0
$19$	−0.618034	−	1.90211i	−0.141787	−	0.436375i	0.854797	−	0.518962i	$-0.173682\pi$
$19$	−0.618034	−	1.90211i	−0.141787	−	0.436375i	−0.996584	+	0.0825877i	$0.973682\pi$
$20$		0			0
$21$	−3.23607			−0.706168
$22$		0			0
$23$	0.618034			0.128869			0.0644345	−	0.997922i	$-0.479476\pi$
$23$	0.618034			0.128869			0.0644345	+	0.997922i	$0.479476\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	−11.7082	−	8.50651i	−2.25324	−	1.63708i
$28$		0			0
$29$	−0.263932	+	0.812299i	−0.0490109	+	0.150840i	−0.972567	−	0.232624i	$-0.925269\pi$
$29$	−0.263932	+	0.812299i	−0.0490109	+	0.150840i	0.923556	+	0.383464i	$0.125269\pi$
$30$		0			0
$31$	3.61803	−	2.62866i	0.649818	−	0.472120i	−0.213391	−	0.976967i	$-0.568451\pi$
$31$	3.61803	−	2.62866i	0.649818	−	0.472120i	0.863209	+	0.504846i	$0.168451\pi$
$32$		0			0
$33$	−5.47214	+	9.23305i	−0.952577	+	1.60727i
$34$		0			0
$35$	1.61803	−	1.17557i	0.273498	−	0.198708i
$36$		0			0
$37$	3.04508	−	9.37181i	0.500609	−	1.54072i	−0.307421	−	0.951574i	$-0.599466\pi$
$37$	3.04508	−	9.37181i	0.500609	−	1.54072i	0.808030	−	0.589142i	$-0.200534\pi$
$38$		0			0
$39$	−8.47214	−	6.15537i	−1.35663	−	0.985648i
$40$		0			0
$41$	3.61803	+	11.1352i	0.565042	+	1.73902i	0.667827	+	0.744317i	$0.267225\pi$
$41$	3.61803	+	11.1352i	0.565042	+	1.73902i	−0.102785	+	0.994704i	$0.532775\pi$
$42$		0			0
$43$	10.8541			1.65524			0.827618	−	0.561292i	$-0.189696\pi$
$43$	10.8541			1.65524			0.827618	+	0.561292i	$0.189696\pi$
$44$		0			0
$45$	14.9443			2.22776
$46$		0			0
$47$	3.09017	+	9.51057i	0.450748	+	1.38726i	0.876056	+	0.482210i	$0.160166\pi$
$47$	3.09017	+	9.51057i	0.450748	+	1.38726i	−0.425308	+	0.905049i	$0.639834\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	−4.00000	+	12.3107i	−0.560112	+	1.72385i
$52$		0			0
$53$	7.78115	−	5.65334i	1.06882	−	0.776546i	0.0931231	−	0.995655i	$-0.470315\pi$
$53$	7.78115	−	5.65334i	1.06882	−	0.776546i	0.975700	+	0.219109i	$0.0703150\pi$
$54$		0			0
$55$	−0.618034	−	6.60440i	−0.0833357	−	0.890536i
$56$		0			0
$57$	5.23607	−	3.80423i	0.693534	−	0.503882i
$58$		0			0
$59$	−1.14590	+	3.52671i	−0.149183	+	0.459139i	−0.997525	−	0.0703099i	$-0.977601\pi$
$59$	−1.14590	+	3.52671i	−0.149183	+	0.459139i	0.848342	+	0.529449i	$0.177601\pi$
$60$		0			0
$61$	−0.381966	−	0.277515i	−0.0489057	−	0.0355321i	0.563064	−	0.826413i	$-0.309623\pi$
$61$	−0.381966	−	0.277515i	−0.0489057	−	0.0355321i	−0.611970	+	0.790881i	$0.709623\pi$
$62$		0			0
$63$	−2.30902	−	7.10642i	−0.290909	−	0.895325i
$64$		0			0
$65$	6.47214			0.802770
$66$		0			0
$67$	0.381966			0.0466646			0.0233323	−	0.999728i	$-0.492572\pi$
$67$	0.381966			0.0466646			0.0233323	+	0.999728i	$0.492572\pi$
$68$		0			0
$69$	0.618034	+	1.90211i	0.0744025	+	0.228988i
$70$		0			0
$71$	−1.54508	−	1.12257i	−0.183368	−	0.133225i	0.492315	−	0.870417i	$-0.336151\pi$
$71$	−1.54508	−	1.12257i	−0.183368	−	0.133225i	−0.675682	+	0.737193i	$0.736151\pi$
$72$		0			0
$73$	−4.52786	+	13.9353i	−0.529946	+	1.63101i	0.224376	+	0.974503i	$0.427966\pi$
$73$	−4.52786	+	13.9353i	−0.529946	+	1.63101i	−0.754322	+	0.656505i	$0.772034\pi$
$74$		0			0
$75$	2.61803	−	1.90211i	0.302305	−	0.219637i
$76$		0			0
$77$	−3.04508	+	1.31433i	−0.347020	+	0.149782i
$78$		0			0
$79$	4.92705	−	3.57971i	0.554337	−	0.402749i	−0.275045	−	0.961431i	$-0.588693\pi$
$79$	4.92705	−	3.57971i	0.554337	−	0.402749i	0.829382	+	0.558682i	$0.188693\pi$
$80$		0			0
$81$	7.54508	−	23.2214i	0.838343	−	2.58015i
$82$		0			0
$83$	−12.0902	−	8.78402i	−1.32707	−	0.964172i	−0.999815	−	0.0192352i	$-0.993877\pi$
$83$	−12.0902	−	8.78402i	−1.32707	−	0.964172i	−0.327254	−	0.944937i	$-0.606123\pi$
$84$		0			0
$85$	−2.47214	−	7.60845i	−0.268141	−	0.825253i
$86$		0			0
$87$	−2.76393			−0.296325
$88$		0			0
$89$	−6.76393			−0.716975			−0.358488	−	0.933534i	$-0.616707\pi$
$89$	−6.76393			−0.716975			−0.358488	+	0.933534i	$0.616707\pi$
$90$		0			0
$91$	−1.00000	−	3.07768i	−0.104828	−	0.322629i
$92$		0			0
$93$	11.7082	+	8.50651i	1.21408	+	0.882084i
$94$		0			0
$95$	−1.23607	+	3.80423i	−0.126818	+	0.390305i
$96$		0			0
$97$	12.4721	−	9.06154i	1.26635	−	0.920060i	0.267302	−	0.963613i	$-0.413868\pi$
$97$	12.4721	−	9.06154i	1.26635	−	0.920060i	0.999051	+	0.0435530i	$0.0138677\pi$
$98$		0			0
$99$	−24.1803	−	5.42882i	−2.43022	−	0.545617i
$100$		0			0
$101$	−0.618034	+	0.449028i	−0.0614967	+	0.0446800i	−0.618109	−	0.786092i	$-0.712101\pi$
$101$	−0.618034	+	0.449028i	−0.0614967	+	0.0446800i	0.556612	+	0.830772i	$0.312101\pi$
$102$		0			0
$103$	3.00000	−	9.23305i	0.295599	−	0.909760i	−0.687421	−	0.726259i	$-0.741257\pi$
$103$	3.00000	−	9.23305i	0.295599	−	0.909760i	0.983020	−	0.183500i	$-0.0587428\pi$
$104$		0			0
$105$	5.23607	+	3.80423i	0.510988	+	0.371254i
$106$		0			0
$107$	−3.89919	−	12.0005i	−0.376949	−	1.16013i	−0.942155	−	0.335179i	$-0.891203\pi$
$107$	−3.89919	−	12.0005i	−0.376949	−	1.16013i	0.565206	−	0.824950i	$-0.308797\pi$
$108$		0			0
$109$	−16.6180			−1.59172			−0.795859	−	0.605481i	$-0.792981\pi$
$109$	−16.6180			−1.59172			−0.795859	+	0.605481i	$0.792981\pi$
$110$		0			0
$111$	31.8885			3.02673
$112$		0			0
$113$	−2.50000	−	7.69421i	−0.235180	−	0.723810i	−0.997097	−	0.0761359i	$-0.975742\pi$
$113$	−2.50000	−	7.69421i	−0.235180	−	0.723810i	0.761917	−	0.647674i	$-0.224258\pi$
$114$		0			0
$115$	−1.00000	−	0.726543i	−0.0932505	−	0.0677504i
$116$		0			0
$117$	7.47214	−	22.9969i	0.690799	−	2.12606i
$118$		0			0
$119$	−3.23607	+	2.35114i	−0.296650	+	0.215529i
$120$		0			0
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$		0			0
$123$	−30.6525	+	22.2703i	−2.76384	+	2.00805i
$124$		0			0
$125$	−3.70820	+	11.4127i	−0.331672	+	1.02078i
$126$		0			0
$127$	−2.97214	−	2.15938i	−0.263734	−	0.191614i	0.448057	−	0.894005i	$-0.352116\pi$
$127$	−2.97214	−	2.15938i	−0.263734	−	0.191614i	−0.711792	+	0.702391i	$0.752116\pi$
$128$		0			0
$129$	10.8541	+	33.4055i	0.955650	+	2.94119i
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	2.00000			0.173422
$134$		0			0
$135$	8.94427	+	27.5276i	0.769800	+	2.36920i
$136$		0			0
$137$	6.50000	+	4.72253i	0.555332	+	0.403473i	0.829748	−	0.558139i	$-0.188484\pi$
$137$	6.50000	+	4.72253i	0.555332	+	0.403473i	−0.274415	+	0.961611i	$0.588484\pi$
$138$		0			0
$139$	0.381966	−	1.17557i	0.0323979	−	0.0997106i	−0.933550	−	0.358447i	$-0.883306\pi$
$139$	0.381966	−	1.17557i	0.0323979	−	0.0997106i	0.965948	+	0.258737i	$0.0833062\pi$
$140$		0			0
$141$	−26.1803	+	19.0211i	−2.20478	+	1.60187i
$142$		0			0
$143$	−10.4721	−	2.35114i	−0.875724	−	0.196612i
$144$		0			0
$145$	1.38197	−	1.00406i	0.114766	−	0.0833824i
$146$		0			0
$147$	1.00000	−	3.07768i	0.0824786	−	0.253843i
$148$		0			0
$149$	6.85410	+	4.97980i	0.561510	+	0.407961i	0.832011	−	0.554759i	$-0.187189\pi$
$149$	6.85410	+	4.97980i	0.561510	+	0.407961i	−0.270501	+	0.962720i	$0.587189\pi$
$150$		0			0
$151$	2.86475	+	8.81678i	0.233130	+	0.717499i	0.997364	+	0.0725606i	$0.0231171\pi$
$151$	2.86475	+	8.81678i	0.233130	+	0.717499i	−0.764234	+	0.644939i	$0.776883\pi$
$152$		0			0
$153$	−29.8885			−2.41635
$154$		0			0
$155$	−8.94427			−0.718421
$156$		0			0
$157$	−5.00000	−	15.3884i	−0.399043	−	1.22813i	−0.925768	−	0.378093i	$-0.876580\pi$
$157$	−5.00000	−	15.3884i	−0.399043	−	1.22813i	0.526724	−	0.850036i	$-0.323420\pi$
$158$		0			0
$159$	25.1803	+	18.2946i	1.99693	+	1.45086i
$160$		0			0
$161$	−0.190983	+	0.587785i	−0.0150516	+	0.0463240i
$162$		0			0
$163$	10.7361	−	7.80021i	0.840914	−	0.610960i	−0.0817120	−	0.996656i	$-0.526039\pi$
$163$	10.7361	−	7.80021i	0.840914	−	0.610960i	0.922626	+	0.385696i	$0.126039\pi$
$164$		0			0
$165$	19.7082	−	8.50651i	1.53428	−	0.662231i
$166$		0			0
$167$	16.9443	−	12.3107i	1.31119	−	0.952633i	0.311190	−	0.950348i	$-0.399273\pi$
$167$	16.9443	−	12.3107i	1.31119	−	0.952633i	0.999997	−	0.00228541i	$-0.000727468\pi$
$168$		0			0
$169$	−0.781153	+	2.40414i	−0.0600887	+	0.184934i
$170$		0			0
$171$	12.0902	+	8.78402i	0.924558	+	0.671731i
$172$		0			0
$173$	3.00000	+	9.23305i	0.228086	+	0.701976i	0.997964	+	0.0637846i	$0.0203171\pi$
$173$	3.00000	+	9.23305i	0.228086	+	0.701976i	−0.769878	+	0.638191i	$0.779683\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	−12.0000			−0.901975
$178$		0			0
$179$	1.42705	+	4.39201i	0.106663	+	0.328274i	0.990117	−	0.140243i	$-0.0447884\pi$
$179$	1.42705	+	4.39201i	0.106663	+	0.328274i	−0.883454	+	0.468517i	$0.844788\pi$
$180$		0			0
$181$	−16.9443	−	12.3107i	−1.25946	−	0.915050i	−0.260727	−	0.965413i	$-0.583962\pi$
$181$	−16.9443	−	12.3107i	−1.25946	−	0.915050i	−0.998731	+	0.0503630i	$0.983962\pi$
$182$		0			0
$183$	0.472136	−	1.45309i	0.0349013	−	0.107415i
$184$		0			0
$185$	−15.9443	+	11.5842i	−1.17225	+	0.851687i
$186$		0			0
$187$	1.23607	+	13.2088i	0.0903902	+	0.965922i
$188$		0			0
$189$	11.7082	−	8.50651i	0.851647	−	0.618757i
$190$		0			0
$191$	2.35410	−	7.24518i	0.170337	−	0.524243i	−0.829053	−	0.559170i	$-0.811120\pi$
$191$	2.35410	−	7.24518i	0.170337	−	0.524243i	0.999390	+	0.0349271i	$0.0111199\pi$
$192$		0			0
$193$	−16.8713	−	12.2577i	−1.21442	−	0.882331i	−0.218799	−	0.975770i	$-0.570214\pi$
$193$	−16.8713	−	12.2577i	−1.21442	−	0.882331i	−0.995625	+	0.0934389i	$0.970214\pi$
$194$		0			0
$195$	6.47214	+	19.9192i	0.463479	+	1.42644i
$196$		0			0
$197$	−18.7984			−1.33933			−0.669664	−	0.742664i	$-0.733562\pi$
$197$	−18.7984			−1.33933			−0.669664	+	0.742664i	$0.733562\pi$
$198$		0			0
$199$	−8.18034			−0.579889			−0.289944	−	0.957043i	$-0.593637\pi$
$199$	−8.18034			−0.579889			−0.289944	+	0.957043i	$0.593637\pi$
$200$		0			0
$201$	0.381966	+	1.17557i	0.0269418	+	0.0829184i
$202$		0			0
$203$	−0.690983	−	0.502029i	−0.0484975	−	0.0352355i
$204$		0			0
$205$	7.23607	−	22.2703i	0.505389	−	1.55543i
$206$		0			0
$207$	−3.73607	+	2.71441i	−0.259675	+	0.188665i
$208$		0			0
$209$	3.38197	−	5.70634i	0.233935	−	0.394716i
$210$		0			0
$211$	9.73607	−	7.07367i	0.670259	−	0.486971i	−0.199853	−	0.979826i	$-0.564047\pi$
$211$	9.73607	−	7.07367i	0.670259	−	0.486971i	0.870112	+	0.492855i	$0.164047\pi$
$212$		0			0
$213$	1.90983	−	5.87785i	0.130859	−	0.402744i
$214$		0			0
$215$	−17.5623	−	12.7598i	−1.19774	−	0.870209i
$216$		0			0
$217$	1.38197	+	4.25325i	0.0938140	+	0.288730i
$218$		0			0
$219$	−47.4164			−3.20410
$220$		0			0
$221$	−12.9443			−0.870726
$222$		0			0
$223$	−3.52786	−	10.8576i	−0.236243	−	0.727082i	−0.996954	−	0.0779910i	$-0.975149\pi$
$223$	−3.52786	−	10.8576i	−0.236243	−	0.727082i	0.760711	−	0.649091i	$-0.224851\pi$
$224$		0			0
$225$	6.04508	+	4.39201i	0.403006	+	0.292801i
$226$		0			0
$227$	−2.29180	+	7.05342i	−0.152112	+	0.468152i	−0.997857	−	0.0654352i	$-0.979156\pi$
$227$	−2.29180	+	7.05342i	−0.152112	+	0.468152i	0.845745	+	0.533587i	$0.179156\pi$
$228$		0			0
$229$	−15.5623	+	11.3067i	−1.02839	+	0.747166i	−0.967985	−	0.251008i	$-0.919238\pi$
$229$	−15.5623	+	11.3067i	−1.02839	+	0.747166i	−0.0604011	+	0.998174i	$0.519238\pi$
$230$		0			0
$231$	−7.09017	−	8.05748i	−0.466499	−	0.530143i
$232$		0			0
$233$	15.7984	−	11.4782i	1.03499	−	0.751961i	0.0656854	−	0.997840i	$-0.479077\pi$
$233$	15.7984	−	11.4782i	1.03499	−	0.751961i	0.969300	+	0.245879i	$0.0790766\pi$
$234$		0			0
$235$	6.18034	−	19.0211i	0.403161	−	1.24080i
$236$		0			0
$237$	15.9443	+	11.5842i	1.03569	+	0.752474i
$238$		0			0
$239$	8.29837	+	25.5398i	0.536777	+	1.65203i	0.739777	+	0.672852i	$0.234931\pi$
$239$	8.29837	+	25.5398i	0.536777	+	1.65203i	−0.203000	+	0.979179i	$0.565069\pi$
$240$		0			0
$241$	2.47214			0.159244			0.0796221	−	0.996825i	$-0.474629\pi$
$241$	2.47214			0.159244			0.0796221	+	0.996825i	$0.474629\pi$
$242$		0			0
$243$	35.5967			2.28353
$244$		0			0
$245$	0.618034	+	1.90211i	0.0394847	+	0.121522i
$246$		0			0
$247$	5.23607	+	3.80423i	0.333163	+	0.242057i
$248$		0			0
$249$	14.9443	−	45.9937i	0.947055	−	2.91473i
$250$		0			0
$251$	11.8541	−	8.61251i	0.748224	−	0.543617i	−0.147052	−	0.989129i	$-0.546978\pi$
$251$	11.8541	−	8.61251i	0.748224	−	0.543617i	0.895276	+	0.445512i	$0.146978\pi$
$252$		0			0
$253$	1.35410	+	1.53884i	0.0851317	+	0.0967462i
$254$		0			0
$255$	20.9443	−	15.2169i	1.31158	−	0.952920i
$256$		0			0
$257$	−2.14590	+	6.60440i	−0.133857	+	0.411971i	−0.995411	−	0.0956966i	$-0.969492\pi$
$257$	−2.14590	+	6.60440i	−0.133857	+	0.411971i	0.861553	+	0.507667i	$0.169492\pi$
$258$		0			0
$259$	7.97214	+	5.79210i	0.495364	+	0.359903i
$260$		0			0
$261$	−1.97214	−	6.06961i	−0.122072	−	0.375699i
$262$		0			0
$263$	15.0344			0.927063			0.463532	−	0.886080i	$-0.346582\pi$
$263$	15.0344			0.927063			0.463532	+	0.886080i	$0.346582\pi$
$264$		0			0
$265$	−19.2361			−1.18166
$266$		0			0
$267$	−6.76393	−	20.8172i	−0.413946	−	1.27399i
$268$		0			0
$269$	6.23607	+	4.53077i	0.380220	+	0.276246i	0.761436	−	0.648240i	$-0.224495\pi$
$269$	6.23607	+	4.53077i	0.380220	+	0.276246i	−0.381216	+	0.924486i	$0.624495\pi$
$270$		0			0
$271$	−1.18034	+	3.63271i	−0.0717005	+	0.220672i	−0.980485	−	0.196595i	$-0.937012\pi$
$271$	−1.18034	+	3.63271i	−0.0717005	+	0.220672i	0.908784	+	0.417266i	$0.137012\pi$
$272$		0			0
$273$	8.47214	−	6.15537i	0.512757	−	0.372540i
$274$		0			0
$275$	1.69098	−	2.85317i	0.101970	−	0.172053i
$276$		0			0
$277$	−21.4443	+	15.5802i	−1.28846	+	0.936122i	−0.999773	−	0.0213011i	$-0.993219\pi$
$277$	−21.4443	+	15.5802i	−1.28846	+	0.936122i	−0.288688	+	0.957423i	$0.593219\pi$
$278$		0			0
$279$	−10.3262	+	31.7809i	−0.618216	+	1.90267i
$280$		0			0
$281$	−0.0729490	−	0.0530006i	−0.00435177	−	0.00316175i	0.585607	−	0.810595i	$-0.300856\pi$
$281$	−0.0729490	−	0.0530006i	−0.00435177	−	0.00316175i	−0.589959	+	0.807433i	$0.700856\pi$
$282$		0			0
$283$	−4.00000	−	12.3107i	−0.237775	−	0.731797i	−0.996741	−	0.0806667i	$-0.974295\pi$
$283$	−4.00000	−	12.3107i	−0.237775	−	0.731797i	0.758966	−	0.651130i	$-0.225705\pi$
$284$		0			0
$285$	−12.9443			−0.766752
$286$		0			0
$287$	−11.7082			−0.691113
$288$		0			0
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$		0			0
$291$	40.3607	+	29.3238i	2.36598	+	1.71899i
$292$		0			0
$293$	−2.76393	+	8.50651i	−0.161471	+	0.496956i	−0.998759	−	0.0498062i	$-0.984140\pi$
$293$	−2.76393	+	8.50651i	−0.161471	+	0.496956i	0.837288	+	0.546762i	$0.184140\pi$
$294$		0			0
$295$	6.00000	−	4.35926i	0.349334	−	0.253806i
$296$		0			0
$297$	−4.47214	−	47.7899i	−0.259500	−	2.77305i
$298$		0			0
$299$	−1.61803	+	1.17557i	−0.0935733	+	0.0679850i
$300$		0			0
$301$	−3.35410	+	10.3229i	−0.193327	+	0.595000i
$302$		0			0
$303$	−2.00000	−	1.45309i	−0.114897	−	0.0834776i
$304$		0			0
$305$	0.291796	+	0.898056i	0.0167082	+	0.0514225i
$306$		0			0
$307$	2.94427			0.168038			0.0840192	−	0.996464i	$-0.473224\pi$
$307$	2.94427			0.168038			0.0840192	+	0.996464i	$0.473224\pi$
$308$		0			0
$309$	31.4164			1.78722
$310$		0			0
$311$	4.23607	+	13.0373i	0.240205	+	0.739276i	0.996388	+	0.0849157i	$0.0270621\pi$
$311$	4.23607	+	13.0373i	0.240205	+	0.739276i	−0.756183	+	0.654360i	$0.772938\pi$
$312$		0			0
$313$	5.38197	+	3.91023i	0.304207	+	0.221019i	0.729407	−	0.684080i	$-0.239796\pi$
$313$	5.38197	+	3.91023i	0.304207	+	0.221019i	−0.425200	+	0.905099i	$0.639796\pi$
$314$		0			0
$315$	−4.61803	+	14.2128i	−0.260197	+	0.800803i
$316$		0			0
$317$	−9.92705	+	7.21242i	−0.557559	+	0.405090i	−0.830565	−	0.556922i	$-0.811982\pi$
$317$	−9.92705	+	7.21242i	−0.557559	+	0.405090i	0.273006	+	0.962012i	$0.411982\pi$
$318$		0			0
$319$	−2.60081	+	1.12257i	−0.145618	+	0.0628519i
$320$		0			0
$321$	33.0344	−	24.0009i	1.84380	−	1.33960i
$322$		0			0
$323$	2.47214	−	7.60845i	0.137553	−	0.423346i
$324$		0			0
$325$	2.61803	+	1.90211i	0.145222	+	0.105510i
$326$		0			0
$327$	−16.6180	−	51.1450i	−0.918979	−	2.82833i
$328$		0			0
$329$	−10.0000			−0.551318
$330$		0			0
$331$	−1.27051			−0.0698335			−0.0349168	−	0.999390i	$-0.511117\pi$
$331$	−1.27051			−0.0698335			−0.0349168	+	0.999390i	$0.511117\pi$
$332$		0			0
$333$	22.7533	+	70.0274i	1.24687	+	3.83748i
$334$		0			0
$335$	−0.618034	−	0.449028i	−0.0337668	−	0.0245330i
$336$		0			0
$337$	−4.48278	+	13.7966i	−0.244193	+	0.751547i	0.751576	+	0.659647i	$0.229294\pi$
$337$	−4.48278	+	13.7966i	−0.244193	+	0.751547i	−0.995768	+	0.0919005i	$0.970706\pi$
$338$		0			0
$339$	21.1803	−	15.3884i	1.15036	−	0.835784i
$340$		0			0
$341$	14.4721	+	3.24920i	0.783710	+	0.175954i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	1.23607	−	3.80423i	0.0665477	−	0.204813i
$346$		0			0
$347$	−3.69098	−	2.68166i	−0.198142	−	0.143959i	0.484290	−	0.874907i	$-0.339078\pi$
$347$	−3.69098	−	2.68166i	−0.198142	−	0.143959i	−0.682433	+	0.730949i	$0.739078\pi$
$348$		0			0
$349$	−3.43769	−	10.5801i	−0.184016	−	0.566342i	0.815914	−	0.578173i	$-0.196234\pi$
$349$	−3.43769	−	10.5801i	−0.184016	−	0.566342i	−0.999930	+	0.0118310i	$0.996234\pi$
$350$		0			0
$351$	46.8328			2.49975
$352$		0			0
$353$	−9.41641			−0.501185			−0.250592	−	0.968093i	$-0.580625\pi$
$353$	−9.41641			−0.501185			−0.250592	+	0.968093i	$0.580625\pi$
$354$		0			0
$355$	1.18034	+	3.63271i	0.0626459	+	0.192804i
$356$		0			0
$357$	−10.4721	−	7.60845i	−0.554244	−	0.402682i
$358$		0			0
$359$	2.19098	−	6.74315i	0.115636	−	0.355890i	−0.876443	−	0.481505i	$-0.840090\pi$
$359$	2.19098	−	6.74315i	0.115636	−	0.355890i	0.992079	+	0.125615i	$0.0400904\pi$
$360$		0			0
$361$	12.1353	−	8.81678i	0.638698	−	0.464041i
$362$		0			0
$363$	−34.9787	+	6.60440i	−1.83591	+	0.346641i
$364$		0			0
$365$	23.7082	−	17.2250i	1.24094	−	0.901599i
$366$		0			0
$367$	−4.85410	+	14.9394i	−0.253382	+	0.779830i	0.740762	+	0.671767i	$0.234465\pi$
$367$	−4.85410	+	14.9394i	−0.253382	+	0.779830i	−0.994144	+	0.108062i	$0.965535\pi$
$368$		0			0
$369$	−70.7771	−	51.4226i	−3.68451	−	2.67695i
$370$		0			0
$371$	2.97214	+	9.14729i	0.154306	+	0.474904i
$372$		0			0
$373$	24.4721			1.26712			0.633560	−	0.773694i	$-0.281593\pi$
$373$	24.4721			1.26712			0.633560	+	0.773694i	$0.281593\pi$
$374$		0			0
$375$	−38.8328			−2.00532
$376$		0			0
$377$	−0.854102	−	2.62866i	−0.0439885	−	0.135383i
$378$		0			0
$379$	10.9721	+	7.97172i	0.563601	+	0.409480i	0.832775	−	0.553612i	$-0.186751\pi$
$379$	10.9721	+	7.97172i	0.563601	+	0.409480i	−0.269174	+	0.963091i	$0.586751\pi$
$380$		0			0
$381$	3.67376	−	11.3067i	0.188213	−	0.579259i
$382$		0			0
$383$	−2.00000	+	1.45309i	−0.102195	+	0.0742492i	−0.637709	−	0.770277i	$-0.720118\pi$
$383$	−2.00000	+	1.45309i	−0.102195	+	0.0742492i	0.535514	+	0.844526i	$0.320118\pi$
$384$		0			0
$385$	6.47214	+	1.45309i	0.329851	+	0.0740561i
$386$		0			0
$387$	−65.6140	+	47.6713i	−3.33535	+	2.42327i
$388$		0			0
$389$	7.69756	−	23.6907i	0.390282	−	1.20116i	−0.542294	−	0.840189i	$-0.682444\pi$
$389$	7.69756	−	23.6907i	0.390282	−	1.20116i	0.932576	−	0.360975i	$-0.117556\pi$
$390$		0			0
$391$	2.00000	+	1.45309i	0.101144	+	0.0734857i
$392$		0			0
$393$	4.00000	+	12.3107i	0.201773	+	0.620994i
$394$		0			0
$395$	−12.1803			−0.612859
$396$		0			0
$397$	−3.34752			−0.168007			−0.0840037	−	0.996465i	$-0.526771\pi$
$397$	−3.34752			−0.168007			−0.0840037	+	0.996465i	$0.526771\pi$
$398$		0			0
$399$	2.00000	+	6.15537i	0.100125	+	0.308154i
$400$		0			0
$401$	0.500000	+	0.363271i	0.0249688	+	0.0181409i	0.600200	−	0.799850i	$-0.295088\pi$
$401$	0.500000	+	0.363271i	0.0249688	+	0.0181409i	−0.575231	+	0.817991i	$0.695088\pi$
$402$		0			0
$403$	−4.47214	+	13.7638i	−0.222773	+	0.685625i
$404$		0			0
$405$	−39.5066	+	28.7032i	−1.96310	+	1.42627i
$406$		0			0
$407$	30.0066	−	12.9515i	1.48737	−	0.641983i
$408$		0			0
$409$	15.4164	−	11.2007i	0.762292	−	0.553838i	−0.137320	−	0.990527i	$-0.543849\pi$
$409$	15.4164	−	11.2007i	0.762292	−	0.553838i	0.899613	+	0.436689i	$0.143849\pi$
$410$		0			0
$411$	−8.03444	+	24.7275i	−0.396310	+	1.21972i
$412$		0			0
$413$	−3.00000	−	2.17963i	−0.147620	−	0.107252i
$414$		0			0
$415$	9.23607	+	28.4257i	0.453381	+	1.39536i
$416$		0			0
$417$	4.00000			0.195881
$418$		0			0
$419$	7.52786			0.367760			0.183880	−	0.982949i	$-0.441134\pi$
$419$	7.52786			0.367760			0.183880	+	0.982949i	$0.441134\pi$
$420$		0			0
$421$	−5.22542	−	16.0822i	−0.254672	−	0.783799i	−0.993894	−	0.110337i	$-0.964807\pi$
$421$	−5.22542	−	16.0822i	−0.254672	−	0.783799i	0.739223	−	0.673461i	$-0.235193\pi$
$422$		0			0
$423$	−60.4508	−	43.9201i	−2.93922	−	2.13547i
$424$		0			0
$425$	1.23607	−	3.80423i	0.0599581	−	0.184532i
$426$		0			0
$427$	0.381966	−	0.277515i	0.0184846	−	0.0134299i
$428$		0			0
$429$	−3.23607	−	34.5811i	−0.156239	−	1.66959i
$430$		0			0
$431$	−11.7361	+	8.52675i	−0.565307	+	0.410719i	−0.833397	−	0.552674i	$-0.813607\pi$
$431$	−11.7361	+	8.52675i	−0.565307	+	0.410719i	0.268091	+	0.963394i	$0.413607\pi$
$432$		0			0
$433$	4.00000	−	12.3107i	0.192228	−	0.591616i	−0.807770	−	0.589498i	$-0.799326\pi$
$433$	4.00000	−	12.3107i	0.192228	−	0.591616i	0.999998	−	0.00211838i	$-0.000674303\pi$
$434$		0			0
$435$	4.47214	+	3.24920i	0.214423	+	0.155787i
$436$		0			0
$437$	−0.381966	−	1.17557i	−0.0182719	−	0.0562352i
$438$		0			0
$439$	−2.65248			−0.126596			−0.0632979	−	0.997995i	$-0.520162\pi$
$439$	−2.65248			−0.126596			−0.0632979	+	0.997995i	$0.520162\pi$
$440$		0			0
$441$	7.47214			0.355816
$442$		0			0
$443$	−6.06231	−	18.6579i	−0.288029	−	0.886462i	−0.985474	−	0.169824i	$-0.945680\pi$
$443$	−6.06231	−	18.6579i	−0.288029	−	0.886462i	0.697446	−	0.716638i	$-0.254320\pi$
$444$		0			0
$445$	10.9443	+	7.95148i	0.518808	+	0.376936i
$446$		0			0
$447$	−8.47214	+	26.0746i	−0.400718	+	1.23328i
$448$		0			0
$449$	2.73607	−	1.98787i	0.129123	−	0.0938134i	−0.521349	−	0.853343i	$-0.674571\pi$
$449$	2.73607	−	1.98787i	0.129123	−	0.0938134i	0.650472	+	0.759530i	$0.274571\pi$
$450$		0			0
$451$	−19.7984	+	33.4055i	−0.932269	+	1.57300i
$452$		0			0
$453$	−24.2705	+	17.6336i	−1.14033	+	0.828497i
$454$		0			0
$455$	−2.00000	+	6.15537i	−0.0937614	+	0.288568i
$456$		0			0
$457$	13.9721	+	10.1514i	0.653589	+	0.474860i	0.864492	−	0.502647i	$-0.167640\pi$
$457$	13.9721	+	10.1514i	0.653589	+	0.474860i	−0.210903	+	0.977507i	$0.567640\pi$
$458$		0			0
$459$	−17.8885	−	55.0553i	−0.834966	−	2.56976i
$460$		0			0
$461$	15.8197			0.736795			0.368398	−	0.929668i	$-0.379907\pi$
$461$	15.8197			0.736795			0.368398	+	0.929668i	$0.379907\pi$
$462$		0			0
$463$	38.4508			1.78696			0.893481	−	0.449100i	$-0.148255\pi$
$463$	38.4508			1.78696			0.893481	+	0.449100i	$0.148255\pi$
$464$		0			0
$465$	−8.94427	−	27.5276i	−0.414781	−	1.27656i
$466$		0			0
$467$	−15.4164	−	11.2007i	−0.713386	−	0.518305i	0.170878	−	0.985292i	$-0.445340\pi$
$467$	−15.4164	−	11.2007i	−0.713386	−	0.518305i	−0.884264	+	0.466987i	$0.845340\pi$
$468$		0			0
$469$	−0.118034	+	0.363271i	−0.00545030	+	0.0167743i
$470$		0			0
$471$	42.3607	−	30.7768i	1.95188	−	1.41812i
$472$		0			0
$473$	23.7812	+	27.0256i	1.09346	+	1.24264i
$474$		0			0
$475$	−1.61803	+	1.17557i	−0.0742405	+	0.0539389i
$476$		0			0
$477$	−22.2082	+	68.3498i	−1.01684	+	3.12952i
$478$		0			0
$479$	2.14590	+	1.55909i	0.0980486	+	0.0712365i	0.635729	−	0.771912i	$-0.280699\pi$
$479$	2.14590	+	1.55909i	0.0980486	+	0.0712365i	−0.537681	+	0.843148i	$0.680699\pi$
$480$		0			0
$481$	9.85410	+	30.3278i	0.449308	+	1.38283i
$482$		0			0
$483$	−2.00000			−0.0910032
$484$		0			0
$485$	−30.8328			−1.40005
$486$		0			0
$487$	0.118034	+	0.363271i	0.00534863	+	0.0164614i	0.953695	−	0.300775i	$-0.0972452\pi$
$487$	0.118034	+	0.363271i	0.00534863	+	0.0164614i	−0.948347	+	0.317236i	$0.897245\pi$
$488$		0			0
$489$	34.7426	+	25.2420i	1.57112	+	1.14148i
$490$		0			0
$491$	−7.70820	+	23.7234i	−0.347866	+	1.07062i	0.612165	+	0.790730i	$0.290299\pi$
$491$	−7.70820	+	23.7234i	−0.347866	+	1.07062i	−0.960031	+	0.279893i	$0.909701\pi$
$492$		0			0
$493$	−2.76393	+	2.00811i	−0.124481	+	0.0904409i
$494$		0			0
$495$	32.7426	+	37.2097i	1.47167	+	1.67245i
$496$		0			0
$497$	1.54508	−	1.12257i	0.0693065	−	0.0503541i
$498$		0			0
$499$	9.88197	−	30.4136i	0.442378	−	1.36150i	−0.442957	−	0.896543i	$-0.646070\pi$
$499$	9.88197	−	30.4136i	0.442378	−	1.36150i	0.885334	−	0.464955i	$-0.153930\pi$
$500$		0			0
$501$	54.8328	+	39.8384i	2.44975	+	1.77985i
$502$		0			0
$503$	−2.76393	−	8.50651i	−0.123238	−	0.379286i	0.870338	−	0.492454i	$-0.163900\pi$
$503$	−2.76393	−	8.50651i	−0.123238	−	0.379286i	−0.993576	+	0.113168i	$0.963900\pi$
$504$		0			0
$505$	1.52786			0.0679891
$506$		0			0
$507$	−8.18034			−0.363302
$508$		0			0
$509$	−1.32624	−	4.08174i	−0.0587845	−	0.180920i	0.917352	−	0.398076i	$-0.130322\pi$
$509$	−1.32624	−	4.08174i	−0.0587845	−	0.180920i	−0.976137	+	0.217156i	$0.930322\pi$
$510$		0			0
$511$	−11.8541	−	8.61251i	−0.524395	−	0.380995i
$512$		0			0
$513$	−8.94427	+	27.5276i	−0.394899	+	1.21537i
$514$		0			0
$515$	−15.7082	+	11.4127i	−0.692186	+	0.502903i
$516$		0			0
$517$	−16.9098	+	28.5317i	−0.743693	+	1.25482i
$518$		0			0
$519$	−25.4164	+	18.4661i	−1.11566	+	0.810572i
$520$		0			0
$521$	8.52786	−	26.2461i	0.373613	−	1.14986i	−0.570797	−	0.821091i	$-0.693366\pi$
$521$	8.52786	−	26.2461i	0.373613	−	1.14986i	0.944410	−	0.328770i	$-0.106634\pi$
$522$		0			0
$523$	18.3262	+	13.3148i	0.801350	+	0.582215i	0.911310	−	0.411721i	$-0.135072\pi$
$523$	18.3262	+	13.3148i	0.801350	+	0.582215i	−0.109960	+	0.993936i	$0.535072\pi$
$524$		0			0
$525$	1.00000	+	3.07768i	0.0436436	+	0.134321i
$526$		0			0
$527$	17.8885			0.779237
$528$		0			0
$529$	−22.6180			−0.983393
$530$		0			0
$531$	−8.56231	−	26.3521i	−0.371572	−	1.14358i
$532$		0			0
$533$	−30.6525	−	22.2703i	−1.32771	−	0.964635i
$534$		0			0
$535$	−7.79837	+	24.0009i	−0.337153	+	1.03765i
$536$		0			0
$537$	−12.0902	+	8.78402i	−0.521729	+	0.379059i
$538$		0			0
$539$	−0.309017	−	3.30220i	−0.0133103	−	0.142236i
$540$		0			0
$541$	−12.9721	+	9.42481i	−0.557716	+	0.405204i	−0.830622	−	0.556836i	$-0.812015\pi$
$541$	−12.9721	+	9.42481i	−0.557716	+	0.405204i	0.272907	+	0.962041i	$0.412015\pi$
$542$		0			0
$543$	20.9443	−	64.4598i	0.898805	−	2.76624i
$544$		0			0
$545$	26.8885	+	19.5357i	1.15178	+	0.836816i
$546$		0			0
$547$	11.4164	+	35.1361i	0.488130	+	1.50231i	0.827395	+	0.561620i	$0.189822\pi$
$547$	11.4164	+	35.1361i	0.488130	+	1.50231i	−0.339265	+	0.940691i	$0.610178\pi$
$548$		0			0
$549$	3.52786			0.150566
$550$		0			0
$551$	1.70820			0.0727719
$552$		0			0
$553$	1.88197	+	5.79210i	0.0800293	+	0.246305i
$554$		0			0
$555$	−51.5967	−	37.4872i	−2.19016	−	1.59124i
$556$		0			0
$557$	−4.97214	+	15.3027i	−0.210676	+	0.648395i	0.788756	+	0.614706i	$0.210725\pi$
$557$	−4.97214	+	15.3027i	−0.210676	+	0.648395i	−0.999432	+	0.0336884i	$0.989275\pi$
$558$		0			0
$559$	−28.4164	+	20.6457i	−1.20189	+	0.873221i
$560$		0			0
$561$	−39.4164	+	17.0130i	−1.66416	+	0.718290i
$562$		0			0
$563$	37.7426	−	27.4216i	1.59066	−	1.15568i	0.687675	−	0.726019i	$-0.258632\pi$
$563$	37.7426	−	27.4216i	1.59066	−	1.15568i	0.902988	−	0.429665i	$-0.141368\pi$
$564$		0			0
$565$	−5.00000	+	15.3884i	−0.210352	+	0.647396i
$566$		0			0
$567$	19.7533	+	14.3516i	0.829560	+	0.602711i
$568$		0			0
$569$	−1.38197	−	4.25325i	−0.0579350	−	0.178306i	0.917901	−	0.396809i	$-0.129883\pi$
$569$	−1.38197	−	4.25325i	−0.0579350	−	0.178306i	−0.975836	+	0.218503i	$0.929883\pi$
$570$		0			0
$571$	4.97871			0.208353			0.104176	−	0.994559i	$-0.466779\pi$
$571$	4.97871			0.208353			0.104176	+	0.994559i	$0.466779\pi$
$572$		0			0
$573$	24.6525			1.02987
$574$		0			0
$575$	−0.190983	−	0.587785i	−0.00796454	−	0.0245123i
$576$		0			0
$577$	−14.7082	−	10.6861i	−0.612311	−	0.444870i	0.237917	−	0.971286i	$-0.423535\pi$
$577$	−14.7082	−	10.6861i	−0.612311	−	0.444870i	−0.850227	+	0.526416i	$0.823535\pi$
$578$		0			0
$579$	20.8541	−	64.1823i	0.866667	−	2.66733i
$580$		0			0
$581$	12.0902	−	8.78402i	0.501585	−	0.364423i
$582$		0			0
$583$	31.1246	+	6.98791i	1.28905	+	0.289410i
$584$		0			0
$585$	−39.1246	+	28.4257i	−1.61760	+	1.17526i
$586$		0			0
$587$	−3.90983	+	12.0332i	−0.161376	+	0.496664i	−0.998751	−	0.0499647i	$-0.984089\pi$
$587$	−3.90983	+	12.0332i	−0.161376	+	0.496664i	0.837375	+	0.546629i	$0.184089\pi$
$588$		0			0
$589$	−7.23607	−	5.25731i	−0.298157	−	0.216624i
$590$		0			0
$591$	−18.7984	−	57.8554i	−0.773262	−	2.37986i
$592$		0			0
$593$	26.7639			1.09906			0.549531	−	0.835473i	$-0.314806\pi$
$593$	26.7639			1.09906			0.549531	+	0.835473i	$0.314806\pi$
$594$		0			0
$595$	8.00000			0.327968
$596$		0			0
$597$	−8.18034	−	25.1765i	−0.334799	−	1.03041i
$598$		0			0
$599$	−12.5000	−	9.08178i	−0.510736	−	0.371072i	0.302367	−	0.953192i	$-0.402223\pi$
$599$	−12.5000	−	9.08178i	−0.510736	−	0.371072i	−0.813103	+	0.582120i	$0.802223\pi$
$600$		0			0
$601$	0.270510	−	0.832544i	0.0110343	−	0.0339602i	−0.945388	−	0.325948i	$-0.894317\pi$
$601$	0.270510	−	0.832544i	0.0110343	−	0.0339602i	0.956422	+	0.291988i	$0.0943166\pi$
$602$		0			0
$603$	−2.30902	+	1.67760i	−0.0940304	+	0.0683171i
$604$		0			0
$605$	15.0902	−	16.0090i	0.613503	−	0.650857i
$606$		0			0
$607$	12.6180	−	9.16754i	0.512150	−	0.372099i	−0.301488	−	0.953470i	$-0.597483\pi$
$607$	12.6180	−	9.16754i	0.512150	−	0.372099i	0.813639	+	0.581371i	$0.197483\pi$
$608$		0			0
$609$	0.854102	−	2.62866i	0.0346100	−	0.106518i
$610$		0			0
$611$	−26.1803	−	19.0211i	−1.05914	−	0.769513i
$612$		0			0
$613$	−1.02786	−	3.16344i	−0.0415150	−	0.127770i	0.928151	−	0.372204i	$-0.121398\pi$
$613$	−1.02786	−	3.16344i	−0.0415150	−	0.127770i	−0.969666	+	0.244434i	$0.921398\pi$
$614$		0			0
$615$	75.7771			3.05563
$616$		0			0
$617$	−0.493422			−0.0198644			−0.00993221	−	0.999951i	$-0.503162\pi$
$617$	−0.493422			−0.0198644			−0.00993221	+	0.999951i	$0.503162\pi$
$618$		0			0
$619$	−3.32624	−	10.2371i	−0.133693	−	0.411464i	0.861692	−	0.507432i	$-0.169405\pi$
$619$	−3.32624	−	10.2371i	−0.133693	−	0.411464i	−0.995384	+	0.0959682i	$0.969405\pi$
$620$		0			0
$621$	−7.23607	−	5.25731i	−0.290373	−	0.210969i
$622$		0			0
$623$	2.09017	−	6.43288i	0.0837409	−	0.257728i
$624$		0			0
$625$	15.3713	−	11.1679i	0.614853	−	0.446717i
$626$		0			0
$627$	20.9443	+	4.70228i	0.836434	+	0.187791i
$628$		0			0
$629$	31.8885	−	23.1684i	1.27148	−	0.923784i
$630$		0			0
$631$	−4.07953	+	12.5555i	−0.162403	+	0.499826i	−0.998836	−	0.0482442i	$-0.984637\pi$
$631$	−4.07953	+	12.5555i	−0.162403	+	0.499826i	0.836432	+	0.548070i	$0.184637\pi$
$632$		0			0
$633$	31.5066	+	22.8909i	1.25227	+	0.909830i
$634$		0			0
$635$	2.27051	+	6.98791i	0.0901024	+	0.277307i
$636$		0			0
$637$	3.23607			0.128218
$638$		0			0
$639$	14.2705			0.564533
$640$		0			0
$641$	5.84752	+	17.9968i	0.230963	+	0.710832i	0.997631	+	0.0687882i	$0.0219133\pi$
$641$	5.84752	+	17.9968i	0.230963	+	0.710832i	−0.766668	+	0.642044i	$0.778087\pi$
$642$		0			0
$643$	−25.5623	−	18.5721i	−1.00808	−	0.732412i	−0.0442737	−	0.999019i	$-0.514097\pi$
$643$	−25.5623	−	18.5721i	−1.00808	−	0.732412i	−0.963805	+	0.266607i	$0.914097\pi$
$644$		0			0
$645$	21.7082	−	66.8110i	0.854760	−	2.63068i
$646$		0			0
$647$	−25.4164	+	18.4661i	−0.999222	+	0.725977i	−0.961921	−	0.273327i	$-0.911876\pi$
$647$	−25.4164	+	18.4661i	−0.999222	+	0.725977i	−0.0373008	+	0.999304i	$0.511876\pi$
$648$		0			0
$649$	−11.2918	+	4.87380i	−0.443242	+	0.191313i
$650$		0			0
$651$	−11.7082	+	8.50651i	−0.458881	+	0.333396i
$652$		0			0
$653$	0.461493	−	1.42033i	0.0180596	−	0.0555818i	−0.941621	−	0.336676i	$-0.890697\pi$
$653$	0.461493	−	1.42033i	0.0180596	−	0.0555818i	0.959680	+	0.281094i	$0.0906973\pi$
$654$		0			0
$655$	−6.47214	−	4.70228i	−0.252887	−	0.183733i
$656$		0			0
$657$	−33.8328	−	104.127i	−1.31994	−	4.06237i
$658$		0			0
$659$	−9.88854			−0.385203			−0.192601	−	0.981277i	$-0.561692\pi$
$659$	−9.88854			−0.385203			−0.192601	+	0.981277i	$0.561692\pi$
$660$		0			0
$661$	−13.5279			−0.526173			−0.263086	−	0.964772i	$-0.584740\pi$
$661$	−13.5279			−0.526173			−0.263086	+	0.964772i	$0.584740\pi$
$662$		0			0
$663$	−12.9443	−	39.8384i	−0.502714	−	1.54719i
$664$		0			0
$665$	−3.23607	−	2.35114i	−0.125489	−	0.0911733i
$666$		0			0
$667$	−0.163119	+	0.502029i	−0.00631599	+	0.0194386i
$668$		0			0
$669$	29.8885	−	21.7153i	1.15556	−	0.839562i
$670$		0			0
$671$	−0.145898	−	1.55909i	−0.00563233	−	0.0601879i
$672$		0			0
$673$	−29.4894	+	21.4253i	−1.13673	+	0.825884i	−0.986660	−	0.162792i	$-0.947950\pi$
$673$	−29.4894	+	21.4253i	−1.13673	+	0.825884i	−0.150071	+	0.988675i	$0.547950\pi$
$674$		0			0
$675$	−4.47214	+	13.7638i	−0.172133	+	0.529770i
$676$		0			0
$677$	−19.2361	−	13.9758i	−0.739302	−	0.537134i	0.153190	−	0.988197i	$-0.451045\pi$
$677$	−19.2361	−	13.9758i	−0.739302	−	0.537134i	−0.892492	+	0.451062i	$0.851045\pi$
$678$		0			0
$679$	4.76393	+	14.6619i	0.182823	+	0.562671i
$680$		0			0
$681$	−24.0000			−0.919682
$682$		0			0
$683$	7.67376			0.293628			0.146814	−	0.989164i	$-0.453098\pi$
$683$	7.67376			0.293628			0.146814	+	0.989164i	$0.453098\pi$
$684$		0			0
$685$	−4.96556	−	15.2824i	−0.189724	−	0.583911i
$686$		0			0
$687$	−50.3607	−	36.5892i	−1.92138	−	1.39596i
$688$		0			0
$689$	−9.61803	+	29.6013i	−0.366418	+	1.12772i
$690$		0			0
$691$	26.8885	−	19.5357i	1.02289	−	0.743172i	0.0560154	−	0.998430i	$-0.482160\pi$
$691$	26.8885	−	19.5357i	1.02289	−	0.743172i	0.966873	+	0.255258i	$0.0821604\pi$
$692$		0			0
$693$	12.6353	−	21.3193i	0.479974	−	0.809852i
$694$		0			0
$695$	−2.00000	+	1.45309i	−0.0758643	+	0.0551187i
$696$		0			0
$697$	−14.4721	+	44.5407i	−0.548171	+	1.68710i
$698$		0			0
$699$	51.1246	+	37.1442i	1.93371	+	1.40492i
$700$		0			0
$701$	−11.2467	−	34.6138i	−0.424782	−	1.30735i	−0.903202	−	0.429215i	$-0.858790\pi$
$701$	−11.2467	−	34.6138i	−0.424782	−	1.30735i	0.478420	−	0.878131i	$-0.341210\pi$
$702$		0			0
$703$	−19.7082			−0.743309
$704$		0			0
$705$	64.7214			2.43755
$706$		0			0
$707$	−0.236068	−	0.726543i	−0.00887825	−	0.0273244i
$708$		0			0
$709$	31.0517	+	22.5604i	1.16617	+	0.847272i	0.990545	−	0.137185i	$-0.0438056\pi$
$709$	31.0517	+	22.5604i	1.16617	+	0.847272i	0.175624	+	0.984457i	$0.443806\pi$
$710$		0			0
$711$	−14.0623	+	43.2793i	−0.527378	+	1.62310i
$712$		0			0
$713$	2.23607	−	1.62460i	0.0837414	−	0.0608417i
$714$		0			0
$715$	14.1803	+	16.1150i	0.530315	+	0.602665i
$716$		0			0
$717$	−70.3050	+	51.0795i	−2.62559	+	1.90760i
$718$		0			0
$719$	8.29180	−	25.5195i	0.309232	−	0.951718i	−0.668832	−	0.743413i	$-0.733206\pi$
$719$	8.29180	−	25.5195i	0.309232	−	0.951718i	0.978064	−	0.208304i	$-0.0667944\pi$
$720$		0			0
$721$	7.85410	+	5.70634i	0.292502	+	0.212515i
$722$		0			0
$723$	2.47214	+	7.60845i	0.0919397	+	0.282961i
$724$		0			0
$725$	0.854102			0.0317206
$726$		0			0
$727$	−23.5279			−0.872600			−0.436300	−	0.899801i	$-0.643711\pi$
$727$	−23.5279			−0.872600			−0.436300	+	0.899801i	$0.643711\pi$
$728$		0			0
$729$	12.9615	+	39.8914i	0.480055	+	1.47746i
$730$		0			0
$731$	35.1246	+	25.5195i	1.29913	+	0.943874i
$732$		0			0
$733$	6.72949	−	20.7112i	0.248559	−	0.764987i	−0.746471	−	0.665418i	$-0.768253\pi$
$733$	6.72949	−	20.7112i	0.248559	−	0.764987i	0.995031	−	0.0995694i	$-0.0317465\pi$
$734$		0			0
$735$	−5.23607	+	3.80423i	−0.193135	+	0.140321i
$736$		0			0
$737$	0.836881	+	0.951057i	0.0308269	+	0.0350326i
$738$		0			0
$739$	10.6353	−	7.72696i	0.391224	−	0.284241i	−0.374733	−	0.927133i	$-0.622266\pi$
$739$	10.6353	−	7.72696i	0.391224	−	0.284241i	0.765957	+	0.642892i	$0.222266\pi$
$740$		0			0
$741$	−6.47214	+	19.9192i	−0.237760	+	0.731750i
$742$		0			0
$743$	−32.9615	−	23.9479i	−1.20924	−	0.878564i	−0.214078	−	0.976816i	$-0.568675\pi$
$743$	−32.9615	−	23.9479i	−1.20924	−	0.878564i	−0.995162	+	0.0982523i	$0.968675\pi$
$744$		0			0
$745$	−5.23607	−	16.1150i	−0.191835	−	0.590406i
$746$		0			0
$747$	111.666			4.08563
$748$		0			0
$749$	12.6180			0.461053
$750$		0			0
$751$	10.9549	+	33.7158i	0.399751	+	1.23031i	0.925200	+	0.379481i	$0.123897\pi$
$751$	10.9549	+	33.7158i	0.399751	+	1.23031i	−0.525449	+	0.850825i	$0.676103\pi$
$752$		0			0
$753$	38.3607	+	27.8707i	1.39794	+	1.01566i
$754$		0			0
$755$	5.72949	−	17.6336i	0.208517	−	0.641751i
$756$		0			0
$757$	43.8156	−	31.8339i	1.59250	−	1.15702i	0.692251	−	0.721656i	$-0.256619\pi$
$757$	43.8156	−	31.8339i	1.59250	−	1.15702i	0.900254	−	0.435366i	$-0.143381\pi$
$758$		0			0
$759$	−3.38197	+	5.70634i	−0.122758	+	0.207127i
$760$		0			0
$761$	−19.6525	+	14.2784i	−0.712402	+	0.517590i	−0.883948	−	0.467586i	$-0.845124\pi$
$761$	−19.6525	+	14.2784i	−0.712402	+	0.517590i	0.171546	+	0.985176i	$0.445124\pi$
$762$		0			0
$763$	5.13525	−	15.8047i	0.185909	−	0.572168i
$764$		0			0
$765$	48.3607	+	35.1361i	1.74848	+	1.27035i
$766$		0			0
$767$	−3.70820	−	11.4127i	−0.133895	−	0.412088i
$768$		0			0
$769$	−24.5410			−0.884972			−0.442486	−	0.896775i	$-0.645903\pi$
$769$	−24.5410			−0.884972			−0.442486	+	0.896775i	$0.645903\pi$
$770$		0			0
$771$	−22.4721			−0.809314
$772$		0			0
$773$	−6.09017	−	18.7436i	−0.219048	−	0.674161i	−0.998841	−	0.0481238i	$-0.984676\pi$
$773$	−6.09017	−	18.7436i	−0.219048	−	0.674161i	0.779793	−	0.626037i	$-0.215324\pi$
$774$		0			0
$775$	−3.61803	−	2.62866i	−0.129964	−	0.0944241i
$776$		0			0
$777$	−9.85410	+	30.3278i	−0.353514	+	1.08800i
$778$		0			0
$779$	18.9443	−	13.7638i	0.678749	−	0.493140i
$780$		0			0
$781$	−0.590170	−	6.30664i	−0.0211179	−	0.225669i
$782$		0			0
$783$	10.0000	−	7.26543i	0.357371	−	0.259645i
$784$		0			0
$785$	−10.0000	+	30.7768i	−0.356915	+	1.09847i
$786$		0			0
$787$	29.5623	+	21.4783i	1.05378	+	0.765618i	0.972928	−	0.231108i	$-0.0742351\pi$
$787$	29.5623	+	21.4783i	1.05378	+	0.765618i	0.0808543	+	0.996726i	$0.474235\pi$
$788$		0			0
$789$	15.0344	+	46.2713i	0.535240	+	1.64730i
$790$		0			0
$791$	8.09017			0.287653
$792$		0			0
$793$	1.52786			0.0542560
$794$		0			0
$795$	−19.2361	−	59.2025i	−0.682233	−	2.09970i
$796$		0			0
$797$	25.1803	+	18.2946i	0.891933	+	0.648028i	0.936381	−	0.350984i	$-0.114153\pi$
$797$	25.1803	+	18.2946i	0.891933	+	0.648028i	−0.0444480	+	0.999012i	$0.514153\pi$
$798$		0			0
$799$	−12.3607	+	38.0423i	−0.437289	+	1.34584i
$800$		0			0
$801$	40.8885	−	29.7073i	1.44473	−	1.04965i
$802$		0			0
$803$	−44.6180	+	19.2582i	−1.57454	+	0.679606i
$804$		0			0
$805$	1.00000	−	0.726543i	0.0352454	−	0.0256073i
$806$		0			0
$807$	−7.70820	+	23.7234i	−0.271342	+	0.835104i
$808$		0			0
$809$	−37.1525	−	26.9929i	−1.30621	−	0.949018i	−0.306216	−	0.951962i	$-0.599063\pi$
$809$	−37.1525	−	26.9929i	−1.30621	−	0.949018i	−0.999996	+	0.00294392i	$0.999063\pi$
$810$		0			0
$811$	8.65248	+	26.6296i	0.303830	+	0.935091i	0.980111	+	0.198448i	$0.0635901\pi$
$811$	8.65248	+	26.6296i	0.303830	+	0.935091i	−0.676282	+	0.736643i	$0.736410\pi$
$812$		0			0
$813$	−12.3607			−0.433508
$814$		0			0
$815$	−26.5410			−0.929691
$816$		0			0
$817$	−6.70820	−	20.6457i	−0.234690	−	0.722303i
$818$		0			0
$819$	19.5623	+	14.2128i	0.683562	+	0.496637i
$820$		0			0
$821$	−5.85410	+	18.0171i	−0.204310	+	0.628800i	0.795431	+	0.606044i	$0.207244\pi$
$821$	−5.85410	+	18.0171i	−0.204310	+	0.628800i	−0.999741	+	0.0227566i	$0.992756\pi$
$822$		0			0
$823$	−10.9271	+	7.93897i	−0.380893	+	0.276735i	−0.761713	−	0.647914i	$-0.775642\pi$
$823$	−10.9271	+	7.93897i	−0.380893	+	0.276735i	0.380820	+	0.924649i	$0.375642\pi$
$824$		0			0
$825$	10.4721	+	2.35114i	0.364593	+	0.0818562i
$826$		0			0
$827$	−1.52786	+	1.11006i	−0.0531290	+	0.0386005i	−0.614033	−	0.789280i	$-0.710454\pi$
$827$	−1.52786	+	1.11006i	−0.0531290	+	0.0386005i	0.560904	+	0.827881i	$0.310454\pi$
$828$		0			0
$829$	−6.11146	+	18.8091i	−0.212260	+	0.653268i	0.787077	+	0.616855i	$0.211593\pi$
$829$	−6.11146	+	18.8091i	−0.212260	+	0.653268i	−0.999337	+	0.0364135i	$0.988407\pi$
$830$		0			0
$831$	−69.3951	−	50.4185i	−2.40729	−	1.74900i
$832$		0			0
$833$	−1.23607	−	3.80423i	−0.0428272	−	0.131809i
$834$		0			0
$835$	−41.8885			−1.44961
$836$		0			0
$837$	−64.7214			−2.23710
$838$		0			0
$839$	14.2918	+	43.9856i	0.493408	+	1.51855i	0.819424	+	0.573188i	$0.194294\pi$
$839$	14.2918	+	43.9856i	0.493408	+	1.51855i	−0.326016	+	0.945364i	$0.605706\pi$
$840$		0			0
$841$	22.8713	+	16.6170i	0.788666	+	0.573000i
$842$		0			0
$843$	0.0901699	−	0.277515i	0.00310562	−	0.00955811i
$844$		0			0
$845$	4.09017	−	2.97168i	0.140706	−	0.102229i
$846$		0			0
$847$	−9.94427	−	4.70228i	−0.341689	−	0.161572i
$848$		0			0
$849$	33.8885	−	24.6215i	1.16305	−	0.845007i
$850$		0			0
$851$	1.88197	−	5.79210i	0.0645130	−	0.198550i
$852$		0			0
$853$	−42.1246	−	30.6053i	−1.44232	−	1.04791i	−0.987551	−	0.157296i	$-0.949722\pi$
$853$	−42.1246	−	30.6053i	−1.44232	−	1.04791i	−0.454768	−	0.890610i	$-0.650278\pi$
$854$		0			0
$855$	−9.23607	−	28.4257i	−0.315867	−	0.972138i
$856$		0			0
$857$	41.8885			1.43089			0.715443	−	0.698671i	$-0.246225\pi$
$857$	41.8885			1.43089			0.715443	+	0.698671i	$0.246225\pi$
$858$		0			0
$859$	−29.5967			−1.00983			−0.504914	−	0.863170i	$-0.668476\pi$
$859$	−29.5967			−1.00983			−0.504914	+	0.863170i	$0.668476\pi$
$860$		0			0
$861$	−11.7082	−	36.0341i	−0.399015	−	1.22804i
$862$		0			0
$863$	−47.1246	−	34.2380i	−1.60414	−	1.16548i	−0.878932	−	0.476947i	$-0.841744\pi$
$863$	−47.1246	−	34.2380i	−1.60414	−	1.16548i	−0.725208	−	0.688530i	$-0.758256\pi$
$864$		0			0
$865$	6.00000	−	18.4661i	0.204006	−	0.627866i
$866$		0			0
$867$	2.61803	−	1.90211i	0.0889131	−	0.0645991i
$868$		0			0
$869$	19.7082	+	4.42477i	0.668555	+	0.150100i
$870$		0			0
$871$	−1.00000	+	0.726543i	−0.0338837	+	0.0246180i
$872$		0			0
$873$	−35.5967	+	109.556i	−1.20477	+	3.70789i
$874$		0			0
$875$	−9.70820	−	7.05342i	−0.328197	−	0.238449i
$876$		0			0
$877$	−16.3328	−	50.2672i	−0.551520	−	1.69740i	−0.704961	−	0.709246i	$-0.749035\pi$
$877$	−16.3328	−	50.2672i	−0.551520	−	1.69740i	0.153441	−	0.988158i	$-0.450965\pi$
$878$		0			0
$879$	−28.9443			−0.976266
$880$		0			0
$881$	−35.0132			−1.17962			−0.589812	−	0.807541i	$-0.700798\pi$
$881$	−35.0132			−1.17962			−0.589812	+	0.807541i	$0.700798\pi$
$882$		0			0
$883$	−4.65248	−	14.3188i	−0.156568	−	0.481868i	0.841748	−	0.539870i	$-0.181527\pi$
$883$	−4.65248	−	14.3188i	−0.156568	−	0.481868i	−0.998316	+	0.0580028i	$0.981527\pi$
$884$		0			0
$885$	19.4164	+	14.1068i	0.652675	+	0.474196i
$886$		0			0
$887$	0.124612	−	0.383516i	0.00418405	−	0.0128772i	−0.948943	−	0.315449i	$-0.897845\pi$
$887$	0.124612	−	0.383516i	0.00418405	−	0.0128772i	0.953127	+	0.302571i	$0.0978450\pi$
$888$		0			0
$889$	2.97214	−	2.15938i	0.0996822	−	0.0724234i
$890$		0			0
$891$	74.3500	−	32.0912i	2.49082	−	1.07509i
$892$		0			0
$893$	16.1803	−	11.7557i	0.541454	−	0.393390i
$894$		0			0
$895$	2.85410	−	8.78402i	0.0954021	−	0.293617i
$896$		0			0
$897$	−5.23607	−	3.80423i	−0.174827	−	0.127019i
$898$		0			0
$899$	1.18034	+	3.63271i	0.0393665	+	0.121158i
$900$		0			0
$901$	38.4721			1.28169
$902$		0			0
$903$	−35.1246			−1.16887
$904$		0			0
$905$	12.9443	+	39.8384i	0.430282	+	1.32427i
$906$		0			0
$907$	−4.16312	−	3.02468i	−0.138234	−	0.100433i	0.516519	−	0.856276i	$-0.327227\pi$
$907$	−4.16312	−	3.02468i	−0.138234	−	0.100433i	−0.654753	+	0.755843i	$0.727227\pi$
$908$		0			0
$909$	1.76393	−	5.42882i	0.0585059	−	0.180063i
$910$		0			0
$911$	−25.8885	+	18.8091i	−0.857726	+	0.623174i	−0.927265	−	0.374405i	$-0.877847\pi$
$911$	−25.8885	+	18.8091i	−0.857726	+	0.623174i	0.0695396	+	0.997579i	$0.477847\pi$
$912$		0			0
$913$	−4.61803	−	49.3489i	−0.152835	−	1.63321i
$914$		0			0
$915$	−2.47214	+	1.79611i	−0.0817263	+	0.0593776i
$916$		0			0
$917$	−1.23607	+	3.80423i	−0.0408186	+	0.125627i
$918$		0			0
$919$	4.78115	+	3.47371i	0.157716	+	0.114587i	0.663844	−	0.747871i	$-0.268924\pi$
$919$	4.78115	+	3.47371i	0.157716	+	0.114587i	−0.506128	+	0.862458i	$0.668924\pi$
$920$		0			0
$921$	2.94427	+	9.06154i	0.0970171	+	0.298588i
$922$		0			0
$923$	6.18034			0.203428
$924$		0			0
$925$	−9.85410			−0.324001
$926$		0			0
$927$	22.4164	+	68.9906i	0.736251	+	2.26595i
$928$		0			0
$929$	1.29180	+	0.938545i	0.0423825	+	0.0307927i	0.608775	−	0.793343i	$-0.291661\pi$
$929$	1.29180	+	0.938545i	0.0423825	+	0.0307927i	−0.566392	+	0.824136i	$0.691661\pi$
$930$		0			0
$931$	−0.618034	+	1.90211i	−0.0202552	+	0.0623392i
$932$		0			0
$933$	−35.8885	+	26.0746i	−1.17494	+	0.853643i
$934$		0			0
$935$	13.5279	−	22.8254i	0.442408	−	0.746469i
$936$		0			0
$937$	−30.0344	+	21.8213i	−0.981182	+	0.712871i	−0.957973	−	0.286860i	$-0.907389\pi$
$937$	−30.0344	+	21.8213i	−0.981182	+	0.712871i	−0.0232099	+	0.999731i	$0.507389\pi$
$938$		0			0
$939$	−6.65248	+	20.4742i	−0.217095	+	0.668151i
$940$		0			0
$941$	−28.9443	−	21.0292i	−0.943556	−	0.685534i	0.00571778	−	0.999984i	$-0.498180\pi$
$941$	−28.9443	−	21.0292i	−0.943556	−	0.685534i	−0.949274	+	0.314450i	$0.898180\pi$
$942$		0			0
$943$	2.23607	+	6.88191i	0.0728164	+	0.224106i
$944$		0			0
$945$	−28.9443			−0.941557
$946$		0			0
$947$	−14.8328			−0.482002			−0.241001	−	0.970525i	$-0.577476\pi$
$947$	−14.8328			−0.482002			−0.241001	+	0.970525i	$0.577476\pi$
$948$		0			0
$949$	−14.6525	−	45.0957i	−0.475639	−	1.46387i
$950$		0			0
$951$	−32.1246	−	23.3399i	−1.04171	−	0.756848i
$952$		0			0
$953$	5.06637	−	15.5927i	0.164116	−	0.505097i	−0.834854	−	0.550471i	$-0.814448\pi$
$953$	5.06637	−	15.5927i	0.164116	−	0.505097i	0.998970	+	0.0453745i	$0.0144481\pi$
$954$		0			0
$955$	−12.3262	+	8.95554i	−0.398868	+	0.289794i
$956$		0			0
$957$	−6.05573	−	6.88191i	−0.195754	−	0.222461i
$958$		0			0
$959$	−6.50000	+	4.72253i	−0.209896	+	0.152498i
$960$		0			0
$961$	−3.39919	+	10.4616i	−0.109651	+	0.337472i
$962$		0			0
$963$	76.2771	+	55.4185i	2.45799	+	1.78584i
$964$		0			0
$965$	12.8885	+	39.6669i	0.414897	+	1.27692i
$966$		0			0
$967$	0.909830			0.0292582			0.0146291	−	0.999893i	$-0.495343\pi$
$967$	0.909830			0.0292582			0.0146291	+	0.999893i	$0.495343\pi$
$968$		0			0
$969$	25.8885			0.831660
$970$		0			0
$971$	7.88854	+	24.2784i	0.253155	+	0.779132i	0.994187	+	0.107663i	$0.0343366\pi$
$971$	7.88854	+	24.2784i	0.253155	+	0.779132i	−0.741032	+	0.671470i	$0.765663\pi$
$972$		0			0
$973$	1.00000	+	0.726543i	0.0320585	+	0.0232919i
$974$		0			0
$975$	−3.23607	+	9.95959i	−0.103637	+	0.318962i
$976$		0			0
$977$	24.2082	−	17.5883i	0.774489	−	0.562699i	−0.128831	−	0.991667i	$-0.541122\pi$
$977$	24.2082	−	17.5883i	0.774489	−	0.562699i	0.903320	+	0.428967i	$0.141122\pi$
$978$		0			0
$979$	−14.8197	−	16.8415i	−0.473638	−	0.538257i
$980$		0			0
$981$	100.457	−	72.9866i	3.20736	−	2.33028i
$982$		0			0
$983$	5.12461	−	15.7719i	0.163450	−	0.503047i	−0.835469	−	0.549538i	$-0.814804\pi$
$983$	5.12461	−	15.7719i	0.163450	−	0.503047i	0.998919	+	0.0464911i	$0.0148039\pi$
$984$		0			0
$985$	30.4164	+	22.0988i	0.969147	+	0.704127i
$986$		0			0
$987$	−10.0000	−	30.7768i	−0.318304	−	0.979637i
$988$		0			0
$989$	6.70820			0.213308
$990$		0			0
$991$	−13.8885			−0.441184			−0.220592	−	0.975366i	$-0.570799\pi$
$991$	−13.8885			−0.441184			−0.220592	+	0.975366i	$0.570799\pi$
$992$		0			0
$993$	−1.27051	−	3.91023i	−0.0403184	−	0.124087i
$994$		0			0
$995$	13.2361	+	9.61657i	0.419612	+	0.304866i
$996$		0			0
$997$	4.14590	−	12.7598i	0.131302	−	0.404106i	−0.863695	−	0.504016i	$-0.831855\pi$
$997$	4.14590	−	12.7598i	0.131302	−	0.404106i	0.994996	+	0.0999098i	$0.0318554\pi$
$998$		0			0
$999$	−115.374	+	83.8240i	−3.65027	+	2.65207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.a.113.1	✓	4
11.2	odd	10		3388.2.a.l.1.2		2
11.4	even	5	inner	308.2.j.a.169.1	yes	4
11.9	even	5		3388.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.a.113.1	✓	4	1.1	even	1	trivial
308.2.j.a.169.1	yes	4	11.4	even	5	inner
3388.2.a.k.1.2		2	11.9	even	5
3388.2.a.l.1.2		2	11.2	odd	10

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 3.07768i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-6.04508 + 4.39201i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 3.07768i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-6.04508 + 4.39201i) q^{9} +(2.19098 + 2.48990i) q^{11} +(-2.61803 + 1.90211i) q^{13} +(2.00000 - 6.15537i) q^{15} +(3.23607 + 2.35114i) q^{17} +(-0.618034 - 1.90211i) q^{19} -3.23607 q^{21} +0.618034 q^{23} +(-0.309017 - 0.951057i) q^{25} +(-11.7082 - 8.50651i) q^{27} +(-0.263932 + 0.812299i) q^{29} +(3.61803 - 2.62866i) q^{31} +(-5.47214 + 9.23305i) q^{33} +(1.61803 - 1.17557i) q^{35} +(3.04508 - 9.37181i) q^{37} +(-8.47214 - 6.15537i) q^{39} +(3.61803 + 11.1352i) q^{41} +10.8541 q^{43} +14.9443 q^{45} +(3.09017 + 9.51057i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-4.00000 + 12.3107i) q^{51} +(7.78115 - 5.65334i) q^{53} +(-0.618034 - 6.60440i) q^{55} +(5.23607 - 3.80423i) q^{57} +(-1.14590 + 3.52671i) q^{59} +(-0.381966 - 0.277515i) q^{61} +(-2.30902 - 7.10642i) q^{63} +6.47214 q^{65} +0.381966 q^{67} +(0.618034 + 1.90211i) q^{69} +(-1.54508 - 1.12257i) q^{71} +(-4.52786 + 13.9353i) q^{73} +(2.61803 - 1.90211i) q^{75} +(-3.04508 + 1.31433i) q^{77} +(4.92705 - 3.57971i) q^{79} +(7.54508 - 23.2214i) q^{81} +(-12.0902 - 8.78402i) q^{83} +(-2.47214 - 7.60845i) q^{85} -2.76393 q^{87} -6.76393 q^{89} +(-1.00000 - 3.07768i) q^{91} +(11.7082 + 8.50651i) q^{93} +(-1.23607 + 3.80423i) q^{95} +(12.4721 - 9.06154i) q^{97} +(-24.1803 - 5.42882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9	\( 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9} + 11 q^{11} - 6 q^{13} + 8 q^{15} + 4 q^{17} + 2 q^{19} - 4 q^{21} - 2 q^{23} + q^{25} - 20 q^{27} - 10 q^{29} + 10 q^{31} - 4 q^{33} + 2 q^{35} + q^{37} - 16 q^{39} + 10 q^{41} + 30 q^{43} + 24 q^{45} - 10 q^{47} - q^{49} - 16 q^{51} + 11 q^{53} + 2 q^{55} + 12 q^{57} - 18 q^{59} - 6 q^{61} - 7 q^{63} + 8 q^{65} + 6 q^{67} - 2 q^{69} + 5 q^{71} - 36 q^{73} + 6 q^{75} - q^{77} + 13 q^{79} + 19 q^{81} - 26 q^{83} + 8 q^{85} - 20 q^{87} - 36 q^{89} - 4 q^{91} + 20 q^{93} + 4 q^{95} + 32 q^{97} - 52 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9 + 11 * q^11 - 6 * q^13 + 8 * q^15 + 4 * q^17 + 2 * q^19 - 4 * q^21 - 2 * q^23 + q^25 - 20 * q^27 - 10 * q^29 + 10 * q^31 - 4 * q^33 + 2 * q^35 + q^37 - 16 * q^39 + 10 * q^41 + 30 * q^43 + 24 * q^45 - 10 * q^47 - q^49 - 16 * q^51 + 11 * q^53 + 2 * q^55 + 12 * q^57 - 18 * q^59 - 6 * q^61 - 7 * q^63 + 8 * q^65 + 6 * q^67 - 2 * q^69 + 5 * q^71 - 36 * q^73 + 6 * q^75 - q^77 + 13 * q^79 + 19 * q^81 - 26 * q^83 + 8 * q^85 - 20 * q^87 - 36 * q^89 - 4 * q^91 + 20 * q^93 + 4 * q^95 + 32 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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