LMFDB - Embedded newform 464.2.bl.b.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(15,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 0, 27]))

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

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

chi := DirichletCharacter("464.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.bl (of order $28$, degree $12$, 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	464.127
Dual form			464.2.bl.b.95.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.09437 - 0.235979i) q^{3} +(1.34729 - 2.79769i) q^{5} +(-2.30768 - 1.84031i) q^{7} +(1.40592 - 0.320892i) q^{9} +O(q^{10})$	\(q+(2.09437 - 0.235979i) q^{3} +(1.34729 - 2.79769i) q^{5} +(-2.30768 - 1.84031i) q^{7} +(1.40592 - 0.320892i) q^{9} +(0.987209 - 0.620305i) q^{11} +(-2.56100 - 0.584532i) q^{13} +(2.16154 - 6.17732i) q^{15} +(3.73220 - 3.73220i) q^{17} +(-0.853070 + 7.57121i) q^{19} +(-5.26741 - 3.30973i) q^{21} +(-0.662879 - 1.37648i) q^{23} +(-2.89439 - 3.62945i) q^{25} +(-3.09926 + 1.08448i) q^{27} +(4.23107 + 3.33138i) q^{29} +(2.96833 + 8.48299i) q^{31} +(1.92120 - 1.53211i) q^{33} +(-8.25774 + 3.97672i) q^{35} +(4.32508 - 6.88332i) q^{37} +(-5.50162 - 0.619884i) q^{39} +(4.31156 + 4.31156i) q^{41} +(7.18386 + 2.51374i) q^{43} +(0.996434 - 4.36566i) q^{45} +(1.48214 + 2.35881i) q^{47} +(0.380985 + 1.66920i) q^{49} +(6.93590 - 8.69734i) q^{51} +(-1.01655 - 0.489545i) q^{53} +(-0.405356 - 3.59763i) q^{55} +16.0582i q^{57} +6.17711i q^{59} +(-0.362218 - 3.21477i) q^{61} +(-3.83496 - 1.84682i) q^{63} +(-5.08576 + 6.37734i) q^{65} +(-2.81368 - 12.3275i) q^{67} +(-1.71314 - 2.72644i) q^{69} +(1.65815 - 7.26482i) q^{71} +(4.24079 + 1.48392i) q^{73} +(-6.91840 - 6.91840i) q^{75} +(-3.41972 - 0.385309i) q^{77} +(-0.529403 + 0.842540i) q^{79} +(-10.1329 + 4.87974i) q^{81} +(5.18722 - 4.13667i) q^{83} +(-5.41316 - 15.4699i) q^{85} +(9.64756 + 5.97870i) q^{87} +(-7.27452 + 2.54547i) q^{89} +(4.83425 + 6.06195i) q^{91} +(8.21858 + 17.0661i) q^{93} +(20.0325 + 12.5873i) q^{95} +(-1.13893 + 10.1082i) q^{97} +(1.18889 - 1.18889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 16 q^{17} + 16 q^{21} + 24 q^{25} + 80 q^{29} + 84 q^{33} + 28 q^{37} + 8 q^{41} - 100 q^{45} + 24 q^{49} - 20 q^{53} + 32 q^{61} + 48 q^{65} + 56 q^{73} - 180 q^{77} - 152 q^{81} - 152 q^{85} - 84 q^{89} - 112 q^{93}+O(q^{100}) $ 48 * q - 16 * q^17 + 16 * q^21 + 24 * q^25 + 80 * q^29 + 84 * q^33 + 28 * q^37 + 8 * q^41 - 100 * q^45 + 24 * q^49 - 20 * q^53 + 32 * q^61 + 48 * q^65 + 56 * q^73 - 180 * q^77 - 152 * q^81 - 152 * q^85 - 84 * q^89 - 112 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{25}{28}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.09437	−	0.235979i	1.20919	−	0.136243i	0.515736	−	0.856748i	$-0.327519\pi$
$3$	2.09437	−	0.235979i	1.20919	−	0.136243i	0.693450	+	0.720505i	$0.256090\pi$
$4$		0			0
$5$	1.34729	−	2.79769i	0.602528	−	1.25116i	−0.347113	−	0.937823i	$-0.612838\pi$
$5$	1.34729	−	2.79769i	0.602528	−	1.25116i	0.949641	−	0.313339i	$-0.101448\pi$
$6$		0			0
$7$	−2.30768	−	1.84031i	−0.872221	−	0.695573i	0.0813684	−	0.996684i	$-0.474071\pi$
$7$	−2.30768	−	1.84031i	−0.872221	−	0.695573i	−0.953589	+	0.301111i	$0.902642\pi$
$8$		0			0
$9$	1.40592	−	0.320892i	0.468640	−	0.106964i
$10$		0			0
$11$	0.987209	−	0.620305i	0.297655	−	0.187029i	−0.374922	−	0.927056i	$-0.622330\pi$
$11$	0.987209	−	0.620305i	0.297655	−	0.187029i	0.672577	+	0.740028i	$0.265188\pi$
$12$		0			0
$13$	−2.56100	−	0.584532i	−0.710294	−	0.162120i	−0.147915	−	0.989000i	$-0.547256\pi$
$13$	−2.56100	−	0.584532i	−0.710294	−	0.162120i	−0.562378	+	0.826880i	$0.690114\pi$
$14$		0			0
$15$	2.16154	−	6.17732i	0.558107	−	1.59498i
$16$		0			0
$17$	3.73220	−	3.73220i	0.905193	−	0.905193i	−0.0906869	−	0.995879i	$-0.528906\pi$
$17$	3.73220	−	3.73220i	0.905193	−	0.905193i	0.995879	+	0.0906869i	$0.0289062\pi$
$18$		0			0
$19$	−0.853070	+	7.57121i	−0.195708	+	1.73695i	0.385066	+	0.922889i	$0.374179\pi$
$19$	−0.853070	+	7.57121i	−0.195708	+	1.73695i	−0.580773	+	0.814065i	$0.697250\pi$
$20$		0			0
$21$	−5.26741	−	3.30973i	−1.14944	−	0.722243i
$22$		0			0
$23$	−0.662879	−	1.37648i	−0.138220	−	0.287016i	0.820356	−	0.571853i	$-0.193775\pi$
$23$	−0.662879	−	1.37648i	−0.138220	−	0.287016i	−0.958576	+	0.284836i	$0.908061\pi$
$24$		0			0
$25$	−2.89439	−	3.62945i	−0.578878	−	0.725890i
$26$		0			0
$27$	−3.09926	+	1.08448i	−0.596452	+	0.208708i
$28$		0			0
$29$	4.23107	+	3.33138i	0.785689	+	0.618622i
$29$	4.23107	+	3.33138i	0.785689	+	0.618622i
$30$		0			0
$31$	2.96833	+	8.48299i	0.533127	+	1.52359i	0.823864	+	0.566787i	$0.191814\pi$
$31$	2.96833	+	8.48299i	0.533127	+	1.52359i	−0.290737	+	0.956803i	$0.593901\pi$
$32$		0			0
$33$	1.92120	−	1.53211i	0.334439	−	0.266706i
$34$		0			0
$35$	−8.25774	+	3.97672i	−1.39581	+	0.672188i
$36$		0			0
$37$	4.32508	−	6.88332i	0.711038	−	1.13161i	−0.274406	−	0.961614i	$-0.588481\pi$
$37$	4.32508	−	6.88332i	0.711038	−	1.13161i	0.985445	−	0.169997i	$-0.0543758\pi$
$38$		0			0
$39$	−5.50162	−	0.619884i	−0.880965	−	0.0992609i
$40$		0			0
$41$	4.31156	+	4.31156i	0.673352	+	0.673352i	0.958487	−	0.285135i	$-0.0920384\pi$
$41$	4.31156	+	4.31156i	0.673352	+	0.673352i	−0.285135	+	0.958487i	$0.592038\pi$
$42$		0			0
$43$	7.18386	+	2.51374i	1.09553	+	0.383342i	0.816737	−	0.577010i	$-0.195780\pi$
$43$	7.18386	+	2.51374i	1.09553	+	0.383342i	0.278791	+	0.960352i	$0.410066\pi$
$44$		0			0
$45$	0.996434	−	4.36566i	0.148540	−	0.650794i
$46$		0			0
$47$	1.48214	+	2.35881i	0.216192	+	0.344068i	0.937160	−	0.348901i	$-0.113445\pi$
$47$	1.48214	+	2.35881i	0.216192	+	0.344068i	−0.720967	+	0.692969i	$0.756302\pi$
$48$		0			0
$49$	0.380985	+	1.66920i	0.0544264	+	0.238458i
$50$		0			0
$51$	6.93590	−	8.69734i	0.971220	−	1.21787i
$52$		0			0
$53$	−1.01655	−	0.489545i	−0.139634	−	0.0672442i	0.362762	−	0.931882i	$-0.381834\pi$
$53$	−1.01655	−	0.489545i	−0.139634	−	0.0672442i	−0.502396	+	0.864638i	$0.667548\pi$
$54$		0			0
$55$	−0.405356	−	3.59763i	−0.0546582	−	0.485105i
$56$		0			0
$57$			16.0582i			2.12696i
$58$		0			0
$59$			6.17711i			0.804191i	0.915598	+	0.402095i	$0.131718\pi$
$59$			6.17711i			0.804191i	−0.915598	+	0.402095i	$0.868282\pi$
$60$		0			0
$61$	−0.362218	−	3.21477i	−0.0463772	−	0.411609i	−0.995355	−	0.0962677i	$-0.969310\pi$
$61$	−0.362218	−	3.21477i	−0.0463772	−	0.411609i	0.948978	−	0.315341i	$-0.102119\pi$
$62$		0			0
$63$	−3.83496	−	1.84682i	−0.483159	−	0.232677i
$64$		0			0
$65$	−5.08576	+	6.37734i	−0.630810	+	0.791011i
$66$		0			0
$67$	−2.81368	−	12.3275i	−0.343745	−	1.50605i	−0.791098	−	0.611689i	$-0.790490\pi$
$67$	−2.81368	−	12.3275i	−0.343745	−	1.50605i	0.447353	−	0.894357i	$-0.352367\pi$
$68$		0			0
$69$	−1.71314	−	2.72644i	−0.206237	−	0.328225i
$70$		0			0
$71$	1.65815	−	7.26482i	0.196786	−	0.862175i	−0.776048	−	0.630673i	$-0.782779\pi$
$71$	1.65815	−	7.26482i	0.196786	−	0.862175i	0.972834	−	0.231502i	$-0.0743640\pi$
$72$		0			0
$73$	4.24079	+	1.48392i	0.496347	+	0.173679i	0.566832	−	0.823833i	$-0.308169\pi$
$73$	4.24079	+	1.48392i	0.496347	+	0.173679i	−0.0704846	+	0.997513i	$0.522455\pi$
$74$		0			0
$75$	−6.91840	−	6.91840i	−0.798868	−	0.798868i
$76$		0			0
$77$	−3.41972	−	0.385309i	−0.389713	−	0.0439101i
$78$		0			0
$79$	−0.529403	+	0.842540i	−0.0595625	+	0.0947932i	−0.875178	−	0.483801i	$-0.839256\pi$
$79$	−0.529403	+	0.842540i	−0.0595625	+	0.0947932i	0.815615	+	0.578595i	$0.196399\pi$
$80$		0			0
$81$	−10.1329	+	4.87974i	−1.12588	+	0.542193i
$82$		0			0
$83$	5.18722	−	4.13667i	0.569371	−	0.454058i	−0.296001	−	0.955188i	$-0.595653\pi$
$83$	5.18722	−	4.13667i	0.569371	−	0.454058i	0.865372	+	0.501129i	$0.167082\pi$
$84$		0			0
$85$	−5.41316	−	15.4699i	−0.587139	−	1.67795i
$86$		0			0
$87$	9.64756	+	5.97870i	1.03433	+	0.640984i
$88$		0			0
$89$	−7.27452	+	2.54547i	−0.771098	+	0.269819i	−0.687018	−	0.726640i	$-0.741081\pi$
$89$	−7.27452	+	2.54547i	−0.771098	+	0.269819i	−0.0840797	+	0.996459i	$0.526795\pi$
$90$		0			0
$91$	4.83425	+	6.06195i	0.506767	+	0.635465i
$92$		0			0
$93$	8.21858	+	17.0661i	0.852227	+	1.76967i
$94$		0			0
$95$	20.0325	+	12.5873i	2.05529	+	1.29143i
$96$		0			0
$97$	−1.13893	+	10.1082i	−0.115640	+	1.02634i	0.793134	+	0.609048i	$0.208448\pi$
$97$	−1.13893	+	10.1082i	−0.115640	+	1.02634i	−0.908774	+	0.417289i	$0.862980\pi$
$98$		0			0
$99$	1.18889	−	1.18889i	0.119488	−	0.119488i
$100$		0			0
$101$	−4.42617	+	12.6493i	−0.440420	+	1.25865i	0.483257	+	0.875478i	$0.339454\pi$
$101$	−4.42617	+	12.6493i	−0.440420	+	1.25865i	−0.923678	+	0.383171i	$0.874832\pi$
$102$		0			0
$103$	−9.59132	−	2.18916i	−0.945061	−	0.215704i	−0.277894	−	0.960612i	$-0.589636\pi$
$103$	−9.59132	−	2.18916i	−0.945061	−	0.215704i	−0.667167	+	0.744908i	$0.732493\pi$
$104$		0			0
$105$	−16.3563	+	10.2774i	−1.59622	+	1.00297i
$106$		0			0
$107$	−16.2627	+	3.71186i	−1.57218	+	0.358839i	−0.917710	−	0.397251i	$-0.869964\pi$
$107$	−16.2627	+	3.71186i	−1.57218	+	0.358839i	−0.654468	+	0.756090i	$0.727107\pi$
$108$		0			0
$109$	−7.40742	−	5.90722i	−0.709503	−	0.565809i	0.200860	−	0.979620i	$-0.435626\pi$
$109$	−7.40742	−	5.90722i	−0.709503	−	0.565809i	−0.910363	+	0.413810i	$0.864198\pi$
$110$		0			0
$111$	7.43400	−	15.4369i	0.705604	−	1.46520i
$112$		0			0
$113$	12.1029	−	1.36367i	1.13855	−	0.128283i	0.477503	−	0.878630i	$-0.341542\pi$
$113$	12.1029	−	1.36367i	1.13855	−	0.128283i	0.661044	+	0.750347i	$0.270113\pi$
$114$		0			0
$115$	−4.74406			−0.442386
$116$		0			0
$117$	−3.78814			−0.350213
$118$		0			0
$119$	−15.4812	+	1.74431i	−1.41915	+	0.159900i
$120$		0			0
$121$	−4.18292	+	8.68592i	−0.380265	+	0.789629i
$122$		0			0
$123$	10.0474	+	8.01257i	0.905947	+	0.722469i
$124$		0			0
$125$	1.08305	−	0.247200i	0.0968712	−	0.0221102i
$126$		0			0
$127$	−14.0909	+	8.85389i	−1.25036	+	0.785656i	−0.983992	−	0.178215i	$-0.942968\pi$
$127$	−14.0909	+	8.85389i	−1.25036	+	0.785656i	−0.266372	+	0.963870i	$0.585825\pi$
$128$		0			0
$129$	15.6389	+	3.56947i	1.37693	+	0.314274i
$130$		0			0
$131$	2.04606	−	5.84730i	0.178765	−	0.510881i	−0.819279	−	0.573395i	$-0.805626\pi$
$131$	2.04606	−	5.84730i	0.178765	−	0.510881i	0.998044	+	0.0625141i	$0.0199118\pi$
$132$		0			0
$133$	15.9020	−	15.9020i	1.37888	−	1.37888i
$134$		0			0
$135$	−1.14159	+	10.1318i	−0.0982520	+	0.872011i
$136$		0			0
$137$	0.943425	+	0.592793i	0.0806022	+	0.0506457i	0.571730	−	0.820442i	$-0.306272\pi$
$137$	0.943425	+	0.592793i	0.0806022	+	0.0506457i	−0.491128	+	0.871087i	$0.663415\pi$
$138$		0			0
$139$	−2.85245	−	5.92318i	−0.241942	−	0.502398i	0.744271	−	0.667877i	$-0.232797\pi$
$139$	−2.85245	−	5.92318i	−0.241942	−	0.502398i	−0.986213	+	0.165480i	$0.947083\pi$
$140$		0			0
$141$	3.66078	+	4.59048i	0.308294	+	0.386588i
$142$		0			0
$143$	−2.89083	+	1.01155i	−0.241743	+	0.0845897i
$144$		0			0
$145$	15.0206	−	7.34884i	1.24740	−	0.610288i
$146$		0			0
$147$	1.19182	+	3.40603i	0.0982997	+	0.280925i
$148$		0			0
$149$	−14.6711	+	11.6998i	−1.20190	+	0.958487i	−0.999782	−	0.0208734i	$-0.993355\pi$
$149$	−14.6711	+	11.6998i	−1.20190	+	0.958487i	−0.202122	+	0.979360i	$0.564784\pi$
$150$		0			0
$151$	6.23281	−	3.00156i	0.507219	−	0.244264i	−0.162730	−	0.986671i	$-0.552030\pi$
$151$	6.23281	−	3.00156i	0.507219	−	0.244264i	0.669949	+	0.742407i	$0.266316\pi$
$152$		0			0
$153$	4.04955	−	6.44482i	0.327387	−	0.521033i
$154$		0			0
$155$	27.7319	+	3.12464i	2.22748	+	0.250977i
$156$		0			0
$157$	−5.35355	−	5.35355i	−0.427260	−	0.427260i	0.460434	−	0.887694i	$-0.347694\pi$
$157$	−5.35355	−	5.35355i	−0.427260	−	0.427260i	−0.887694	+	0.460434i	$0.847694\pi$
$158$		0			0
$159$	−2.24456	−	0.785405i	−0.178005	−	0.0622866i
$160$		0			0
$161$	−1.00345	+	4.39638i	−0.0790826	+	0.346483i
$162$		0			0
$163$	−10.1118	−	16.0928i	−0.792014	−	1.26048i	−0.961461	−	0.274943i	$-0.911341\pi$
$163$	−10.1118	−	16.0928i	−0.792014	−	1.26048i	0.169447	−	0.985539i	$-0.445802\pi$
$164$		0			0
$165$	−1.69793	−	7.43912i	−0.132184	−	0.579135i
$166$		0			0
$167$	−15.3968	+	19.3069i	−1.19144	+	1.49401i	−0.364979	+	0.931016i	$0.618924\pi$
$167$	−15.3968	+	19.3069i	−1.19144	+	1.49401i	−0.826457	+	0.562999i	$0.809647\pi$
$168$		0			0
$169$	−5.49555	−	2.64652i	−0.422735	−	0.203578i
$170$		0			0
$171$	1.23019	+	10.9183i	0.0940752	+	0.834941i
$172$		0			0
$173$			7.05771i			0.536587i	0.963337	+	0.268294i	$0.0864598\pi$
$173$			7.05771i			0.536587i	−0.963337	+	0.268294i	$0.913540\pi$
$174$		0			0
$175$			13.7022i			1.03579i
$176$		0			0
$177$	1.45767	+	12.9372i	0.109565	+	0.972416i
$178$		0			0
$179$	−22.9964	−	11.0745i	−1.71883	−	0.827745i	−0.989664	−	0.143408i	$-0.954194\pi$
$179$	−22.9964	−	11.0745i	−1.71883	−	0.827745i	−0.729166	−	0.684337i	$-0.760092\pi$
$180$		0			0
$181$	3.41861	−	4.28680i	0.254103	−	0.318635i	−0.638375	−	0.769725i	$-0.720393\pi$
$181$	3.41861	−	4.28680i	0.254103	−	0.318635i	0.892478	+	0.451090i	$0.148965\pi$
$182$		0			0
$183$	−1.51724	−	6.64745i	−0.112157	−	0.491393i
$184$		0			0
$185$	−13.4302	−	21.3741i	−0.987409	−	1.57145i
$186$		0			0
$187$	1.36936	−	5.99957i	0.100138	−	0.438732i
$188$		0			0
$189$	9.14786	+	3.20098i	0.665409	+	0.232837i
$190$		0			0
$191$	8.71514	+	8.71514i	0.630605	+	0.630605i	0.948220	−	0.317615i	$-0.102882\pi$
$191$	8.71514	+	8.71514i	0.630605	+	0.630605i	−0.317615	+	0.948220i	$0.602882\pi$
$192$		0			0
$193$	3.61876	+	0.407736i	0.260484	+	0.0293495i	0.241241	−	0.970465i	$-0.422446\pi$
$193$	3.61876	+	0.407736i	0.260484	+	0.0293495i	0.0192434	+	0.999815i	$0.493874\pi$
$194$		0			0
$195$	−9.14654	+	14.5566i	−0.654998	+	1.04242i
$196$		0			0
$197$	−21.6907	+	10.4457i	−1.54540	+	0.744224i	−0.995830	−	0.0912250i	$-0.970922\pi$
$197$	−21.6907	+	10.4457i	−1.54540	+	0.744224i	−0.549567	+	0.835449i	$0.685207\pi$
$198$		0			0
$199$	16.1895	−	12.9107i	1.14764	−	0.915216i	0.150343	−	0.988634i	$-0.451962\pi$
$199$	16.1895	−	12.9107i	1.14764	−	0.915216i	0.997301	+	0.0734183i	$0.0233908\pi$
$200$		0			0
$201$	−8.80192	−	25.1544i	−0.620840	−	1.77426i
$202$		0			0
$203$	−3.63316	−	15.4742i	−0.254998	−	1.08608i
$204$		0			0
$205$	17.8713	−	6.25345i	1.24819	−	0.436760i
$206$		0			0
$207$	−1.37366	−	1.72251i	−0.0954758	−	0.119723i
$208$		0			0
$209$	3.85430	+	8.00353i	0.266607	+	0.553616i
$210$		0			0
$211$	21.3418	+	13.4100i	1.46923	+	0.923180i	0.999178	+	0.0405424i	$0.0129086\pi$
$211$	21.3418	+	13.4100i	1.46923	+	0.923180i	0.470054	+	0.882637i	$0.344234\pi$
$212$		0			0
$213$	1.75843	−	15.6065i	0.120486	−	1.06934i
$214$		0			0
$215$	16.7114	−	16.7114i	1.13971	−	1.13971i
$216$		0			0
$217$	8.76141	−	25.0387i	0.594763	−	1.69974i
$218$		0			0
$219$	9.23197	+	2.10714i	0.623839	+	0.142387i
$220$		0			0
$221$	−11.7398	+	7.37659i	−0.789702	+	0.496203i
$222$		0			0
$223$	−2.58349	+	0.589664i	−0.173003	+	0.0394868i	−0.308145	−	0.951339i	$-0.599708\pi$
$223$	−2.58349	+	0.589664i	−0.173003	+	0.0394868i	0.135142	+	0.990826i	$0.456851\pi$
$224$		0			0
$225$	−5.23395	−	4.17393i	−0.348930	−	0.278262i
$226$		0			0
$227$	4.89134	−	10.1570i	0.324649	−	0.674142i	−0.673216	−	0.739446i	$-0.735088\pi$
$227$	4.89134	−	10.1570i	0.324649	−	0.674142i	0.997865	+	0.0653044i	$0.0208018\pi$
$228$		0			0
$229$	−14.2156	+	1.60172i	−0.939396	+	0.105845i	−0.568366	−	0.822776i	$-0.692424\pi$
$229$	−14.2156	+	1.60172i	−0.939396	+	0.105845i	−0.371031	+	0.928621i	$0.620995\pi$
$230$		0			0
$231$	−7.25308			−0.477218
$232$		0			0
$233$	13.6749			0.895872			0.447936	−	0.894066i	$-0.352159\pi$
$233$	13.6749			0.895872			0.447936	+	0.894066i	$0.352159\pi$
$234$		0			0
$235$	8.59610	−	0.968547i	0.560747	−	0.0631811i
$236$		0			0
$237$	−0.909945	+	1.88952i	−0.0591073	+	0.122738i
$238$		0			0
$239$	8.30159	+	6.62029i	0.536985	+	0.428231i	0.854064	−	0.520168i	$-0.174131\pi$
$239$	8.30159	+	6.62029i	0.536985	+	0.428231i	−0.317079	+	0.948399i	$0.602702\pi$
$240$		0			0
$241$	21.0142	−	4.79635i	1.35364	−	0.308960i	0.516660	−	0.856191i	$-0.327175\pi$
$241$	21.0142	−	4.79635i	1.35364	−	0.308960i	0.836982	+	0.547231i	$0.184318\pi$
$242$		0			0
$243$	−11.7298	+	7.37032i	−0.752467	+	0.472806i
$244$		0			0
$245$	5.18321	+	1.18303i	0.331143	+	0.0755812i
$246$		0			0
$247$	6.61033	−	18.8912i	0.420605	−	1.20202i
$248$		0			0
$249$	9.88779	−	9.88779i	0.626613	−	0.626613i
$250$		0			0
$251$	2.82321	−	25.0567i	0.178200	−	1.58157i	−0.512669	−	0.858586i	$-0.671343\pi$
$251$	2.82321	−	25.0567i	0.178200	−	1.58157i	0.690869	−	0.722980i	$-0.257228\pi$
$252$		0			0
$253$	−1.50824	−	0.947689i	−0.0948221	−	0.0595807i
$254$		0			0
$255$	−14.9877	−	31.1223i	−0.938568	−	1.94896i
$256$		0			0
$257$	−6.70885	−	8.41263i	−0.418487	−	0.524766i	0.527245	−	0.849713i	$-0.323225\pi$
$257$	−6.70885	−	8.41263i	−0.418487	−	0.524766i	−0.945732	+	0.324947i	$0.894653\pi$
$258$		0			0
$259$	−22.6483	+	7.92500i	−1.40730	+	0.492435i
$260$		0			0
$261$	7.01756	+	3.32594i	0.434376	+	0.205871i
$262$		0			0
$263$	2.82427	+	8.07131i	0.174152	+	0.497698i	0.997565	−	0.0697448i	$-0.0222185\pi$
$263$	2.82427	+	8.07131i	0.174152	+	0.497698i	−0.823413	+	0.567443i	$0.807933\pi$
$264$		0			0
$265$	−2.73919	+	2.18443i	−0.168267	+	0.134188i
$266$		0			0
$267$	−14.6349	+	7.04778i	−0.895640	+	0.431317i
$268$		0			0
$269$	11.7074	−	18.6323i	0.713816	−	1.13603i	−0.271026	−	0.962572i	$-0.587363\pi$
$269$	11.7074	−	18.6323i	0.713816	−	1.13603i	0.984841	−	0.173459i	$-0.0554943\pi$
$270$		0			0
$271$	−0.307953	−	0.0346980i	−0.0187068	−	0.00210775i	0.102606	−	0.994722i	$-0.467282\pi$
$271$	−0.307953	−	0.0346980i	−0.0187068	−	0.00210775i	−0.121313	+	0.992614i	$0.538710\pi$
$272$		0			0
$273$	11.5552	+	11.5552i	0.699352	+	0.699352i
$274$		0			0
$275$	−5.10873	−	1.78762i	−0.308068	−	0.107798i
$276$		0			0
$277$	6.91767	−	30.3083i	0.415642	−	1.82105i	−0.140647	−	0.990060i	$-0.544918\pi$
$277$	6.91767	−	30.3083i	0.415642	−	1.82105i	0.556290	−	0.830989i	$-0.312225\pi$
$278$		0			0
$279$	6.89536	+	10.9739i	0.412814	+	0.656990i
$280$		0			0
$281$	−1.72954	−	7.57763i	−0.103176	−	0.452043i	−0.999954	−	0.00956320i	$-0.996956\pi$
$281$	−1.72954	−	7.57763i	−0.103176	−	0.452043i	0.896778	−	0.442480i	$-0.145901\pi$
$282$		0			0
$283$	6.86684	−	8.61075i	0.408191	−	0.511856i	−0.534661	−	0.845067i	$-0.679561\pi$
$283$	6.86684	−	8.61075i	0.408191	−	0.511856i	0.942852	+	0.333211i	$0.108132\pi$
$284$		0			0
$285$	44.9259	+	21.6352i	2.66118	+	1.28156i
$286$		0			0
$287$	−2.01508	−	17.8843i	−0.118946	−	1.05568i
$288$		0			0
$289$		−	10.8587i		−	0.638747i
$290$		0			0
$291$			21.4392i			1.25679i
$292$		0			0
$293$	1.61435	+	14.3278i	0.0943115	+	0.837038i	0.948436	+	0.316969i	$0.102665\pi$
$293$	1.61435	+	14.3278i	0.0943115	+	0.837038i	−0.854124	+	0.520069i	$0.825906\pi$
$294$		0			0
$295$	17.2816	+	8.32238i	1.00617	+	0.484548i
$296$		0			0
$297$	−2.38691	+	2.99309i	−0.138502	+	0.173677i
$298$		0			0
$299$	0.893036	+	3.91264i	0.0516456	+	0.226274i
$300$		0			0
$301$	−11.9520	−	19.0215i	−0.688900	−	1.09638i
$302$		0			0
$303$	−6.28508	+	27.5367i	−0.361069	+	1.58194i
$304$		0			0
$305$	−9.48193	−	3.31787i	−0.542934	−	0.189981i
$306$		0			0
$307$	7.59248	+	7.59248i	0.433326	+	0.433326i	0.889758	−	0.456432i	$-0.150873\pi$
$307$	7.59248	+	7.59248i	0.433326	+	0.433326i	−0.456432	+	0.889758i	$0.650873\pi$
$308$		0			0
$309$	−20.6044	−	2.32156i	−1.17214	−	0.132069i
$310$		0			0
$311$	5.27706	−	8.39839i	0.299234	−	0.476229i	−0.662936	−	0.748676i	$-0.730690\pi$
$311$	5.27706	−	8.39839i	0.299234	−	0.476229i	0.962171	+	0.272447i	$0.0878329\pi$
$312$		0			0
$313$	7.41861	−	3.57262i	0.419325	−	0.201936i	−0.212310	−	0.977202i	$-0.568099\pi$
$313$	7.41861	−	3.57262i	0.419325	−	0.201936i	0.631635	+	0.775266i	$0.282384\pi$
$314$		0			0
$315$	−10.3336	+	8.24079i	−0.582234	+	0.464316i
$316$		0			0
$317$	9.70532	+	27.7362i	0.545105	+	1.55782i	0.805670	+	0.592365i	$0.201806\pi$
$317$	9.70532	+	27.7362i	0.545105	+	1.55782i	−0.260565	+	0.965456i	$0.583909\pi$
$318$		0			0
$319$	6.24342	+	0.664219i	0.349564	+	0.0371891i
$320$		0			0
$321$	−33.1843	+	11.6117i	−1.85217	+	0.648101i
$322$		0			0
$323$	25.0735	+	31.4411i	1.39513	+	1.74943i
$324$		0			0
$325$	5.29101	+	10.9869i	0.293492	+	0.609443i
$326$		0			0
$327$	−16.9079	−	10.6239i	−0.935008	−	0.587504i
$328$		0			0
$329$	0.920649	−	8.17098i	0.0507570	−	0.450481i
$330$		0			0
$331$	−12.6785	+	12.6785i	−0.696872	+	0.696872i	−0.963735	−	0.266863i	$-0.914013\pi$
$331$	−12.6785	+	12.6785i	−0.696872	+	0.696872i	0.266863	+	0.963735i	$0.414013\pi$
$332$		0			0
$333$	3.87191	−	11.0653i	0.212179	−	0.606374i
$334$		0			0
$335$	−38.2794	−	8.73702i	−2.09143	−	0.477354i
$336$		0			0
$337$	−18.4993	+	11.6239i	−1.00772	+	0.633193i	−0.931441	−	0.363894i	$-0.881447\pi$
$337$	−18.4993	+	11.6239i	−1.00772	+	0.633193i	−0.0762800	+	0.997086i	$0.524304\pi$
$338$		0			0
$339$	25.0262	−	5.71207i	1.35924	−	0.310237i
$340$		0			0
$341$	8.19240	+	6.53322i	0.443643	+	0.353794i
$342$		0			0
$343$	−6.77199	+	14.0622i	−0.365653	+	0.759286i
$344$		0			0
$345$	−9.93581	+	1.11950i	−0.534926	+	0.0602717i
$346$		0			0
$347$	2.98192			0.160078			0.0800389	−	0.996792i	$-0.474496\pi$
$347$	2.98192			0.160078			0.0800389	+	0.996792i	$0.474496\pi$
$348$		0			0
$349$	16.0459			0.858917			0.429458	−	0.903087i	$-0.358704\pi$
$349$	16.0459			0.858917			0.429458	+	0.903087i	$0.358704\pi$
$350$		0			0
$351$	8.57111	−	0.965732i	0.457492	−	0.0515469i
$352$		0			0
$353$	0.503281	−	1.04507i	0.0267869	−	0.0556236i	−0.887146	−	0.461489i	$-0.847315\pi$
$353$	0.503281	−	1.04507i	0.0267869	−	0.0556236i	0.913933	+	0.405865i	$0.133030\pi$
$354$		0			0
$355$	−18.0907	−	14.4268i	−0.960153	−	0.765696i
$356$		0			0
$357$	−32.0117	+	7.30645i	−1.69424	+	0.386698i
$358$		0			0
$359$	−7.98355	+	5.01640i	−0.421356	+	0.264755i	−0.725978	−	0.687718i	$-0.758613\pi$
$359$	−7.98355	+	5.01640i	−0.421356	+	0.264755i	0.304622	+	0.952473i	$0.401470\pi$
$360$		0			0
$361$	−38.0719	−	8.68965i	−2.00378	−	0.457350i
$362$		0			0
$363$	−6.71089	+	19.1786i	−0.352230	+	1.00662i
$364$		0			0
$365$	9.86513	−	9.86513i	0.516365	−	0.516365i
$366$		0			0
$367$	−1.04407	+	9.26640i	−0.0545001	+	0.483702i	0.936582	+	0.350449i	$0.113971\pi$
$367$	−1.04407	+	9.26640i	−0.0545001	+	0.483702i	−0.991082	+	0.133253i	$0.957458\pi$
$368$		0			0
$369$	7.44526	+	4.67816i	0.387585	+	0.243536i
$370$		0			0
$371$	1.44496	+	3.00048i	0.0750184	+	0.155777i
$372$		0			0
$373$	1.52198	+	1.90850i	0.0788049	+	0.0988182i	0.819671	−	0.572834i	$-0.194156\pi$
$373$	1.52198	+	1.90850i	0.0788049	+	0.0988182i	−0.740866	+	0.671653i	$0.765585\pi$
$374$		0			0
$375$	2.20998	−	0.773306i	0.114123	−	0.0399333i
$376$		0			0
$377$	−8.88846	−	11.0049i	−0.457779	−	0.566779i
$378$		0			0
$379$	0.383516	+	1.09603i	0.0196999	+	0.0562991i	0.953313	−	0.301983i	$-0.0976485\pi$
$379$	0.383516	+	1.09603i	0.0196999	+	0.0562991i	−0.933614	+	0.358282i	$0.883363\pi$
$380$		0			0
$381$	−27.4222	+	21.8685i	−1.40488	+	1.12036i
$382$		0			0
$383$	−19.7833	+	9.52714i	−1.01088	+	0.486814i	−0.864617	−	0.502432i	$-0.832439\pi$
$383$	−19.7833	+	9.52714i	−1.01088	+	0.486814i	−0.146263	+	0.989246i	$0.546724\pi$
$384$		0			0
$385$	−5.68534	+	9.04816i	−0.289752	+	0.461137i
$386$		0			0
$387$	10.9066	+	1.22888i	0.554413	+	0.0624673i
$388$		0			0
$389$	19.8252	+	19.8252i	1.00518	+	1.00518i	0.999987	+	0.00519035i	$0.00165215\pi$
$389$	19.8252	+	19.8252i	1.00518	+	1.00518i	0.00519035	+	0.999987i	$0.498348\pi$
$390$		0			0
$391$	−7.61131	−	2.66331i	−0.384921	−	0.134690i
$392$		0			0
$393$	2.90537	−	12.7292i	0.146556	−	0.642105i
$394$		0			0
$395$	1.64390	+	2.61625i	0.0827136	+	0.131638i
$396$		0			0
$397$	3.37636	+	14.7928i	0.169454	+	0.742428i	0.986217	+	0.165455i	$0.0529092\pi$
$397$	3.37636	+	14.7928i	0.169454	+	0.742428i	−0.816763	+	0.576973i	$0.804234\pi$
$398$		0			0
$399$	29.5522	−	37.0572i	1.47946	−	1.85518i
$400$		0			0
$401$	35.2210	+	16.9615i	1.75885	+	0.847018i	0.973740	+	0.227662i	$0.0731080\pi$
$401$	35.2210	+	16.9615i	1.75885	+	0.847018i	0.785110	+	0.619356i	$0.212606\pi$
$402$		0			0
$403$	−2.64331	−	23.4600i	−0.131673	−	1.16863i
$404$		0			0
$405$			34.9230i			1.73534i
$406$		0			0
$407$		−	9.47814i		−	0.469814i
$408$		0			0
$409$	3.33611	+	29.6088i	0.164960	+	1.46406i	0.754489	+	0.656313i	$0.227885\pi$
$409$	3.33611	+	29.6088i	0.164960	+	1.46406i	−0.589529	+	0.807747i	$0.700687\pi$
$410$		0			0
$411$	2.11577	+	1.01890i	0.104363	+	0.0502587i
$412$		0			0
$413$	11.3678	−	14.2548i	0.559373	−	0.701432i
$414$		0			0
$415$	−4.58439	−	20.0855i	−0.225039	−	0.985959i
$416$		0			0
$417$	−7.37184	−	11.7322i	−0.361001	−	0.574529i
$418$		0			0
$419$	2.56850	−	11.2533i	0.125479	−	0.549760i	−0.872635	−	0.488373i	$-0.837590\pi$
$419$	2.56850	−	11.2533i	0.125479	−	0.549760i	0.998114	−	0.0613870i	$-0.0195524\pi$
$420$		0			0
$421$	−33.9911	−	11.8940i	−1.65662	−	0.579678i	−0.669952	−	0.742404i	$-0.733685\pi$
$421$	−33.9911	−	11.8940i	−1.65662	−	0.579678i	−0.986671	+	0.162727i	$0.947971\pi$
$422$		0			0
$423$	2.84070	+	2.84070i	0.138119	+	0.138119i
$424$		0			0
$425$	−24.3483	−	2.74340i	−1.18107	−	0.133074i
$426$		0			0
$427$	−5.08030	+	8.08525i	−0.245853	+	0.391273i
$428$		0			0
$429$	−5.81577	+	2.80073i	−0.280788	+	0.135220i
$430$		0			0
$431$	16.6480	−	13.2763i	0.801906	−	0.639499i	−0.134304	−	0.990940i	$-0.542880\pi$
$431$	16.6480	−	13.2763i	0.801906	−	0.639499i	0.936210	+	0.351442i	$0.114308\pi$
$432$		0			0
$433$	−5.39115	−	15.4070i	−0.259082	−	0.740414i	−0.997794	−	0.0663923i	$-0.978851\pi$
$433$	−5.39115	−	15.4070i	−0.259082	−	0.740414i	0.738712	−	0.674022i	$-0.235435\pi$
$434$		0			0
$435$	29.7246	−	18.9358i	1.42519	−	0.907900i
$436$		0			0
$437$	10.9871	−	3.84456i	0.525585	−	0.183910i
$438$		0			0
$439$	2.87858	+	3.60962i	0.137387	+	0.172278i	0.845765	−	0.533555i	$-0.179144\pi$
$439$	2.87858	+	3.60962i	0.137387	+	0.172278i	−0.708378	+	0.705833i	$0.750573\pi$
$440$		0			0
$441$	1.07127	+	2.22451i	0.0510128	+	0.105929i
$442$		0			0
$443$	−15.7193	−	9.87707i	−0.746845	−	0.469274i	0.104075	−	0.994569i	$-0.466812\pi$
$443$	−15.7193	−	9.87707i	−0.746845	−	0.469274i	−0.850920	+	0.525296i	$0.823955\pi$
$444$		0			0
$445$	−2.67951	+	23.7813i	−0.127021	+	1.12734i
$446$		0			0
$447$	−27.9658	+	27.9658i	−1.32274	+	1.32274i
$448$		0			0
$449$	−0.704079	+	2.01214i	−0.0332276	+	0.0949589i	−0.959302	−	0.282381i	$-0.908876\pi$
$449$	−0.704079	+	2.01214i	−0.0332276	+	0.0949589i	0.926075	+	0.377340i	$0.123161\pi$
$450$		0			0
$451$	6.93089	+	1.58193i	0.326363	+	0.0744902i
$452$		0			0
$453$	12.3455	−	7.75720i	0.580043	−	0.364465i
$454$		0			0
$455$	23.4726	−	5.35746i	1.10041	−	0.251162i
$456$		0			0
$457$	12.8054	+	10.2120i	0.599013	+	0.477697i	0.875433	−	0.483340i	$-0.160577\pi$
$457$	12.8054	+	10.2120i	0.599013	+	0.477697i	−0.276420	+	0.961037i	$0.589148\pi$
$458$		0			0
$459$	−7.51957	+	15.6145i	−0.350983	+	0.728824i
$460$		0			0
$461$	−18.1185	+	2.04147i	−0.843865	+	0.0950807i	−0.523303	−	0.852147i	$-0.675300\pi$
$461$	−18.1185	+	2.04147i	−0.843865	+	0.0950807i	−0.320562	+	0.947228i	$0.603872\pi$
$462$		0			0
$463$	16.9869			0.789447			0.394724	−	0.918800i	$-0.370840\pi$
$463$	16.9869			0.789447			0.394724	+	0.918800i	$0.370840\pi$
$464$		0			0
$465$	58.8183			2.72763
$466$		0			0
$467$	−1.71710	+	0.193471i	−0.0794580	+	0.00895277i	−0.151604	−	0.988441i	$-0.548444\pi$
$467$	−1.71710	+	0.193471i	−0.0794580	+	0.00895277i	0.0721459	+	0.997394i	$0.477015\pi$
$468$		0			0
$469$	−16.1934	+	33.6260i	−0.747743	+	1.55270i
$470$		0			0
$471$	−12.4757	−	9.94900i	−0.574848	−	0.458426i
$472$		0			0
$473$	8.65126	−	1.97459i	0.397785	−	0.0907919i
$474$		0			0
$475$	29.9485	−	18.8179i	1.37413	−	0.863423i
$476$		0			0
$477$	−1.58628	−	0.362058i	−0.0726308	−	0.0165775i
$478$		0			0
$479$	5.34825	−	15.2844i	0.244368	−	0.698363i	−0.754736	−	0.656029i	$-0.772235\pi$
$479$	5.34825	−	15.2844i	0.244368	−	0.698363i	0.999104	−	0.0423339i	$-0.0134793\pi$
$480$		0			0
$481$	−15.1000	+	15.1000i	−0.688503	+	0.688503i
$482$		0			0
$483$	−1.06413	+	9.44445i	−0.0484198	+	0.429737i
$484$		0			0
$485$	26.7452	+	16.8051i	1.21444	+	0.763082i
$486$		0			0
$487$	5.04874	+	10.4838i	0.228780	+	0.475067i	0.983483	−	0.180999i	$-0.0579332\pi$
$487$	5.04874	+	10.4838i	0.228780	+	0.475067i	−0.754703	+	0.656067i	$0.772219\pi$
$488$		0			0
$489$	−24.9753	−	31.3181i	−1.12942	−	1.41625i
$490$		0			0
$491$	−16.8546	+	5.89768i	−0.760637	+	0.266158i	−0.682600	−	0.730792i	$-0.739151\pi$
$491$	−16.8546	+	5.89768i	−0.760637	+	0.266158i	−0.0780370	+	0.996950i	$0.524865\pi$
$492$		0			0
$493$	28.2246	−	3.35781i	1.27117	−	0.151228i
$494$		0			0
$495$	−1.72435	−	4.92791i	−0.0775038	−	0.221493i
$496$		0			0
$497$	−17.1960	+	13.7134i	−0.771346	+	0.615128i
$498$		0			0
$499$	−6.22583	+	2.99820i	−0.278706	+	0.134218i	−0.568016	−	0.823018i	$-0.692289\pi$
$499$	−6.22583	+	2.99820i	−0.278706	+	0.134218i	0.289309	+	0.957236i	$0.406574\pi$
$500$		0			0
$501$	−27.6905	+	44.0692i	−1.23712	+	1.96887i
$502$		0			0
$503$	0.235790	+	0.0265672i	0.0105134	+	0.00118457i	0.117220	−	0.993106i	$-0.462602\pi$
$503$	0.235790	+	0.0265672i	0.0105134	+	0.00118457i	−0.106706	+	0.994291i	$0.534030\pi$
$504$		0			0
$505$	29.4253	+	29.4253i	1.30941	+	1.30941i
$506$		0			0
$507$	−12.1342	−	4.24595i	−0.538901	−	0.188569i
$508$		0			0
$509$	2.80650	−	12.2961i	0.124396	−	0.545014i	−0.873871	−	0.486158i	$-0.838398\pi$
$509$	2.80650	−	12.2961i	0.124396	−	0.545014i	0.998267	−	0.0588554i	$-0.0187451\pi$
$510$		0			0
$511$	−7.05552	−	11.2288i	−0.312118	−	0.496733i
$512$		0			0
$513$	−5.56691	−	24.3902i	−0.245785	−	1.07686i
$514$		0			0
$515$	−19.0469	+	23.8841i	−0.839307	+	1.05246i
$516$		0			0
$517$	2.92636	+	1.40926i	0.128701	+	0.0619793i
$518$		0			0
$519$	1.66547	+	14.7815i	0.0731060	+	0.648834i
$520$		0			0
$521$		−	33.2575i		−	1.45704i	−0.685025	−	0.728519i	$-0.740209\pi$
$521$		−	33.2575i		−	1.45704i	0.685025	−	0.728519i	$-0.259791\pi$
$522$		0			0
$523$		−	32.1986i		−	1.40795i	−0.710227	−	0.703973i	$-0.751408\pi$
$523$		−	32.1986i		−	1.40795i	0.710227	−	0.703973i	$-0.248592\pi$
$524$		0			0
$525$	3.23343	+	28.6975i	0.141118	+	1.25246i
$526$		0			0
$527$	42.7387	+	20.5819i	1.86172	+	0.896559i
$528$		0			0
$529$	12.8850	−	16.1572i	0.560216	−	0.702489i
$530$		0			0
$531$	1.98219	+	8.68452i	0.0860195	+	0.376876i
$532$		0			0
$533$	−8.52166	−	13.5621i	−0.369114	−	0.587442i
$534$		0			0
$535$	−11.5261	+	50.4990i	−0.498315	+	2.18326i
$536$		0			0
$537$	−50.7763	−	17.7674i	−2.19116	−	0.766720i
$538$		0			0
$539$	1.41153	+	1.41153i	0.0607988	+	0.0607988i
$540$		0			0
$541$	−20.9034	−	2.35525i	−0.898709	−	0.101260i	−0.349492	−	0.936939i	$-0.613646\pi$
$541$	−20.9034	−	2.35525i	−0.898709	−	0.101260i	−0.549218	+	0.835679i	$0.685074\pi$
$542$		0			0
$543$	6.14824	−	9.78487i	0.263846	−	0.419909i
$544$		0			0
$545$	−26.5065	+	12.7649i	−1.13542	+	0.546787i
$546$		0			0
$547$	30.3576	−	24.2094i	1.29800	−	1.03512i	0.301334	−	0.953519i	$-0.402568\pi$
$547$	30.3576	−	24.2094i	1.29800	−	1.03512i	0.996665	−	0.0816013i	$-0.0260034\pi$
$548$		0			0
$549$	−1.54084	−	4.40348i	−0.0657616	−	0.187936i
$550$		0			0
$551$	−28.8320	+	29.1924i	−1.22828	+	1.24364i
$552$		0			0
$553$	2.77223	−	0.970045i	0.117887	−	0.0412505i
$554$		0			0
$555$	−33.1717	−	41.5960i	−1.40806	−	1.76565i
$556$		0			0
$557$	−3.20118	−	6.64731i	−0.135638	−	0.281656i	0.822076	−	0.569378i	$-0.192816\pi$
$557$	−3.20118	−	6.64731i	−0.135638	−	0.281656i	−0.957714	+	0.287723i	$0.907102\pi$
$558$		0			0
$559$	−16.9285	−	10.6369i	−0.716000	−	0.449893i
$560$		0			0
$561$	1.45218	−	12.8885i	0.0613111	−	0.544151i
$562$		0			0
$563$	18.0130	−	18.0130i	0.759158	−	0.759158i	−0.217011	−	0.976169i	$-0.569631\pi$
$563$	18.0130	−	18.0130i	0.759158	−	0.759158i	0.976169	+	0.217011i	$0.0696308\pi$
$564$		0			0
$565$	12.4911	−	35.6974i	0.525503	−	1.50180i
$566$		0			0
$567$	32.3637	+	7.38680i	1.35915	+	0.310216i
$568$		0			0
$569$	4.17358	−	2.62243i	0.174966	−	0.109938i	−0.441702	−	0.897162i	$-0.645625\pi$
$569$	4.17358	−	2.62243i	0.174966	−	0.109938i	0.616668	+	0.787224i	$0.288482\pi$
$570$		0			0
$571$	−5.26217	+	1.20106i	−0.220215	+	0.0502626i	−0.331205	−	0.943559i	$-0.607455\pi$
$571$	−5.26217	+	1.20106i	−0.220215	+	0.0502626i	0.110990	+	0.993822i	$0.464598\pi$
$572$		0			0
$573$	20.3093	+	16.1961i	0.848434	+	0.676603i
$574$		0			0
$575$	−3.07724	+	6.38996i	−0.128330	+	0.266480i
$576$		0			0
$577$	18.5482	−	2.08987i	0.772170	−	0.0870026i	0.282917	−	0.959145i	$-0.408698\pi$
$577$	18.5482	−	2.08987i	0.772170	−	0.0870026i	0.489253	+	0.872142i	$0.337269\pi$
$578$		0			0
$579$	7.67524			0.318972
$580$		0			0
$581$	−19.5832			−0.812448
$582$		0			0
$583$	−1.30722	+	0.147288i	−0.0541393	+	0.00610004i
$584$		0			0
$585$	−5.10373	+	10.5980i	−0.211013	+	0.438174i
$586$		0			0
$587$	−13.9818	−	11.1501i	−0.577090	−	0.460214i	0.290929	−	0.956745i	$-0.406036\pi$
$587$	−13.9818	−	11.1501i	−0.577090	−	0.460214i	−0.868019	+	0.496530i	$0.834607\pi$
$588$		0			0
$589$	−66.7587	+	15.2372i	−2.75074	+	0.627839i
$590$		0			0
$591$	−42.9634	+	26.9957i	−1.76728	+	1.11045i
$592$		0			0
$593$	32.1417	+	7.33613i	1.31990	+	0.301259i	0.823738	−	0.566971i	$-0.191885\pi$
$593$	32.1417	+	7.33613i	1.31990	+	0.301259i	0.496162	+	0.868230i	$0.334742\pi$
$594$		0			0
$595$	−15.9776	+	45.6615i	−0.655020	+	1.87194i
$596$		0			0
$597$	30.8602	−	30.8602i	1.26302	−	1.26302i
$598$		0			0
$599$	0.807847	−	7.16984i	0.0330077	−	0.292952i	−0.966354	−	0.257217i	$-0.917194\pi$
$599$	0.807847	−	7.16984i	0.0330077	−	0.292952i	0.999361	−	0.0357344i	$-0.0113770\pi$
$600$		0			0
$601$	−2.32564	−	1.46129i	−0.0948647	−	0.0596074i	0.483764	−	0.875198i	$-0.339269\pi$
$601$	−2.32564	−	1.46129i	−0.0948647	−	0.0596074i	−0.578629	+	0.815591i	$0.696412\pi$
$602$		0			0
$603$	−7.91161	−	16.4286i	−0.322186	−	0.669026i
$604$		0			0
$605$	18.6648	+	23.4050i	0.758834	+	0.951547i
$606$		0			0
$607$	7.80951	−	2.73267i	0.316978	−	0.110915i	−0.167101	−	0.985940i	$-0.553440\pi$
$607$	7.80951	−	2.73267i	0.316978	−	0.110915i	0.484079	+	0.875024i	$0.339155\pi$
$608$		0			0
$609$	−11.2608	−	31.5514i	−0.456310	−	1.27853i
$610$		0			0
$611$	−2.41696	−	6.90728i	−0.0977798	−	0.279439i
$612$		0			0
$613$	−14.6864	+	11.7120i	−0.593178	+	0.473044i	−0.873475	−	0.486870i	$-0.838139\pi$
$613$	−14.6864	+	11.7120i	−0.593178	+	0.473044i	0.280296	+	0.959914i	$0.409567\pi$
$614$		0			0
$615$	35.9535	−	17.3143i	1.44978	−	0.698180i
$616$		0			0
$617$	−8.79225	+	13.9928i	−0.353963	+	0.563328i	−0.975484	−	0.220069i	$-0.929372\pi$
$617$	−8.79225	+	13.9928i	−0.353963	+	0.563328i	0.621522	+	0.783397i	$0.286515\pi$
$618$		0			0
$619$	−32.2639	−	3.63527i	−1.29679	−	0.146114i	−0.563552	−	0.826081i	$-0.690566\pi$
$619$	−32.2639	−	3.63527i	−1.29679	−	0.146114i	−0.733243	+	0.679967i	$0.761994\pi$
$620$		0			0
$621$	3.54719	+	3.54719i	0.142344	+	0.142344i
$622$		0			0
$623$	21.4717	+	7.51328i	0.860246	+	0.301013i
$624$		0			0
$625$	5.93258	−	25.9924i	0.237303	−	1.03969i
$626$		0			0
$627$	9.96099	+	15.8528i	0.397804	+	0.633101i
$628$		0			0
$629$	−9.54789	−	41.8320i	−0.380699	−	1.66795i
$630$		0			0
$631$	−18.8126	+	23.5902i	−0.748917	+	0.939112i	−0.999580	−	0.0289625i	$-0.990780\pi$
$631$	−18.8126	+	23.5902i	−0.748917	+	0.939112i	0.250664	+	0.968074i	$0.419351\pi$
$632$		0			0
$633$	47.8622	+	23.0492i	1.90235	+	0.916124i
$634$		0			0
$635$	5.78583	+	51.3506i	0.229604	+	2.03779i
$636$		0			0
$637$		−	4.49753i		−	0.178199i
$638$		0			0
$639$		−	10.7458i		−	0.425099i
$640$		0			0
$641$	3.24307	+	28.7830i	0.128094	+	1.13686i	0.879124	+	0.476594i	$0.158129\pi$
$641$	3.24307	+	28.7830i	0.128094	+	1.13686i	−0.751030	+	0.660268i	$0.770443\pi$
$642$		0			0
$643$	−29.5116	−	14.2120i	−1.16382	−	0.560468i	−0.250666	−	0.968074i	$-0.580650\pi$
$643$	−29.5116	−	14.2120i	−1.16382	−	0.560468i	−0.913158	+	0.407605i	$0.866364\pi$
$644$		0			0
$645$	31.0564	−	38.9435i	1.22284	−	1.53340i
$646$		0			0
$647$	7.38113	+	32.3388i	0.290182	+	1.27137i	0.884272	+	0.466972i	$0.154655\pi$
$647$	7.38113	+	32.3388i	0.290182	+	1.27137i	−0.594090	+	0.804399i	$0.702488\pi$
$648$		0			0
$649$	3.83169	+	6.09809i	0.150407	+	0.239371i
$650$		0			0
$651$	12.4410	−	54.5078i	0.487603	−	2.13633i
$652$		0			0
$653$	6.16818	+	2.15834i	0.241380	+	0.0844624i	0.448258	−	0.893904i	$-0.352045\pi$
$653$	6.16818	+	2.15834i	0.241380	+	0.0844624i	−0.206878	+	0.978367i	$0.566330\pi$
$654$		0			0
$655$	−13.6023	−	13.6023i	−0.531484	−	0.531484i
$656$		0			0
$657$	6.43840	+	0.725433i	0.251186	+	0.0283019i
$658$		0			0
$659$	−8.93208	+	14.2153i	−0.347945	+	0.553751i	−0.974148	−	0.225909i	$-0.927465\pi$
$659$	−8.93208	+	14.2153i	−0.347945	+	0.553751i	0.626204	+	0.779659i	$0.284608\pi$
$660$		0			0
$661$	5.88821	−	2.83561i	0.229025	−	0.110293i	−0.315852	−	0.948808i	$-0.602290\pi$
$661$	5.88821	−	2.83561i	0.229025	−	0.110293i	0.544877	+	0.838516i	$0.316576\pi$
$662$		0			0
$663$	−22.8467	+	18.2196i	−0.887293	+	0.707593i
$664$		0			0
$665$	−23.0641	−	65.9135i	−0.894388	−	2.55601i
$666$		0			0
$667$	1.78090	−	8.03229i	0.0689567	−	0.311011i
$668$		0			0
$669$	−5.27163	+	1.84462i	−0.203813	+	0.0713173i
$670$		0			0
$671$	−2.35172	−	2.94896i	−0.0907872	−	0.113844i
$672$		0			0
$673$	7.62327	+	15.8299i	0.293855	+	0.610197i	0.994666	−	0.103151i	$-0.0328923\pi$
$673$	7.62327	+	15.8299i	0.293855	+	0.610197i	−0.700810	+	0.713348i	$0.747178\pi$
$674$		0			0
$675$	12.9065	+	8.10970i	0.496772	+	0.312142i
$676$		0			0
$677$	1.71169	−	15.1916i	0.0657854	−	0.583862i	−0.916971	−	0.398955i	$-0.869373\pi$
$677$	1.71169	−	15.1916i	0.0657854	−	0.583862i	0.982756	−	0.184907i	$-0.0591984\pi$
$678$		0			0
$679$	21.2306	−	21.2306i	0.814756	−	0.814756i
$680$		0			0
$681$	7.84745	−	22.4267i	0.300715	−	0.859393i
$682$		0			0
$683$	7.51491	+	1.71523i	0.287550	+	0.0656314i	0.363863	−	0.931453i	$-0.381458\pi$
$683$	7.51491	+	1.71523i	0.287550	+	0.0656314i	−0.0763129	+	0.997084i	$0.524315\pi$
$684$		0			0
$685$	2.92952	−	1.84074i	0.111931	−	0.0703310i
$686$		0			0
$687$	−29.3949	+	6.70919i	−1.12148	+	0.255971i
$688$		0			0
$689$	2.31723	+	1.84793i	0.0882795	+	0.0704006i
$690$		0			0
$691$	−13.9014	+	28.8666i	−0.528836	+	1.09814i	0.449912	+	0.893073i	$0.351455\pi$
$691$	−13.9014	+	28.8666i	−0.528836	+	1.09814i	−0.978748	+	0.205066i	$0.934259\pi$
$692$		0			0
$693$	−4.93149	+	0.555646i	−0.187332	+	0.0211072i
$694$		0			0
$695$	−20.4143			−0.774358
$696$		0			0
$697$	32.1832			1.21903
$698$		0			0
$699$	28.6403	−	3.22699i	1.08328	−	0.122056i
$700$		0			0
$701$	8.78683	−	18.2460i	0.331874	−	0.689144i	−0.666538	−	0.745471i	$-0.732225\pi$
$701$	8.78683	−	18.2460i	0.331874	−	0.689144i	0.998412	+	0.0563272i	$0.0179390\pi$
$702$		0			0
$703$	48.4255	+	38.6180i	1.82640	+	1.45651i
$704$		0			0
$705$	17.7749	−	4.05700i	0.669440	−	0.152795i
$706$		0			0
$707$	33.4928	−	21.0449i	1.25963	−	0.791475i
$708$		0			0
$709$	−11.5019	−	2.62523i	−0.431962	−	0.0985925i	0.00101071	−	0.999999i	$-0.499678\pi$
$709$	−11.5019	−	2.62523i	−0.431962	−	0.0985925i	−0.432973	+	0.901407i	$0.642535\pi$
$710$		0			0
$711$	−0.473934	+	1.35443i	−0.0177739	+	0.0507950i
$712$		0			0
$713$	9.70904	−	9.70904i	0.363606	−	0.363606i
$714$		0			0
$715$	−1.06481	+	9.45048i	−0.0398218	+	0.353428i
$716$		0			0
$717$	18.9489	+	11.9064i	0.707658	+	0.444651i
$718$		0			0
$719$	3.57892	+	7.43170i	0.133471	+	0.277156i	0.956983	−	0.290143i	$-0.0937029\pi$
$719$	3.57892	+	7.43170i	0.133471	+	0.277156i	−0.823512	+	0.567298i	$0.807989\pi$
$720$		0			0
$721$	18.1050	+	22.7029i	0.674264	+	0.845500i
$722$		0			0
$723$	42.8796	−	15.0042i	1.59471	−	0.558014i
$724$		0			0
$725$	−0.155277	−	24.9988i	−0.00576684	−	0.928431i
$726$		0			0
$727$	−7.60870	−	21.7444i	−0.282191	−	0.806456i	−0.994514	−	0.104604i	$-0.966643\pi$
$727$	−7.60870	−	21.7444i	−0.282191	−	0.806456i	0.712323	−	0.701852i	$-0.247643\pi$
$728$		0			0
$729$	3.55164	−	2.83234i	0.131542	−	0.104901i
$730$		0			0
$731$	36.1934	−	17.4298i	1.33866	−	0.644666i
$732$		0			0
$733$	14.3027	−	22.7626i	0.528282	−	0.840756i	−0.470859	−	0.882209i	$-0.656056\pi$
$733$	14.3027	−	22.7626i	0.528282	−	0.840756i	0.999140	+	0.0414531i	$0.0131987\pi$
$734$		0			0
$735$	11.1347	+	1.25458i	0.410711	+	0.0462760i
$736$		0			0
$737$	−10.4245	−	10.4245i	−0.383992	−	0.383992i
$738$		0			0
$739$	−37.0526	−	12.9653i	−1.36300	−	0.476935i	−0.452989	−	0.891516i	$-0.649642\pi$
$739$	−37.0526	−	12.9653i	−1.36300	−	0.476935i	−0.910012	+	0.414581i	$0.863928\pi$
$740$		0			0
$741$	9.38654	−	41.1251i	0.344823	−	1.51077i
$742$		0			0
$743$	−17.6332	−	28.0631i	−0.646899	−	1.02953i	−0.995727	−	0.0923472i	$-0.970563\pi$
$743$	−17.6332	−	28.0631i	−0.646899	−	1.02953i	0.348828	−	0.937187i	$-0.386580\pi$
$744$		0			0
$745$	12.9661	+	56.8083i	0.475042	+	2.08129i
$746$		0			0
$747$	5.96539	−	7.48037i	0.218262	−	0.273692i
$748$		0			0
$749$	44.3602	+	21.3627i	1.62088	+	0.780577i
$750$		0			0
$751$	−1.61357	−	14.3208i	−0.0588800	−	0.522575i	−0.988185	−	0.153263i	$-0.951022\pi$
$751$	−1.61357	−	14.3208i	−0.0588800	−	0.522575i	0.929305	−	0.369312i	$-0.120407\pi$
$752$		0			0
$753$		−	53.1443i		−	1.93669i
$754$		0			0
$755$		−	21.4814i		−	0.781789i
$756$		0			0
$757$	−0.918137	−	8.14869i	−0.0333703	−	0.296169i	−0.999301	−	0.0373704i	$-0.988102\pi$
$757$	−0.918137	−	8.14869i	−0.0333703	−	0.296169i	0.965931	−	0.258799i	$-0.0833267\pi$
$758$		0			0
$759$	−3.38244	−	1.62890i	−0.122775	−	0.0591253i
$760$		0			0
$761$	−7.27965	+	9.12839i	−0.263887	+	0.330904i	−0.896068	−	0.443917i	$-0.853589\pi$
$761$	−7.27965	+	9.12839i	−0.263887	+	0.330904i	0.632181	+	0.774821i	$0.282160\pi$
$762$		0			0
$763$	6.22282	+	27.2640i	0.225281	+	0.987021i
$764$		0			0
$765$	−12.5746	−	20.0124i	−0.454637	−	0.723551i
$766$		0			0
$767$	3.61071	−	15.8196i	0.130375	−	0.571212i
$768$		0			0
$769$	−27.7974	−	9.72673i	−1.00240	−	0.350755i	−0.221330	−	0.975199i	$-0.571040\pi$
$769$	−27.7974	−	9.72673i	−1.00240	−	0.350755i	−0.781070	+	0.624444i	$0.785326\pi$
$770$		0			0
$771$	−16.0360	−	16.0360i	−0.577524	−	0.577524i
$772$		0			0
$773$	−15.0114	−	1.69138i	−0.539922	−	0.0608346i	−0.162208	−	0.986757i	$-0.551861\pi$
$773$	−15.0114	−	1.69138i	−0.539922	−	0.0608346i	−0.377715	+	0.925922i	$0.623290\pi$
$774$		0			0
$775$	22.1971	−	35.3265i	0.797343	−	1.26896i
$776$		0			0
$777$	−45.5639	+	21.9424i	−1.63460	+	0.787180i
$778$		0			0
$779$	−36.3218	+	28.9657i	−1.30136	+	1.03780i
$780$		0			0
$781$	−2.86946	−	8.20045i	−0.102677	−	0.293435i
$782$		0			0
$783$	−16.7260	−	5.73631i	−0.597737	−	0.204999i
$784$		0			0
$785$	−22.1904	+	7.76474i	−0.792008	+	0.277136i
$786$		0			0
$787$	−0.453293	−	0.568411i	−0.0161581	−	0.0202617i	0.773687	−	0.633568i	$-0.218410\pi$
$787$	−0.453293	−	0.568411i	−0.0161581	−	0.0202617i	−0.789845	+	0.613307i	$0.789839\pi$
$788$		0			0
$789$	7.81973	+	16.2378i	0.278390	+	0.578083i
$790$		0			0
$791$	−30.4392	−	19.1262i	−1.08229	−	0.680051i
$792$		0			0
$793$	−0.951495	+	8.44476i	−0.0337886	+	0.299882i
$794$		0			0
$795$	−5.22139	+	5.22139i	−0.185184	+	0.185184i
$796$		0			0
$797$	13.1404	−	37.5530i	0.465455	−	1.33019i	−0.437020	−	0.899452i	$-0.643966\pi$
$797$	13.1404	−	37.5530i	0.465455	−	1.33019i	0.902475	−	0.430743i	$-0.141748\pi$
$798$		0			0
$799$	14.3352	+	3.27192i	0.507144	+	0.115752i
$800$		0			0
$801$	−9.41058	+	5.91306i	−0.332507	+	0.208928i
$802$		0			0
$803$	5.10703	−	1.16565i	0.180223	−	0.0411348i
$804$		0			0
$805$	10.9478	+	8.73055i	0.385858	+	0.307711i
$806$		0			0
$807$	20.1229	−	41.7856i	0.708360	−	1.47092i
$808$		0			0
$809$	−38.6610	+	4.35605i	−1.35925	+	0.153151i	−0.761308	−	0.648390i	$-0.775443\pi$
$809$	−38.6610	+	4.35605i	−1.35925	+	0.153151i	−0.597941	+	0.801540i	$0.704014\pi$
$810$		0			0
$811$	−12.2107			−0.428774			−0.214387	−	0.976749i	$-0.568775\pi$
$811$	−12.2107			−0.428774			−0.214387	+	0.976749i	$0.568775\pi$
$812$		0			0
$813$	−0.653157			−0.0229072
$814$		0			0
$815$	−58.6460	+	6.60782i	−2.05428	+	0.231462i
$816$		0			0
$817$	−25.1604	+	52.2461i	−0.880251	+	1.82786i
$818$		0			0
$819$	8.74180	+	6.97135i	0.305463	+	0.243599i
$820$		0			0
$821$	−21.4152	+	4.88788i	−0.747395	+	0.170588i	−0.579223	−	0.815169i	$-0.696644\pi$
$821$	−21.4152	+	4.88788i	−0.747395	+	0.170588i	−0.168173	+	0.985758i	$0.553787\pi$
$822$		0			0
$823$	23.5330	−	14.7868i	0.820308	−	0.515434i	−0.0552919	−	0.998470i	$-0.517609\pi$
$823$	23.5330	−	14.7868i	0.820308	−	0.515434i	0.875600	+	0.483036i	$0.160466\pi$
$824$		0			0
$825$	−11.1214	−	2.53839i	−0.387198	−	0.0883755i
$826$		0			0
$827$	−3.41569	+	9.76149i	−0.118775	+	0.339440i	−0.987887	−	0.155176i	$-0.950406\pi$
$827$	−3.41569	+	9.76149i	−0.118775	+	0.339440i	0.869112	+	0.494616i	$0.164691\pi$
$828$		0			0
$829$	−0.841520	+	0.841520i	−0.0292272	+	0.0292272i	−0.721569	−	0.692342i	$-0.756579\pi$
$829$	−0.841520	+	0.841520i	−0.0292272	+	0.0292272i	0.692342	+	0.721569i	$0.256579\pi$
$830$		0			0
$831$	7.33605	−	65.1092i	0.254485	−	2.25861i
$832$		0			0
$833$	7.65173	+	4.80790i	0.265117	+	0.166584i
$834$		0			0
$835$	33.2707	+	69.0874i	1.15138	+	2.39087i
$836$		0			0
$837$	−18.3992	−	23.0719i	−0.635969	−	0.797481i
$838$		0			0
$839$	37.7758	−	13.2183i	1.30417	−	0.456347i	0.413292	−	0.910598i	$-0.364379\pi$
$839$	37.7758	−	13.2183i	1.30417	−	0.456347i	0.890874	+	0.454251i	$0.150093\pi$
$840$		0			0
$841$	6.80382	+	28.1906i	0.234615	+	0.972088i
$842$		0			0
$843$	−5.41047	−	15.4622i	−0.186346	−	0.532547i
$844$		0			0
$845$	−14.8082	+	11.8092i	−0.509419	+	0.406248i
$846$		0			0
$847$	25.6376	−	12.3464i	0.880919	−	0.424228i
$848$		0			0
$849$	12.3498	−	19.6545i	0.423843	−	0.674542i
$850$		0			0
$851$	−12.3418	−	1.39058i	−0.423070	−	0.0476686i
$852$		0			0
$853$	1.17047	+	1.17047i	0.0400761	+	0.0400761i	0.726861	−	0.686785i	$-0.240978\pi$
$853$	1.17047	+	1.17047i	0.0400761	+	0.0400761i	−0.686785	+	0.726861i	$0.740978\pi$
$854$		0			0
$855$	32.2033	+	11.2684i	1.10133	+	0.385372i
$856$		0			0
$857$	−8.88259	+	38.9172i	−0.303423	+	1.32938i	0.561498	+	0.827478i	$0.310225\pi$
$857$	−8.88259	+	38.9172i	−0.303423	+	1.32938i	−0.864922	+	0.501907i	$0.832632\pi$
$858$		0			0
$859$	22.3731	+	35.6065i	0.763359	+	1.21488i	0.971560	+	0.236794i	$0.0760965\pi$
$859$	22.3731	+	35.6065i	0.763359	+	1.21488i	−0.208201	+	0.978086i	$0.566761\pi$
$860$		0			0
$861$	−8.44064	−	36.9809i	−0.287656	−	1.26030i
$862$		0			0
$863$	−16.1782	+	20.2869i	−0.550713	+	0.690573i	−0.976811	−	0.214105i	$-0.931317\pi$
$863$	−16.1782	+	20.2869i	−0.550713	+	0.690573i	0.426097	+	0.904677i	$0.359888\pi$
$864$		0			0
$865$	19.7452	+	9.50881i	0.671358	+	0.323309i
$866$		0			0
$867$	−2.56243	−	22.7422i	−0.0870245	−	0.772364i
$868$		0			0
$869$			1.16015i			0.0393556i
$870$		0			0
$871$			33.2155i			1.12546i
$872$		0			0
$873$	1.64242	+	14.5769i	0.0555874	+	0.493352i
$874$		0			0
$875$	−2.95426	−	1.42270i	−0.0998723	−	0.0480960i
$876$		0			0
$877$	−0.729178	+	0.914360i	−0.0246226	+	0.0308758i	−0.793990	−	0.607930i	$-0.792000\pi$
$877$	−0.729178	+	0.914360i	−0.0246226	+	0.0308758i	0.769368	+	0.638806i	$0.220571\pi$
$878$		0			0
$879$	6.76211	+	29.6267i	0.228080	+	0.999285i
$880$		0			0
$881$	−21.5579	−	34.3091i	−0.726303	−	1.15590i	−0.981951	−	0.189134i	$-0.939432\pi$
$881$	−21.5579	−	34.3091i	−0.726303	−	1.15590i	0.255649	−	0.966770i	$-0.417711\pi$
$882$		0			0
$883$	4.69502	−	20.5702i	0.158000	−	0.692243i	−0.832419	−	0.554147i	$-0.813045\pi$
$883$	4.69502	−	20.5702i	0.158000	−	0.692243i	0.990419	−	0.138096i	$-0.0440983\pi$
$884$		0			0
$885$	38.1580	+	13.3521i	1.28267	+	0.448824i
$886$		0			0
$887$	5.50303	+	5.50303i	0.184774	+	0.184774i	0.793432	−	0.608659i	$-0.208292\pi$
$887$	5.50303	+	5.50303i	0.184774	+	0.184774i	−0.608659	+	0.793432i	$0.708292\pi$
$888$		0			0
$889$	48.8111	+	5.49970i	1.63707	+	0.184454i
$890$		0			0
$891$	−6.97635	+	11.1028i	−0.233716	+	0.371957i
$892$		0			0
$893$	−19.1234	+	9.20936i	−0.639941	+	0.308180i
$894$		0			0
$895$	−61.9658	+	49.4160i	−2.07129	+	1.65180i
$896$		0			0
$897$	2.79365	+	7.98379i	0.0932773	+	0.266571i
$898$		0			0
$899$	−15.7009	+	45.7807i	−0.523653	+	1.52687i
$900$		0			0
$901$	−5.62106	+	1.96689i	−0.187265	+	0.0655267i
$902$		0			0
$903$	−29.5205	−	37.0176i	−0.982382	−	1.23187i
$904$		0			0
$905$	−7.38724	−	15.3398i	−0.245560	−	0.509911i
$906$		0			0
$907$	15.8551	+	9.96242i	0.526460	+	0.330797i	0.768899	−	0.639370i	$-0.220805\pi$
$907$	15.8551	+	9.96242i	0.526460	+	0.330797i	−0.242439	+	0.970167i	$0.577948\pi$
$908$		0			0
$909$	−2.16379	+	19.2042i	−0.0717685	+	0.636963i
$910$		0			0
$911$	−12.3577	+	12.3577i	−0.409430	+	0.409430i	−0.881540	−	0.472110i	$-0.843493\pi$
$911$	−12.3577	+	12.3577i	−0.409430	+	0.409430i	0.472110	+	0.881540i	$0.343493\pi$
$912$		0			0
$913$	2.55487	−	7.30141i	0.0845540	−	0.241641i
$914$		0			0
$915$	−20.6416	−	4.71132i	−0.682391	−	0.155751i
$916$		0			0
$917$	−15.4825	+	9.72830i	−0.511277	+	0.321257i
$918$		0			0
$919$	−8.34866	+	1.90553i	−0.275397	+	0.0628576i	−0.357989	−	0.933726i	$-0.616537\pi$
$919$	−8.34866	+	1.90553i	−0.275397	+	0.0628576i	0.0825917	+	0.996583i	$0.473680\pi$
$920$		0			0
$921$	17.6931	+	14.1098i	0.583009	+	0.464934i
$922$		0			0
$923$	−8.49303	+	17.6360i	−0.279552	+	0.580495i
$924$		0			0
$925$	−37.5011	+	4.22536i	−1.23303	+	0.138929i
$926$		0			0
$927$	−14.1871			−0.465966
$928$		0			0
$929$	0.147927			0.00485333			0.00242666	−	0.999997i	$-0.499228\pi$
$929$	0.147927			0.00485333			0.00242666	+	0.999997i	$0.499228\pi$
$930$		0			0
$931$	−12.9629	+	1.46057i	−0.424842	+	0.0478682i
$932$		0			0
$933$	9.07027	−	18.8346i	0.296947	−	0.616618i
$934$		0			0
$935$	−14.9400	−	11.9142i	−0.488589	−	0.389637i
$936$		0			0
$937$	2.03147	−	0.463670i	0.0663652	−	0.0151474i	−0.189209	−	0.981937i	$-0.560592\pi$
$937$	2.03147	−	0.463670i	0.0663652	−	0.0151474i	0.255575	+	0.966789i	$0.417735\pi$
$938$		0			0
$939$	14.6943	−	9.23302i	0.479529	−	0.301308i
$940$		0			0
$941$	42.1888	+	9.62931i	1.37532	+	0.313907i	0.845395	−	0.534141i	$-0.179365\pi$
$941$	42.1888	+	9.62931i	1.37532	+	0.313907i	0.529920	+	0.848048i	$0.322222\pi$
$942$		0			0
$943$	3.07674	−	8.79282i	0.100193	−	0.286334i
$944$		0			0
$945$	21.2802	−	21.2802i	0.692244	−	0.692244i
$946$		0			0
$947$	−1.75156	+	15.5455i	−0.0569181	+	0.505162i	0.932617	+	0.360868i	$0.117520\pi$
$947$	−1.75156	+	15.5455i	−0.0569181	+	0.505162i	−0.989535	+	0.144294i	$0.953909\pi$
$948$		0			0
$949$	−9.99328	−	6.27919i	−0.324396	−	0.203831i
$950$		0			0
$951$	26.8717	+	55.7997i	0.871375	+	1.80943i
$952$		0			0
$953$	−8.06113	−	10.1083i	−0.261126	−	0.327441i	0.633934	−	0.773387i	$-0.281439\pi$
$953$	−8.06113	−	10.1083i	−0.261126	−	0.327441i	−0.895060	+	0.445946i	$0.852868\pi$
$954$		0			0
$955$	36.1241	−	12.6404i	1.16895	−	0.409032i
$956$		0			0
$957$	13.2328	−	0.0821938i	0.427755	−	0.00265695i
$958$		0			0
$959$	−1.08620	−	3.10417i	−0.0350751	−	0.100239i
$960$		0			0
$961$	−38.9134	+	31.0324i	−1.25527	+	1.00104i
$962$		0			0
$963$	−21.6730	+	10.4372i	−0.698403	+	0.336333i
$964$		0			0
$965$	6.01625	−	9.57481i	0.193670	−	0.308224i
$966$		0			0
$967$	−24.9376	−	2.80979i	−0.801938	−	0.0903567i	−0.298524	−	0.954402i	$-0.596494\pi$
$967$	−24.9376	−	2.80979i	−0.801938	−	0.0903567i	−0.503414	+	0.864046i	$0.667923\pi$
$968$		0			0
$969$	59.9326	+	59.9326i	1.92531	+	1.92531i
$970$		0			0
$971$	19.4163	+	6.79407i	0.623100	+	0.218032i	0.623319	−	0.781968i	$-0.285784\pi$
$971$	19.4163	+	6.79407i	0.623100	+	0.218032i	−0.000218879		1.00000i	$0.500070\pi$
$972$		0			0
$973$	−4.31796	+	18.9182i	−0.138427	+	0.606490i
$974$		0			0
$975$	13.6740	+	21.7621i	0.437919	+	0.696944i
$976$		0			0
$977$	9.76689	+	42.7915i	0.312470	+	1.36902i	0.850446	+	0.526062i	$0.176332\pi$
$977$	9.76689	+	42.7915i	0.312470	+	1.36902i	−0.537976	+	0.842960i	$0.680811\pi$
$978$		0			0
$979$	−5.60251	+	7.02533i	−0.179057	+	0.224530i
$980$		0			0
$981$	−12.3098	−	5.92810i	−0.393023	−	0.189270i
$982$		0			0
$983$	−1.55760	−	13.8241i	−0.0496798	−	0.440920i	−0.993788	−	0.111286i	$-0.964503\pi$
$983$	−1.55760	−	13.8241i	−0.0496798	−	0.440920i	0.944109	−	0.329634i	$-0.106925\pi$
$984$		0			0
$985$			74.7571i			2.38196i
$986$		0			0
$987$		−	17.3303i		−	0.551630i
$988$		0			0
$989$	−1.30191	−	11.5548i	−0.0413983	−	0.367420i
$990$		0			0
$991$	−6.07680	−	2.92643i	−0.193036	−	0.0929611i	0.334869	−	0.942265i	$-0.391308\pi$
$991$	−6.07680	−	2.92643i	−0.193036	−	0.0929611i	−0.527905	+	0.849304i	$0.677022\pi$
$992$		0			0
$993$	−23.5616	+	29.5453i	−0.747704	+	0.937591i
$994$		0			0
$995$	−14.3081	−	62.6877i	−0.453596	−	1.98733i
$996$		0			0
$997$	−7.56480	−	12.0393i	−0.239580	−	0.381289i	0.705193	−	0.709015i	$-0.250860\pi$
$997$	−7.56480	−	12.0393i	−0.239580	−	0.381289i	−0.944773	+	0.327727i	$0.893718\pi$
$998$		0			0
$999$	−5.93972	+	26.0236i	−0.187924	+	0.823351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.bl.b.127.4	yes	48
4.3	odd	2	inner	464.2.bl.b.127.1	yes	48
29.8	odd	28	inner	464.2.bl.b.95.1	✓	48
116.95	even	28	inner	464.2.bl.b.95.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.bl.b.95.1	✓	48	29.8	odd	28	inner
464.2.bl.b.95.4	yes	48	116.95	even	28	inner
464.2.bl.b.127.1	yes	48	4.3	odd	2	inner
464.2.bl.b.127.4	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.bl (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.09437 - 0.235979i) q^{3} +(1.34729 - 2.79769i) q^{5} +(-2.30768 - 1.84031i) q^{7} +(1.40592 - 0.320892i) q^{9} +O(q^{10})\)	\(q+(2.09437 - 0.235979i) q^{3} +(1.34729 - 2.79769i) q^{5} +(-2.30768 - 1.84031i) q^{7} +(1.40592 - 0.320892i) q^{9} +(0.987209 - 0.620305i) q^{11} +(-2.56100 - 0.584532i) q^{13} +(2.16154 - 6.17732i) q^{15} +(3.73220 - 3.73220i) q^{17} +(-0.853070 + 7.57121i) q^{19} +(-5.26741 - 3.30973i) q^{21} +(-0.662879 - 1.37648i) q^{23} +(-2.89439 - 3.62945i) q^{25} +(-3.09926 + 1.08448i) q^{27} +(4.23107 + 3.33138i) q^{29} +(2.96833 + 8.48299i) q^{31} +(1.92120 - 1.53211i) q^{33} +(-8.25774 + 3.97672i) q^{35} +(4.32508 - 6.88332i) q^{37} +(-5.50162 - 0.619884i) q^{39} +(4.31156 + 4.31156i) q^{41} +(7.18386 + 2.51374i) q^{43} +(0.996434 - 4.36566i) q^{45} +(1.48214 + 2.35881i) q^{47} +(0.380985 + 1.66920i) q^{49} +(6.93590 - 8.69734i) q^{51} +(-1.01655 - 0.489545i) q^{53} +(-0.405356 - 3.59763i) q^{55} +16.0582i q^{57} +6.17711i q^{59} +(-0.362218 - 3.21477i) q^{61} +(-3.83496 - 1.84682i) q^{63} +(-5.08576 + 6.37734i) q^{65} +(-2.81368 - 12.3275i) q^{67} +(-1.71314 - 2.72644i) q^{69} +(1.65815 - 7.26482i) q^{71} +(4.24079 + 1.48392i) q^{73} +(-6.91840 - 6.91840i) q^{75} +(-3.41972 - 0.385309i) q^{77} +(-0.529403 + 0.842540i) q^{79} +(-10.1329 + 4.87974i) q^{81} +(5.18722 - 4.13667i) q^{83} +(-5.41316 - 15.4699i) q^{85} +(9.64756 + 5.97870i) q^{87} +(-7.27452 + 2.54547i) q^{89} +(4.83425 + 6.06195i) q^{91} +(8.21858 + 17.0661i) q^{93} +(20.0325 + 12.5873i) q^{95} +(-1.13893 + 10.1082i) q^{97} +(1.18889 - 1.18889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 16 q^{17} + 16 q^{21} + 24 q^{25} + 80 q^{29} + 84 q^{33} + 28 q^{37} + 8 q^{41} - 100 q^{45} + 24 q^{49} - 20 q^{53} + 32 q^{61} + 48 q^{65} + 56 q^{73} - 180 q^{77} - 152 q^{81} - 152 q^{85} - 84 q^{89} - 112 q^{93}+O(q^{100}) \) 48 * q - 16 * q^17 + 16 * q^21 + 24 * q^25 + 80 * q^29 + 84 * q^33 + 28 * q^37 + 8 * q^41 - 100 * q^45 + 24 * q^49 - 20 * q^53 + 32 * q^61 + 48 * q^65 + 56 * q^73 - 180 * q^77 - 152 * q^81 - 152 * q^85 - 84 * q^89 - 112 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more