LMFDB - Embedded newform 864.2.y.d.193.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.10
Character	$\chi$	$=$	864.193
Dual form			864.2.y.d.385.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72168 + 0.189239i) q^{3} +(0.679279 - 3.85238i) q^{5} +(2.91962 - 2.44985i) q^{7} +(2.92838 + 0.651618i) q^{9} +O(q^{10})$	\(q+(1.72168 + 0.189239i) q^{3} +(0.679279 - 3.85238i) q^{5} +(2.91962 - 2.44985i) q^{7} +(2.92838 + 0.651618i) q^{9} +(0.633200 + 3.59106i) q^{11} +(-3.51692 + 1.28005i) q^{13} +(1.89852 - 6.50403i) q^{15} +(0.124612 - 0.215834i) q^{17} +(-0.305590 - 0.529297i) q^{19} +(5.49027 - 3.66536i) q^{21} +(2.82720 + 2.37230i) q^{23} +(-9.68095 - 3.52358i) q^{25} +(4.91842 + 1.67604i) q^{27} +(5.62879 + 2.04871i) q^{29} +(-8.17429 - 6.85905i) q^{31} +(0.410602 + 6.30248i) q^{33} +(-7.45453 - 12.9116i) q^{35} +(-5.67746 + 9.83365i) q^{37} +(-6.29725 + 1.53831i) q^{39} +(-5.35669 + 1.94967i) q^{41} +(-0.212301 - 1.20402i) q^{43} +(4.49946 - 10.8386i) q^{45} +(7.67765 - 6.44231i) q^{47} +(1.30687 - 7.41164i) q^{49} +(0.255386 - 0.348016i) q^{51} -4.91781 q^{53} +14.2642 q^{55} +(-0.425965 - 0.969111i) q^{57} +(-0.145128 + 0.823062i) q^{59} +(-1.38093 + 1.15873i) q^{61} +(10.1461 - 5.27162i) q^{63} +(2.54229 + 14.4180i) q^{65} +(-6.96862 + 2.53637i) q^{67} +(4.41861 + 4.61937i) q^{69} +(1.92575 - 3.33550i) q^{71} +(-1.51159 - 2.61815i) q^{73} +(-16.0007 - 7.89849i) q^{75} +(10.6463 + 8.93328i) q^{77} +(14.6114 + 5.31813i) q^{79} +(8.15079 + 3.81637i) q^{81} +(10.7700 + 3.91997i) q^{83} +(-0.746827 - 0.626662i) q^{85} +(9.30329 + 4.59242i) q^{87} +(7.19807 + 12.4674i) q^{89} +(-7.13213 + 12.3532i) q^{91} +(-12.7755 - 13.3560i) q^{93} +(-2.24663 + 0.817708i) q^{95} +(-0.634167 - 3.59654i) q^{97} +(-0.485747 + 10.9286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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
$3$	1.72168	+	0.189239i	0.994014	+	0.109257i
$3$	1.72168	+	0.189239i	0.994014	+	0.109257i
$4$		0			0
$5$	0.679279	−	3.85238i	0.303783	−	1.72284i	−0.325398	−	0.945577i	$-0.605498\pi$
$5$	0.679279	−	3.85238i	0.303783	−	1.72284i	0.629180	−	0.777259i	$-0.283391\pi$
$6$		0			0
$7$	2.91962	−	2.44985i	1.10351	−	0.925958i	0.105857	−	0.994381i	$-0.466241\pi$
$7$	2.91962	−	2.44985i	1.10351	−	0.925958i	0.997656	+	0.0684238i	$0.0217970\pi$
$8$		0			0
$9$	2.92838	+	0.651618i	0.976126	+	0.217206i
$10$		0			0
$11$	0.633200	+	3.59106i	0.190917	+	1.08274i	0.918114	+	0.396316i	$0.129711\pi$
$11$	0.633200	+	3.59106i	0.190917	+	1.08274i	−0.727197	+	0.686429i	$0.759177\pi$
$12$		0			0
$13$	−3.51692	+	1.28005i	−0.975418	+	0.355023i	−0.780057	−	0.625708i	$-0.784810\pi$
$13$	−3.51692	+	1.28005i	−0.975418	+	0.355023i	−0.195361	+	0.980731i	$0.562588\pi$
$14$		0			0
$15$	1.89852	−	6.50403i	0.490196	−	1.67933i
$16$		0			0
$17$	0.124612	−	0.215834i	0.0302228	−	0.0523473i	−0.850518	−	0.525945i	$-0.823712\pi$
$17$	0.124612	−	0.215834i	0.0302228	−	0.0523473i	0.880741	+	0.473598i	$0.157045\pi$
$18$		0			0
$19$	−0.305590	−	0.529297i	−0.0701071	−	0.121429i	0.828841	−	0.559484i	$-0.189001\pi$
$19$	−0.305590	−	0.529297i	−0.0701071	−	0.121429i	−0.898948	+	0.438055i	$0.855667\pi$
$20$		0			0
$21$	5.49027	−	3.66536i	1.19807	−	0.799848i
$22$		0			0
$23$	2.82720	+	2.37230i	0.589512	+	0.494660i	0.888055	−	0.459737i	$-0.152056\pi$
$23$	2.82720	+	2.37230i	0.589512	+	0.494660i	−0.298543	+	0.954396i	$0.596501\pi$
$24$		0			0
$25$	−9.68095	−	3.52358i	−1.93619	−	0.704716i
$26$		0			0
$27$	4.91842	+	1.67604i	0.946551	+	0.322554i
$28$		0			0
$29$	5.62879	+	2.04871i	1.04524	+	0.380436i	0.806865	−	0.590737i	$-0.201163\pi$
$29$	5.62879	+	2.04871i	1.04524	+	0.380436i	0.238376	+	0.971173i	$0.423385\pi$
$30$		0			0
$31$	−8.17429	−	6.85905i	−1.46815	−	1.23192i	−0.917835	−	0.396962i	$-0.870065\pi$
$31$	−8.17429	−	6.85905i	−1.46815	−	1.23192i	−0.550311	−	0.834960i	$-0.685491\pi$
$32$		0			0
$33$	0.410602	+	6.30248i	0.0714767	+	1.09712i
$34$		0			0
$35$	−7.45453	−	12.9116i	−1.26005	−	2.18246i
$36$		0			0
$37$	−5.67746	+	9.83365i	−0.933369	+	1.61664i	−0.155852	+	0.987780i	$0.549812\pi$
$37$	−5.67746	+	9.83365i	−0.933369	+	1.61664i	−0.777517	+	0.628862i	$0.783521\pi$
$38$		0			0
$39$	−6.29725	+	1.53831i	−1.00837	+	0.246327i
$40$		0			0
$41$	−5.35669	+	1.94967i	−0.836574	+	0.304488i	−0.724554	−	0.689218i	$-0.757954\pi$
$41$	−5.35669	+	1.94967i	−0.836574	+	0.304488i	−0.112020	+	0.993706i	$0.535732\pi$
$42$		0			0
$43$	−0.212301	−	1.20402i	−0.0323756	−	0.183611i	0.964331	−	0.264697i	$-0.0852721\pi$
$43$	−0.212301	−	1.20402i	−0.0323756	−	0.183611i	−0.996707	+	0.0810865i	$0.974161\pi$
$44$		0			0
$45$	4.49946	−	10.8386i	0.670740	−	1.61572i
$46$		0			0
$47$	7.67765	−	6.44231i	1.11990	−	0.939708i	0.121301	−	0.992616i	$-0.461294\pi$
$47$	7.67765	−	6.44231i	1.11990	−	0.939708i	0.998599	+	0.0529082i	$0.0168491\pi$
$48$		0			0
$49$	1.30687	−	7.41164i	0.186696	−	1.05881i
$50$		0			0
$51$	0.255386	−	0.348016i	0.0357611	−	0.0487319i
$52$		0			0
$53$	−4.91781			−0.675513			−0.337757	−	0.941234i	$-0.609668\pi$
$53$	−4.91781			−0.675513			−0.337757	+	0.941234i	$0.609668\pi$
$54$		0			0
$55$	14.2642			1.92339
$56$		0			0
$57$	−0.425965	−	0.969111i	−0.0564205	−	0.128362i
$58$		0			0
$59$	−0.145128	+	0.823062i	−0.0188941	+	0.107154i	−0.992796	−	0.119814i	$-0.961770\pi$
$59$	−0.145128	+	0.823062i	−0.0188941	+	0.107154i	0.973902	+	0.226968i	$0.0728812\pi$
$60$		0			0
$61$	−1.38093	+	1.15873i	−0.176809	+	0.148361i	−0.726898	−	0.686746i	$-0.759039\pi$
$61$	−1.38093	+	1.15873i	−0.176809	+	0.148361i	0.550088	+	0.835107i	$0.314594\pi$
$62$		0			0
$63$	10.1461	−	5.27162i	1.27829	−	0.664161i
$64$		0			0
$65$	2.54229	+	14.4180i	0.315332	+	1.78834i
$66$		0			0
$67$	−6.96862	+	2.53637i	−0.851352	+	0.309867i	−0.730592	−	0.682815i	$-0.760756\pi$
$67$	−6.96862	+	2.53637i	−0.851352	+	0.309867i	−0.120761	+	0.992682i	$0.538533\pi$
$68$		0			0
$69$	4.41861	+	4.61937i	0.531938	+	0.556107i
$70$		0			0
$71$	1.92575	−	3.33550i	0.228545	−	0.395851i	−0.728832	−	0.684692i	$-0.759937\pi$
$71$	1.92575	−	3.33550i	0.228545	−	0.395851i	0.957377	+	0.288841i	$0.0932699\pi$
$72$		0			0
$73$	−1.51159	−	2.61815i	−0.176918	−	0.306432i	0.763905	−	0.645329i	$-0.223280\pi$
$73$	−1.51159	−	2.61815i	−0.176918	−	0.306432i	−0.940824	+	0.338897i	$0.889946\pi$
$74$		0			0
$75$	−16.0007	−	7.89849i	−1.84760	−	0.912039i
$76$		0			0
$77$	10.6463	+	8.93328i	1.21325	+	1.01804i
$78$		0			0
$79$	14.6114	+	5.31813i	1.64391	+	0.598336i	0.987717	−	0.156253i	$-0.0499414\pi$
$79$	14.6114	+	5.31813i	1.64391	+	0.598336i	0.656198	+	0.754589i	$0.272164\pi$
$80$		0			0
$81$	8.15079	+	3.81637i	0.905643	+	0.424041i
$82$		0			0
$83$	10.7700	+	3.91997i	1.18216	+	0.430273i	0.856966	−	0.515373i	$-0.172347\pi$
$83$	10.7700	+	3.91997i	1.18216	+	0.430273i	0.325199	+	0.945646i	$0.394569\pi$
$84$		0			0
$85$	−0.746827	−	0.626662i	−0.0810048	−	0.0679711i
$86$		0			0
$87$	9.30329	+	4.59242i	0.997418	+	0.492359i
$88$		0			0
$89$	7.19807	+	12.4674i	0.762994	+	1.32154i	0.941301	+	0.337569i	$0.109605\pi$
$89$	7.19807	+	12.4674i	0.762994	+	1.32154i	−0.178307	+	0.983975i	$0.557062\pi$
$90$		0			0
$91$	−7.13213	+	12.3532i	−0.747650	+	1.29497i
$92$		0			0
$93$	−12.7755	−	13.3560i	−1.32476	−	1.38495i
$94$		0			0
$95$	−2.24663	+	0.817708i	−0.230500	+	0.0838951i
$96$		0			0
$97$	−0.634167	−	3.59654i	−0.0643899	−	0.365173i	−0.999929	−	0.0119491i	$-0.996196\pi$
$97$	−0.634167	−	3.59654i	−0.0643899	−	0.365173i	0.935539	−	0.353224i	$-0.114915\pi$
$98$		0			0
$99$	−0.485747	+	10.9286i	−0.0488194	+	1.09836i
$100$		0			0
$101$	−3.43094	+	2.87890i	−0.341391	+	0.286461i	−0.797322	−	0.603554i	$-0.793751\pi$
$101$	−3.43094	+	2.87890i	−0.341391	+	0.286461i	0.455931	+	0.890015i	$0.349306\pi$
$102$		0			0
$103$	−0.988563	+	5.60642i	−0.0974060	+	0.552417i	0.896577	+	0.442887i	$0.146046\pi$
$103$	−0.988563	+	5.60642i	−0.0974060	+	0.552417i	−0.993983	+	0.109530i	$0.965065\pi$
$104$		0			0
$105$	−10.3910	−	23.6404i	−1.01405	−	2.30707i
$106$		0			0
$107$	−3.56541			−0.344681			−0.172340	−	0.985037i	$-0.555133\pi$
$107$	−3.56541			−0.344681			−0.172340	+	0.985037i	$0.555133\pi$
$108$		0			0
$109$	−3.76604			−0.360721			−0.180361	−	0.983601i	$-0.557726\pi$
$109$	−3.76604			−0.360721			−0.180361	+	0.983601i	$0.557726\pi$
$110$		0			0
$111$	−11.6357	+	15.8560i	−1.10441	+	1.50499i
$112$		0			0
$113$	1.09679	−	6.22023i	0.103178	−	0.585150i	−0.888755	−	0.458383i	$-0.848429\pi$
$113$	1.09679	−	6.22023i	0.103178	−	0.585150i	0.991932	−	0.126767i	$-0.0404601\pi$
$114$		0			0
$115$	11.0595	−	9.28000i	1.03130	−	0.865365i
$116$		0			0
$117$	−11.1330	+	1.45679i	−1.02924	+	0.134681i
$118$		0			0
$119$	−0.164942	−	0.935433i	−0.0151202	−	0.0857510i
$120$		0			0
$121$	−2.15813	+	0.785494i	−0.196193	+	0.0714085i
$122$		0			0
$123$	−9.59147	+	2.34303i	−0.864833	+	0.211264i
$124$		0			0
$125$	−10.3707	+	17.9626i	−0.927584	+	1.60662i
$126$		0			0
$127$	−7.72900	−	13.3870i	−0.685838	−	1.18791i	−0.973173	−	0.230076i	$-0.926103\pi$
$127$	−7.72900	−	13.3870i	−0.685838	−	1.18791i	0.287335	−	0.957830i	$-0.407231\pi$
$128$		0			0
$129$	−0.137668	−	2.11311i	−0.0121210	−	0.186049i
$130$		0			0
$131$	7.18290	+	6.02717i	0.627573	+	0.526596i	0.900174	−	0.435531i	$-0.143439\pi$
$131$	7.18290	+	6.02717i	0.627573	+	0.526596i	−0.272601	+	0.962127i	$0.587884\pi$
$132$		0			0
$133$	−2.18891	−	0.796697i	−0.189802	−	0.0690824i
$134$		0			0
$135$	9.79773	−	17.8091i	0.843254	−	1.53277i
$136$		0			0
$137$	5.46573	+	1.98936i	0.466969	+	0.169963i	0.564779	−	0.825242i	$-0.308961\pi$
$137$	5.46573	+	1.98936i	0.466969	+	0.169963i	−0.0978097	+	0.995205i	$0.531184\pi$
$138$		0			0
$139$	4.06235	+	3.40871i	0.344564	+	0.289123i	0.798603	−	0.601859i	$-0.205573\pi$
$139$	4.06235	+	3.40871i	0.344564	+	0.289123i	−0.454039	+	0.890982i	$0.650017\pi$
$140$		0			0
$141$	14.4376	−	9.63870i	1.21587	−	0.811725i
$142$		0			0
$143$	−6.82366	−	11.8189i	−0.570623	−	0.988348i
$144$		0			0
$145$	11.7159	−	20.2926i	0.972956	−	1.68521i
$146$		0			0
$147$	3.65258	−	12.5132i	0.301260	−	1.03207i
$148$		0			0
$149$	−13.9451	+	5.07560i	−1.14243	+	0.415809i	−0.842789	−	0.538244i	$-0.819088\pi$
$149$	−13.9451	+	5.07560i	−1.14243	+	0.415809i	−0.299637	+	0.954053i	$0.596866\pi$
$150$		0			0
$151$	0.539231	+	3.05813i	0.0438820	+	0.248867i	0.998856	−	0.0478229i	$-0.0152283\pi$
$151$	0.539231	+	3.05813i	0.0438820	+	0.248867i	−0.954974	+	0.296690i	$0.904117\pi$
$152$		0			0
$153$	0.505551	−	0.550843i	0.0408714	−	0.0445330i
$154$		0			0
$155$	−31.9763	+	26.8313i	−2.56840	+	2.15514i
$156$		0			0
$157$	0.289741	−	1.64320i	0.0231239	−	0.131142i	−0.971060	−	0.238834i	$-0.923235\pi$
$157$	0.289741	−	1.64320i	0.0231239	−	0.131142i	0.994184	+	0.107692i	$0.0343460\pi$
$158$		0			0
$159$	−8.46690	−	0.930640i	−0.671469	−	0.0738046i
$160$		0			0
$161$	14.0662			1.10857
$162$		0			0
$163$	−5.82562			−0.456297			−0.228149	−	0.973626i	$-0.573267\pi$
$163$	−5.82562			−0.456297			−0.228149	+	0.973626i	$0.573267\pi$
$164$		0			0
$165$	24.5585	+	2.69935i	1.91187	+	0.210144i
$166$		0			0
$167$	−3.19530	+	18.1214i	−0.247260	+	1.40228i	0.567927	+	0.823079i	$0.307746\pi$
$167$	−3.19530	+	18.1214i	−0.247260	+	1.40228i	−0.815186	+	0.579199i	$0.803365\pi$
$168$		0			0
$169$	0.771610	−	0.647458i	0.0593546	−	0.0498045i
$170$		0			0
$171$	−0.549983	−	1.74911i	−0.0420583	−	0.133758i
$172$		0			0
$173$	−2.13403	−	12.1027i	−0.162247	−	0.920149i	−0.951858	−	0.306541i	$-0.900828\pi$
$173$	−2.13403	−	12.1027i	−0.162247	−	0.920149i	0.789610	−	0.613608i	$-0.210283\pi$
$174$		0			0
$175$	−36.8970	+	13.4294i	−2.78915	+	1.01517i
$176$		0			0
$177$	−0.405619	+	1.38959i	−0.0304882	+	0.104448i
$178$		0			0
$179$	−0.416765	+	0.721859i	−0.0311505	+	0.0539543i	−0.881180	−	0.472780i	$-0.843250\pi$
$179$	−0.416765	+	0.721859i	−0.0311505	+	0.0539543i	0.850030	+	0.526734i	$0.176584\pi$
$180$		0			0
$181$	−4.90777	−	8.50052i	−0.364792	−	0.631838i	0.623951	−	0.781464i	$-0.285527\pi$
$181$	−4.90777	−	8.50052i	−0.364792	−	0.631838i	−0.988743	+	0.149625i	$0.952193\pi$
$182$		0			0
$183$	−2.59679	+	1.73365i	−0.191960	+	0.128155i
$184$		0			0
$185$	34.0264	+	28.5515i	2.50167	+	2.09915i
$186$		0			0
$187$	0.853975	+	0.310821i	0.0624488	+	0.0227295i
$188$		0			0
$189$	18.4660	−	7.15601i	1.34320	−	0.520523i
$190$		0			0
$191$	−9.91905	−	3.61024i	−0.717717	−	0.261228i	−0.0427609	−	0.999085i	$-0.513615\pi$
$191$	−9.91905	−	3.61024i	−0.717717	−	0.261228i	−0.674956	+	0.737858i	$0.735838\pi$
$192$		0			0
$193$	−2.88568	−	2.42137i	−0.207715	−	0.174294i	0.532995	−	0.846118i	$-0.321066\pi$
$193$	−2.88568	−	2.42137i	−0.207715	−	0.174294i	−0.740710	+	0.671824i	$0.765511\pi$
$194$		0			0
$195$	1.64856	+	25.3044i	0.118056	+	1.81208i
$196$		0			0
$197$	−6.85853	−	11.8793i	−0.488650	−	0.846367i	0.511265	−	0.859423i	$-0.329177\pi$
$197$	−6.85853	−	11.8793i	−0.488650	−	0.846367i	−0.999915	+	0.0130565i	$0.995844\pi$
$198$		0			0
$199$	4.90406	−	8.49409i	0.347640	−	0.602130i	−0.638190	−	0.769879i	$-0.720317\pi$
$199$	4.90406	−	8.49409i	0.347640	−	0.602130i	0.985830	+	0.167749i	$0.0536499\pi$
$200$		0			0
$201$	−12.4777	+	3.04809i	−0.880111	+	0.214996i
$202$		0			0
$203$	21.4530	−	7.80825i	1.50570	−	0.548032i
$204$		0			0
$205$	3.87221	+	21.9604i	0.270447	+	1.53378i
$206$		0			0
$207$	6.73328	+	8.78926i	0.467995	+	0.610896i
$208$		0			0
$209$	1.70724	−	1.43254i	0.118092	−	0.0990910i
$210$		0			0
$211$	−0.268264	+	1.52140i	−0.0184680	+	0.104737i	−0.992648	−	0.121034i	$-0.961379\pi$
$211$	−0.268264	+	1.52140i	−0.0184680	+	0.104737i	0.974180	+	0.225771i	$0.0724902\pi$
$212$		0			0
$213$	3.94674	−	5.37825i	0.270426	−	0.368511i
$214$		0			0
$215$	−4.78255			−0.326167
$216$		0			0
$217$	−40.6695			−2.76083
$218$		0			0
$219$	−2.10702	−	4.79368i	−0.142379	−	0.323927i
$220$		0			0
$221$	−0.161970	+	0.918579i	−0.0108953	+	0.0617903i
$222$		0			0
$223$	−16.0975	+	13.5074i	−1.07797	+	0.904522i	−0.995750	−	0.0920922i	$-0.970645\pi$
$223$	−16.0975	+	13.5074i	−1.07797	+	0.904522i	−0.0822172	+	0.996614i	$0.526200\pi$
$224$		0			0
$225$	−26.0535	−	16.6266i	−1.73690	−	1.10844i
$226$		0			0
$227$	3.43974	+	19.5077i	0.228304	+	1.29477i	0.856268	+	0.516532i	$0.172777\pi$
$227$	3.43974	+	19.5077i	0.228304	+	1.29477i	−0.627964	+	0.778242i	$0.716112\pi$
$228$		0			0
$229$	−15.3024	+	5.56962i	−1.01121	+	0.368051i	−0.793898	−	0.608051i	$-0.791952\pi$
$229$	−15.3024	+	5.56962i	−1.01121	+	0.368051i	−0.217313	+	0.976102i	$0.569729\pi$
$230$		0			0
$231$	16.6390	+	17.3950i	1.09476	+	1.14450i
$232$		0			0
$233$	7.53233	−	13.0464i	0.493459	−	0.854696i	−0.506512	−	0.862233i	$-0.669066\pi$
$233$	7.53233	−	13.0464i	0.493459	−	0.854696i	0.999972	+	0.00753629i	$0.00239890\pi$
$234$		0			0
$235$	−19.6030	−	33.9533i	−1.27876	−	2.21487i
$236$		0			0
$237$	24.1498	+	11.9212i	1.56870	+	0.774363i
$238$		0			0
$239$	5.02801	+	4.21900i	0.325235	+	0.272905i	0.790755	−	0.612133i	$-0.209688\pi$
$239$	5.02801	+	4.21900i	0.325235	+	0.272905i	−0.465520	+	0.885037i	$0.654133\pi$
$240$		0			0
$241$	−10.3231	−	3.75729i	−0.664968	−	0.242029i	−0.0125882	−	0.999921i	$-0.504007\pi$
$241$	−10.3231	−	3.75729i	−0.664968	−	0.242029i	−0.652380	+	0.757892i	$0.726229\pi$
$242$		0			0
$243$	13.3109	+	8.11301i	0.853892	+	0.520450i
$244$		0			0
$245$	−27.6647	−	10.0691i	−1.76743	−	0.643293i
$246$		0			0
$247$	1.75226	+	1.47032i	0.111494	+	0.0935545i
$248$		0			0
$249$	17.8008	+	8.78705i	1.12808	+	0.556857i
$250$		0			0
$251$	−0.173054	−	0.299738i	−0.0109231	−	0.0189193i	0.860512	−	0.509430i	$-0.170144\pi$
$251$	−0.173054	−	0.299738i	−0.0109231	−	0.0189193i	−0.871435	+	0.490511i	$0.836810\pi$
$252$		0			0
$253$	−6.72889	+	11.6548i	−0.423042	+	0.732730i
$254$		0			0
$255$	−1.16721	−	1.22024i	−0.0730935	−	0.0764145i
$256$		0			0
$257$	−23.0101	+	8.37499i	−1.43533	+	0.522417i	−0.938454	−	0.345404i	$-0.887742\pi$
$257$	−23.0101	+	8.37499i	−1.43533	+	0.522417i	−0.496876	+	0.867822i	$0.665520\pi$
$258$		0			0
$259$	7.51497	+	42.6195i	0.466957	+	2.64825i
$260$		0			0
$261$	15.1483	+	9.66723i	0.937653	+	0.598386i
$262$		0			0
$263$	2.55667	−	2.14530i	0.157651	−	0.132285i	−0.560550	−	0.828121i	$-0.689410\pi$
$263$	2.55667	−	2.14530i	0.157651	−	0.132285i	0.718201	+	0.695836i	$0.244966\pi$
$264$		0			0
$265$	−3.34056	+	18.9453i	−0.205209	+	1.16380i
$266$		0			0
$267$	10.0335	+	22.8271i	0.614038	+	1.39700i
$268$		0			0
$269$	12.6609			0.771947			0.385974	−	0.922510i	$-0.373866\pi$
$269$	12.6609			0.771947			0.385974	+	0.922510i	$0.373866\pi$
$270$		0			0
$271$	27.4148			1.66533			0.832666	−	0.553775i	$-0.186813\pi$
$271$	27.4148			1.66533			0.832666	+	0.553775i	$0.186813\pi$
$272$		0			0
$273$	−14.6170	+	19.9186i	−0.884659	+	1.20553i
$274$		0			0
$275$	6.52339	−	36.9960i	0.393375	−	2.23094i
$276$		0			0
$277$	14.5937	−	12.2456i	0.876853	−	0.735767i	−0.0886765	−	0.996060i	$-0.528264\pi$
$277$	14.5937	−	12.2456i	0.876853	−	0.735767i	0.965530	+	0.260293i	$0.0838193\pi$
$278$		0			0
$279$	−19.4679	−	25.4124i	−1.16552	−	1.52140i
$280$		0			0
$281$	−1.60388	−	9.09603i	−0.0956792	−	0.542624i	−0.994537	−	0.104384i	$-0.966713\pi$
$281$	−1.60388	−	9.09603i	−0.0956792	−	0.542624i	0.898858	−	0.438240i	$-0.144398\pi$
$282$		0			0
$283$	28.6606	−	10.4316i	1.70370	−	0.620096i	0.707460	−	0.706753i	$-0.249841\pi$
$283$	28.6606	−	10.4316i	1.70370	−	0.620096i	0.996238	+	0.0866574i	$0.0276185\pi$
$284$		0			0
$285$	−4.02273	+	0.982683i	−0.238286	+	0.0582091i
$286$		0			0
$287$	−10.8631	+	18.8154i	−0.641228	+	1.11064i
$288$		0			0
$289$	8.46894	+	14.6686i	0.498173	+	0.862861i
$290$		0			0
$291$	−0.411229	−	6.31211i	−0.0241067	−	0.370022i
$292$		0			0
$293$	−14.4469	−	12.1224i	−0.843998	−	0.708198i	0.114461	−	0.993428i	$-0.463486\pi$
$293$	−14.4469	−	12.1224i	−0.843998	−	0.708198i	−0.958459	+	0.285229i	$0.907930\pi$
$294$		0			0
$295$	3.07216	+	1.11818i	0.178868	+	0.0651028i
$296$		0			0
$297$	−2.90441	+	18.7236i	−0.168531	+	1.08645i
$298$		0			0
$299$	−12.9797	−	4.72423i	−0.750637	−	0.273209i
$300$		0			0
$301$	−3.56950	−	2.99517i	−0.205743	−	0.172639i
$302$		0			0
$303$	−6.45178	+	4.30728i	−0.370645	+	0.247447i
$304$		0			0
$305$	3.52585	+	6.10696i	0.201890	+	0.349683i
$306$		0			0
$307$	11.8413	−	20.5098i	0.675820	−	1.17055i	−0.300408	−	0.953811i	$-0.597123\pi$
$307$	11.8413	−	20.5098i	0.675820	−	1.17055i	0.976228	−	0.216744i	$-0.0695437\pi$
$308$		0			0
$309$	−2.76294	+	9.46540i	−0.157178	+	0.538468i
$310$		0			0
$311$	30.4825	−	11.0947i	1.72851	−	0.629125i	0.729984	−	0.683465i	$-0.239528\pi$
$311$	30.4825	−	11.0947i	1.72851	−	0.629125i	0.998523	+	0.0543398i	$0.0173054\pi$
$312$		0			0
$313$	3.45718	+	19.6066i	0.195411	+	1.10823i	0.911832	+	0.410563i	$0.134668\pi$
$313$	3.45718	+	19.6066i	0.195411	+	1.10823i	−0.716421	+	0.697668i	$0.754221\pi$
$314$		0			0
$315$	−13.4162	−	42.6676i	−0.755919	−	2.40405i
$316$		0			0
$317$	−1.22090	+	1.02446i	−0.0685728	+	0.0575394i	−0.676430	−	0.736507i	$-0.736474\pi$
$317$	−1.22090	+	1.02446i	−0.0685728	+	0.0575394i	0.607857	+	0.794046i	$0.292029\pi$
$318$		0			0
$319$	−3.79289	+	21.5106i	−0.212361	+	1.20436i
$320$		0			0
$321$	−6.13850	−	0.674713i	−0.342617	−	0.0376588i
$322$		0			0
$323$	−0.152320			−0.00847532
$324$		0			0
$325$	38.5575			2.13879
$326$		0			0
$327$	−6.48392	−	0.712681i	−0.358562	−	0.0394113i
$328$		0			0
$329$	6.63311	−	37.6182i	0.365695	−	2.07396i
$330$		0			0
$331$	−16.6109	+	13.9382i	−0.913018	+	0.766113i	−0.972691	−	0.232105i	$-0.925439\pi$
$331$	−16.6109	+	13.9382i	−0.913018	+	0.766113i	0.0596726	+	0.998218i	$0.480994\pi$
$332$		0			0
$333$	−23.0335	+	25.0971i	−1.26223	+	1.37531i
$334$		0			0
$335$	5.03743	+	28.5687i	0.275224	+	1.56087i
$336$		0			0
$337$	−7.32164	+	2.66486i	−0.398835	+	0.145164i	−0.533647	−	0.845707i	$-0.679179\pi$
$337$	−7.32164	+	2.66486i	−0.398835	+	0.145164i	0.134812	+	0.990871i	$0.456957\pi$
$338$		0			0
$339$	3.06544	−	10.5017i	0.166492	−	0.570374i
$340$		0			0
$341$	19.4553	−	33.6975i	1.05356	−	1.82482i
$342$		0			0
$343$	−1.00232	−	1.73606i	−0.0541200	−	0.0937386i
$344$		0			0
$345$	20.7970	−	13.8843i	1.11967	−	0.747507i
$346$		0			0
$347$	−11.1042	−	9.31753i	−0.596105	−	0.500191i	0.294086	−	0.955779i	$-0.404985\pi$
$347$	−11.1042	−	9.31753i	−0.596105	−	0.500191i	−0.890191	+	0.455588i	$0.849429\pi$
$348$		0			0
$349$	−23.0978	−	8.40693i	−1.23640	−	0.450013i	−0.360615	−	0.932715i	$-0.617433\pi$
$349$	−23.0978	−	8.40693i	−1.23640	−	0.450013i	−0.875785	+	0.482702i	$0.839655\pi$
$350$		0			0
$351$	−19.4431	+	0.401346i	−1.03780	+	0.0214223i
$352$		0			0
$353$	20.7632	+	7.55720i	1.10512	+	0.402229i	0.829200	−	0.558953i	$-0.188797\pi$
$353$	20.7632	+	7.55720i	1.10512	+	0.402229i	0.275916	+	0.961182i	$0.411019\pi$
$354$		0			0
$355$	−11.5415	−	9.68447i	−0.612559	−	0.513998i
$356$		0			0
$357$	−0.106958	−	1.64173i	−0.00566080	−	0.0868896i
$358$		0			0
$359$	−0.220362	−	0.381678i	−0.0116302	−	0.0201442i	0.860152	−	0.510038i	$-0.170369\pi$
$359$	−0.220362	−	0.381678i	−0.0116302	−	0.0201442i	−0.871782	+	0.489894i	$0.837035\pi$
$360$		0			0
$361$	9.31323	−	16.1310i	0.490170	−	0.848999i
$362$		0			0
$363$	−3.86425	+	0.943969i	−0.202821	+	0.0495455i
$364$		0			0
$365$	−11.1129	+	4.04477i	−0.581676	+	0.211713i
$366$		0			0
$367$	−1.00182	−	5.68161i	−0.0522946	−	0.296577i	0.947432	−	0.319957i	$-0.103668\pi$
$367$	−1.00182	−	5.68161i	−0.0522946	−	0.296577i	−0.999727	+	0.0233796i	$0.992557\pi$
$368$		0			0
$369$	−16.9568	+	2.21887i	−0.882738	+	0.115510i
$370$		0			0
$371$	−14.3581	+	12.0479i	−0.745438	+	0.625496i
$372$		0			0
$373$	−4.74075	+	26.8861i	−0.245467	+	1.39211i	0.573940	+	0.818898i	$0.305414\pi$
$373$	−4.74075	+	26.8861i	−0.245467	+	1.39211i	−0.819406	+	0.573213i	$0.805697\pi$
$374$		0			0
$375$	−21.2543	+	28.9633i	−1.09757	+	1.49566i
$376$		0			0
$377$	−22.4185			−1.15461
$378$		0			0
$379$	−6.76975			−0.347739			−0.173869	−	0.984769i	$-0.555627\pi$
$379$	−6.76975			−0.347739			−0.173869	+	0.984769i	$0.555627\pi$
$380$		0			0
$381$	−10.7735	−	24.5108i	−0.551945	−	1.25573i
$382$		0			0
$383$	4.80381	−	27.2438i	0.245463	−	1.39209i	−0.573950	−	0.818890i	$-0.694590\pi$
$383$	4.80381	−	27.2438i	0.245463	−	1.39209i	0.819414	−	0.573202i	$-0.194299\pi$
$384$		0			0
$385$	41.6462	−	34.9453i	2.12249	−	1.78098i
$386$		0			0
$387$	0.162862	−	3.66416i	0.00827876	−	0.186260i
$388$		0			0
$389$	2.95788	+	16.7750i	0.149970	+	0.850524i	0.963241	+	0.268638i	$0.0865737\pi$
$389$	2.95788	+	16.7750i	0.149970	+	0.850524i	−0.813271	+	0.581885i	$0.802315\pi$
$390$		0			0
$391$	0.864325	−	0.314589i	0.0437108	−	0.0159094i
$392$		0			0
$393$	11.2261	+	11.7361i	0.566281	+	0.592010i
$394$		0			0
$395$	30.4127	−	52.6763i	1.53023	−	2.65043i
$396$		0			0
$397$	−9.03841	−	15.6550i	−0.453625	−	0.785701i	0.544983	−	0.838447i	$-0.316536\pi$
$397$	−9.03841	−	15.6550i	−0.453625	−	0.785701i	−0.998608	+	0.0527456i	$0.983203\pi$
$398$		0			0
$399$	−3.61784	−	1.78589i	−0.181118	−	0.0894061i
$400$		0			0
$401$	5.45116	+	4.57407i	0.272218	+	0.228418i	0.768669	−	0.639647i	$-0.220919\pi$
$401$	5.45116	+	4.57407i	0.272218	+	0.228418i	−0.496451	+	0.868065i	$0.665364\pi$
$402$		0			0
$403$	37.5283	+	13.6592i	1.86942	+	0.680412i
$404$		0			0
$405$	20.2387	−	28.8076i	1.00567	−	1.43146i
$406$		0			0
$407$	−38.9082	−	14.1614i	−1.92861	−	0.701955i
$408$		0			0
$409$	−16.7429	−	14.0489i	−0.827881	−	0.694674i	0.126923	−	0.991913i	$-0.459490\pi$
$409$	−16.7429	−	14.0489i	−0.827881	−	0.694674i	−0.954803	+	0.297238i	$0.903934\pi$
$410$		0			0
$411$	9.03379	+	4.45938i	0.445604	+	0.219965i
$412$		0			0
$413$	1.59266	+	2.75857i	0.0783698	+	0.135740i
$414$		0			0
$415$	22.4171	−	38.8275i	1.10041	−	1.90597i
$416$		0			0
$417$	6.34901	+	6.63747i	0.310912	+	0.325038i
$418$		0			0
$419$	27.0976	−	9.86271i	1.32380	−	0.481825i	0.419128	−	0.907927i	$-0.362336\pi$
$419$	27.0976	−	9.86271i	1.32380	−	0.481825i	0.904675	+	0.426102i	$0.140114\pi$
$420$		0			0
$421$	3.28908	+	18.6533i	0.160300	+	0.909105i	0.953779	+	0.300508i	$0.0971563\pi$
$421$	3.28908	+	18.6533i	0.160300	+	0.909105i	−0.793479	+	0.608597i	$0.791733\pi$
$422$		0			0
$423$	26.6810	−	13.8626i	1.29727	−	0.674024i
$424$		0			0
$425$	−1.96687	+	1.65040i	−0.0954070	+	0.0800560i
$426$		0			0
$427$	−1.19305	+	6.76613i	−0.0577358	+	0.327436i
$428$		0			0
$429$	−9.51158	−	21.6397i	−0.459223	−	1.04478i
$430$		0			0
$431$	−37.2852			−1.79596			−0.897982	−	0.440032i	$-0.854967\pi$
$431$	−37.2852			−1.79596			−0.897982	+	0.440032i	$0.854967\pi$
$432$		0			0
$433$	24.7565			1.18972			0.594861	−	0.803828i	$-0.297207\pi$
$433$	24.7565			1.18972			0.594861	+	0.803828i	$0.297207\pi$
$434$		0			0
$435$	24.0113	−	32.7203i	1.15125	−	1.56882i
$436$		0			0
$437$	0.391690	−	2.22138i	0.0187371	−	0.106263i
$438$		0			0
$439$	17.7744	−	14.9145i	0.848328	−	0.711832i	−0.111093	−	0.993810i	$-0.535435\pi$
$439$	17.7744	−	14.9145i	0.848328	−	0.711832i	0.959421	+	0.281978i	$0.0909907\pi$
$440$		0			0
$441$	8.65657	−	20.8525i	0.412217	−	0.992975i
$442$		0			0
$443$	−1.94156	−	11.0111i	−0.0922463	−	0.523155i	−0.995556	−	0.0941668i	$-0.969981\pi$
$443$	−1.94156	−	11.0111i	−0.0922463	−	0.523155i	0.903310	−	0.428988i	$-0.141130\pi$
$444$		0			0
$445$	52.9187	−	19.2608i	2.50859	−	0.913052i
$446$		0			0
$447$	−24.9695	+	6.09961i	−1.18102	+	0.288502i
$448$		0			0
$449$	−13.7509	+	23.8172i	−0.648944	+	1.12400i	0.334432	+	0.942420i	$0.391456\pi$
$449$	−13.7509	+	23.8172i	−0.648944	+	1.12400i	−0.983376	+	0.181583i	$0.941878\pi$
$450$		0			0
$451$	−10.3932	−	18.0016i	−0.489399	−	0.847664i
$452$		0			0
$453$	0.349667	+	5.36717i	0.0164288	+	0.252172i
$454$		0			0
$455$	42.7446	+	35.8670i	2.00390	+	1.68147i
$456$		0			0
$457$	10.8010	+	3.93124i	0.505249	+	0.183896i	0.582053	−	0.813151i	$-0.302249\pi$
$457$	10.8010	+	3.93124i	0.505249	+	0.183896i	−0.0768043	+	0.997046i	$0.524472\pi$
$458$		0			0
$459$	0.974639	−	0.852707i	0.0454922	−	0.0398010i
$460$		0			0
$461$	2.09918	+	0.764038i	0.0977684	+	0.0355848i	0.390441	−	0.920628i	$-0.372322\pi$
$461$	2.09918	+	0.764038i	0.0977684	+	0.0355848i	−0.292673	+	0.956213i	$0.594545\pi$
$462$		0			0
$463$	3.35403	+	2.81437i	0.155875	+	0.130795i	0.717390	−	0.696672i	$-0.245337\pi$
$463$	3.35403	+	2.81437i	0.155875	+	0.130795i	−0.561515	+	0.827467i	$0.689781\pi$
$464$		0			0
$465$	−60.1305	+	40.1438i	−2.78849	+	1.86162i
$466$		0			0
$467$	14.9232	+	25.8478i	0.690565	+	1.19609i	0.971653	+	0.236412i	$0.0759715\pi$
$467$	14.9232	+	25.8478i	0.690565	+	1.19609i	−0.281088	+	0.959682i	$0.590695\pi$
$468$		0			0
$469$	−14.1320	+	24.4773i	−0.652555	+	1.13026i
$470$		0			0
$471$	0.809800	−	2.77424i	0.0373136	−	0.127830i
$472$		0			0
$473$	4.18927	−	1.52477i	0.192623	−	0.0701089i
$474$		0			0
$475$	1.09338	+	6.20087i	0.0501677	+	0.284515i
$476$		0			0
$477$	−14.4012	−	3.20453i	−0.659386	−	0.146725i
$478$		0			0
$479$	−8.48200	+	7.11724i	−0.387552	+	0.325195i	−0.815659	−	0.578533i	$-0.803625\pi$
$479$	−8.48200	+	7.11724i	−0.387552	+	0.325195i	0.428106	+	0.903728i	$0.359181\pi$
$480$		0			0
$481$	7.37957	−	41.8516i	0.336480	−	1.90827i
$482$		0			0
$483$	24.2174	+	2.66186i	1.10193	+	0.121119i
$484$		0			0
$485$	−14.2860			−0.648695
$486$		0			0
$487$	−39.7909			−1.80310			−0.901548	−	0.432678i	$-0.857569\pi$
$487$	−39.7909			−1.80310			−0.901548	+	0.432678i	$0.857569\pi$
$488$		0			0
$489$	−10.0299	−	1.10243i	−0.453566	−	0.0498537i
$490$		0			0
$491$	−0.628340	+	3.56349i	−0.0283566	+	0.160818i	−0.995698	−	0.0926593i	$-0.970463\pi$
$491$	−0.628340	+	3.56349i	−0.0283566	+	0.160818i	0.967341	+	0.253477i	$0.0815744\pi$
$492$		0			0
$493$	1.14359	−	0.959589i	0.0515049	−	0.0432177i
$494$		0			0
$495$	41.7711	+	9.29483i	1.87747	+	0.417771i
$496$		0			0
$497$	−2.54902	−	14.4562i	−0.114339	−	0.648450i
$498$		0			0
$499$	−13.4158	+	4.88294i	−0.600572	+	0.218590i	−0.624373	−	0.781126i	$-0.714645\pi$
$499$	−13.4158	+	4.88294i	−0.600572	+	0.218590i	0.0238008	+	0.999717i	$0.492423\pi$
$500$		0			0
$501$	−8.93056	+	30.5947i	−0.398988	+	1.36687i
$502$		0			0
$503$	14.0862	−	24.3981i	0.628074	−	1.08786i	−0.359864	−	0.933005i	$-0.617177\pi$
$503$	14.0862	−	24.3981i	0.628074	−	1.08786i	0.987938	−	0.154851i	$-0.0494899\pi$
$504$		0			0
$505$	8.76005	+	15.1728i	0.389817	+	0.675183i
$506$		0			0
$507$	1.45099	−	0.968698i	0.0644408	−	0.0430214i
$508$		0			0
$509$	−15.1684	−	12.7278i	−0.672329	−	0.564151i	0.241424	−	0.970420i	$-0.422385\pi$
$509$	−15.1684	−	12.7278i	−0.672329	−	0.564151i	−0.913754	+	0.406268i	$0.866830\pi$
$510$		0			0
$511$	−10.8274	−	3.94084i	−0.478975	−	0.174332i
$512$		0			0
$513$	−0.615897	−	3.11549i	−0.0271925	−	0.137552i
$514$		0			0
$515$	20.9265	+	7.61664i	0.922134	+	0.335629i
$516$		0			0
$517$	27.9962	+	23.4916i	1.23127	+	1.03316i
$518$		0			0
$519$	−1.38382	−	21.2408i	−0.0607431	−	0.932367i
$520$		0			0
$521$	−14.3476	−	24.8507i	−0.628579	−	1.08873i	−0.987837	−	0.155492i	$-0.950304\pi$
$521$	−14.3476	−	24.8507i	−0.628579	−	1.08873i	0.359258	−	0.933238i	$-0.383030\pi$
$522$		0			0
$523$	14.4552	−	25.0372i	0.632083	−	1.09480i	−0.355042	−	0.934851i	$-0.615533\pi$
$523$	14.4552	−	25.0372i	0.632083	−	1.09480i	0.987125	−	0.159950i	$-0.0511334\pi$
$524$		0			0
$525$	−66.0662	+	16.1388i	−2.88336	+	0.704356i
$526$		0			0
$527$	−2.49902	+	0.909571i	−0.108859	+	0.0396215i
$528$		0			0
$529$	−1.62866	−	9.23662i	−0.0708115	−	0.401592i
$530$		0			0
$531$	−0.961311	+	2.31567i	−0.0417174	+	0.100491i
$532$		0			0
$533$	16.3434	−	13.7137i	0.707909	−	0.594006i
$534$		0			0
$535$	−2.42190	+	13.7353i	−0.104708	+	0.593829i
$536$		0			0
$537$	−0.854141	+	1.16394i	−0.0368589	+	0.0502278i
$538$		0			0
$539$	27.4431			1.18206
$540$		0			0
$541$	34.7633			1.49459			0.747295	−	0.664493i	$-0.231352\pi$
$541$	34.7633			1.49459			0.747295	+	0.664493i	$0.231352\pi$
$542$		0			0
$543$	−6.84100	−	15.5639i	−0.293575	−	0.667912i
$544$		0			0
$545$	−2.55819	+	14.5082i	−0.109581	+	0.621464i
$546$		0			0
$547$	4.38422	−	3.67880i	0.187456	−	0.157294i	−0.544230	−	0.838936i	$-0.683178\pi$
$547$	4.38422	−	3.67880i	0.187456	−	0.157294i	0.731686	+	0.681642i	$0.238734\pi$
$548$		0			0
$549$	−4.79893	+	2.49338i	−0.204813	+	0.106415i
$550$		0			0
$551$	−0.635724	−	3.60537i	−0.0270828	−	0.153594i
$552$		0			0
$553$	55.6885	−	20.2690i	2.36812	−	0.861924i
$554$		0			0
$555$	53.1796	+	55.5958i	2.25735	+	2.35991i
$556$		0			0
$557$	−5.84528	+	10.1243i	−0.247673	+	0.428981i	−0.962880	−	0.269931i	$-0.912999\pi$
$557$	−5.84528	+	10.1243i	−0.247673	+	0.428981i	0.715207	+	0.698913i	$0.246332\pi$
$558$		0			0
$559$	2.28785	+	3.96268i	0.0967659	+	0.167603i
$560$		0			0
$561$	1.41145	+	0.696741i	0.0595916	+	0.0294164i
$562$		0			0
$563$	−9.98246	−	8.37628i	−0.420711	−	0.353018i	0.407723	−	0.913106i	$-0.366323\pi$
$563$	−9.98246	−	8.37628i	−0.420711	−	0.353018i	−0.828433	+	0.560088i	$0.810767\pi$
$564$		0			0
$565$	−23.2177	−	8.45054i	−0.976775	−	0.355517i
$566$		0			0
$567$	33.1468	−	8.82589i	1.39203	−	0.370653i
$568$		0			0
$569$	−26.5694	−	9.67045i	−1.11385	−	0.405407i	−0.281443	−	0.959578i	$-0.590813\pi$
$569$	−26.5694	−	9.67045i	−1.11385	−	0.405407i	−0.832403	+	0.554171i	$0.813035\pi$
$570$		0			0
$571$	5.26501	+	4.41787i	0.220334	+	0.184882i	0.746273	−	0.665640i	$-0.231841\pi$
$571$	5.26501	+	4.41787i	0.220334	+	0.184882i	−0.525939	+	0.850522i	$0.676286\pi$
$572$		0			0
$573$	−16.3943	−	8.09275i	−0.684880	−	0.338080i
$574$		0			0
$575$	−19.0110	−	32.9280i	−0.792814	−	1.37319i
$576$		0			0
$577$	−8.40038	+	14.5499i	−0.349713	+	0.605720i	−0.986198	−	0.165569i	$-0.947054\pi$
$577$	−8.40038	+	14.5499i	−0.349713	+	0.605720i	0.636486	+	0.771288i	$0.280387\pi$
$578$		0			0
$579$	−4.51000	−	4.71491i	−0.187429	−	0.195945i
$580$		0			0
$581$	41.0478	−	14.9402i	1.70295	−	0.619823i
$582$		0			0
$583$	−3.11396	−	17.6601i	−0.128967	−	0.731408i
$584$		0			0
$585$	−1.95027	+	43.8780i	−0.0806336	+	1.81413i
$586$		0			0
$587$	−15.5729	+	13.0672i	−0.642761	+	0.539340i	−0.904865	−	0.425700i	$-0.860028\pi$
$587$	−15.5729	+	13.0672i	−0.642761	+	0.539340i	0.262104	+	0.965040i	$0.415584\pi$
$588$		0			0
$589$	−1.13249	+	6.42269i	−0.0466636	+	0.264642i
$590$		0			0
$591$	−9.56018	−	21.7503i	−0.393253	−	0.894688i
$592$		0			0
$593$	0.267129			0.0109697			0.00548483	−	0.999985i	$-0.498254\pi$
$593$	0.267129			0.0109697			0.00548483	+	0.999985i	$0.498254\pi$
$594$		0			0
$595$	−3.71568			−0.152328
$596$		0			0
$597$	10.0506	−	13.6961i	0.411346	−	0.560543i
$598$		0			0
$599$	−3.42761	+	19.4390i	−0.140049	+	0.794255i	0.831162	+	0.556031i	$0.187676\pi$
$599$	−3.42761	+	19.4390i	−0.140049	+	0.794255i	−0.971210	+	0.238224i	$0.923435\pi$
$600$		0			0
$601$	3.46409	−	2.90672i	0.141303	−	0.118568i	−0.569396	−	0.822063i	$-0.692823\pi$
$601$	3.46409	−	2.90672i	0.141303	−	0.118568i	0.710700	+	0.703496i	$0.248379\pi$
$602$		0			0
$603$	−22.0595	+	2.88657i	−0.898332	+	0.117550i
$604$		0			0
$605$	1.56005	+	8.84749i	0.0634251	+	0.359702i
$606$		0			0
$607$	−13.9646	+	5.08270i	−0.566806	+	0.206300i	−0.609498	−	0.792788i	$-0.708629\pi$
$607$	−13.9646	+	5.08270i	−0.566806	+	0.206300i	0.0426920	+	0.999088i	$0.486407\pi$
$608$		0			0
$609$	38.4128	−	9.38359i	1.55657	−	0.380242i
$610$		0			0
$611$	−18.7552	+	32.4849i	−0.758753	+	1.31420i
$612$		0			0
$613$	7.20658	+	12.4822i	0.291071	+	0.504149i	0.974063	−	0.226276i	$-0.0726551\pi$
$613$	7.20658	+	12.4822i	0.291071	+	0.504149i	−0.682992	+	0.730425i	$0.739322\pi$
$614$		0			0
$615$	2.51095	+	38.5415i	0.101251	+	1.55415i
$616$		0			0
$617$	−18.8922	−	15.8525i	−0.760573	−	0.638196i	0.177703	−	0.984084i	$-0.443133\pi$
$617$	−18.8922	−	15.8525i	−0.760573	−	0.638196i	−0.938276	+	0.345888i	$0.887578\pi$
$618$		0			0
$619$	−0.521034	−	0.189641i	−0.0209421	−	0.00762231i	0.331528	−	0.943445i	$-0.392436\pi$
$619$	−0.521034	−	0.189641i	−0.0209421	−	0.00762231i	−0.352470	+	0.935823i	$0.614658\pi$
$620$		0			0
$621$	9.92930	+	16.4065i	0.398449	+	0.658370i
$622$		0			0
$623$	51.5590	+	18.7659i	2.06567	+	0.751842i
$624$		0			0
$625$	22.6942	+	19.0427i	0.907767	+	0.761707i
$626$		0			0
$627$	3.21041	−	2.14331i	0.128211	−	0.0855954i
$628$		0			0
$629$	1.41496	+	2.45077i	0.0564180	+	0.0977188i
$630$		0			0
$631$	−16.6649	+	28.8644i	−0.663419	+	1.14908i	0.316292	+	0.948662i	$0.397562\pi$
$631$	−16.6649	+	28.8644i	−0.663419	+	1.14908i	−0.979711	+	0.200414i	$0.935771\pi$
$632$		0			0
$633$	−0.749772	+	2.56860i	−0.0298008	+	0.102093i
$634$		0			0
$635$	−56.8220	+	20.6815i	−2.25491	+	0.820721i
$636$		0			0
$637$	4.89113	+	27.7390i	0.193794	+	1.09906i
$638$		0			0
$639$	7.81280	−	8.51275i	0.309070	−	0.336759i
$640$		0			0
$641$	−4.27803	+	3.58970i	−0.168972	+	0.141784i	−0.723352	−	0.690479i	$-0.757400\pi$
$641$	−4.27803	+	3.58970i	−0.168972	+	0.141784i	0.554380	+	0.832263i	$0.312955\pi$
$642$		0			0
$643$	8.34634	−	47.3344i	0.329147	−	1.86669i	−0.149616	−	0.988744i	$-0.547804\pi$
$643$	8.34634	−	47.3344i	0.329147	−	1.86669i	0.478764	−	0.877944i	$-0.341085\pi$
$644$		0			0
$645$	−8.23402	−	0.905043i	−0.324214	−	0.0356360i
$646$		0			0
$647$	−46.7676			−1.83863			−0.919313	−	0.393528i	$-0.871254\pi$
$647$	−46.7676			−1.83863			−0.919313	+	0.393528i	$0.871254\pi$
$648$		0			0
$649$	−3.04756			−0.119627
$650$		0			0
$651$	−70.0200	−	7.69625i	−2.74430	−	0.301640i
$652$		0			0
$653$	3.45106	−	19.5719i	0.135050	−	0.765908i	−0.839774	−	0.542935i	$-0.817313\pi$
$653$	3.45106	−	19.5719i	0.135050	−	0.765908i	0.974825	−	0.222973i	$-0.0715761\pi$
$654$		0			0
$655$	28.0981	−	23.5771i	1.09788	−	0.921234i
$656$		0			0
$657$	−2.72048	−	8.65192i	−0.106136	−	0.337544i
$658$		0			0
$659$	−2.69668	−	15.2936i	−0.105048	−	0.595755i	−0.991201	−	0.132363i	$-0.957743\pi$
$659$	−2.69668	−	15.2936i	−0.105048	−	0.595755i	0.886154	−	0.463391i	$-0.153368\pi$
$660$		0			0
$661$	−39.9255	+	14.5317i	−1.55292	+	0.565218i	−0.969101	−	0.246665i	$-0.920665\pi$
$661$	−39.9255	+	14.5317i	−1.55292	+	0.565218i	−0.583821	+	0.811882i	$0.698443\pi$
$662$		0			0
$663$	−0.452692	+	1.55085i	−0.0175811	+	0.0602300i
$664$		0			0
$665$	−4.55606	+	7.89132i	−0.176676	+	0.306012i
$666$		0			0
$667$	11.0536	+	19.1453i	0.427996	+	0.741310i
$668$		0			0
$669$	−30.2709	+	20.2092i	−1.17034	+	0.781332i
$670$		0			0
$671$	−5.03548	−	4.22527i	−0.194393	−	0.163115i
$672$		0			0
$673$	−24.4175	−	8.88723i	−0.941224	−	0.342577i	−0.174575	−	0.984644i	$-0.555855\pi$
$673$	−24.4175	−	8.88723i	−0.941224	−	0.342577i	−0.766649	+	0.642067i	$0.778077\pi$
$674$		0			0
$675$	−41.7093	−	33.5561i	−1.60539	−	1.29158i
$676$		0			0
$677$	28.5860	+	10.4044i	1.09865	+	0.399875i	0.826818	−	0.562470i	$-0.190149\pi$
$677$	28.5860	+	10.4044i	1.09865	+	0.399875i	0.271831	+	0.962345i	$0.412371\pi$
$678$		0			0
$679$	−10.6625	−	8.94692i	−0.409190	−	0.343351i
$680$		0			0
$681$	2.23052	+	34.2371i	0.0854737	+	1.31197i
$682$		0			0
$683$	−1.37482	−	2.38126i	−0.0526060	−	0.0911163i	0.838523	−	0.544866i	$-0.183419\pi$
$683$	−1.37482	−	2.38126i	−0.0526060	−	0.0911163i	−0.891129	+	0.453750i	$0.850086\pi$
$684$		0			0
$685$	11.3765	−	19.7048i	0.434675	−	0.752880i
$686$		0			0
$687$	−27.3999	+	6.69331i	−1.04537	+	0.255366i
$688$		0			0
$689$	17.2955	−	6.29506i	0.658908	−	0.239823i
$690$		0			0
$691$	4.61384	+	26.1664i	0.175519	+	0.995417i	0.937543	+	0.347869i	$0.113095\pi$
$691$	4.61384	+	26.1664i	0.175519	+	0.995417i	−0.762024	+	0.647548i	$0.775794\pi$
$692$		0			0
$693$	25.3552	+	33.0973i	0.963165	+	1.25726i
$694$		0			0
$695$	15.8911	−	13.3342i	0.602785	−	0.505796i
$696$		0			0
$697$	−0.246700	+	1.39911i	−0.00934443	+	0.0529949i
$698$		0			0
$699$	15.4372	−	21.0363i	0.583887	−	0.795666i
$700$		0			0
$701$	−20.5452			−0.775980			−0.387990	−	0.921663i	$-0.626831\pi$
$701$	−20.5452			−0.775980			−0.387990	+	0.921663i	$0.626831\pi$
$702$		0			0
$703$	6.93990			0.261743
$704$		0			0
$705$	−27.3248	−	62.1665i	−1.02911	−	2.34133i
$706$		0			0
$707$	−2.96416	+	16.8106i	−0.111479	+	0.632227i
$708$		0			0
$709$	6.68993	−	5.61352i	0.251246	−	0.210820i	−0.508463	−	0.861084i	$-0.669786\pi$
$709$	6.68993	−	5.61352i	0.251246	−	0.210820i	0.759709	+	0.650264i	$0.225342\pi$
$710$		0			0
$711$	39.3224	+	25.0946i	1.47471	+	0.941119i
$712$		0			0
$713$	−6.83863	−	38.7838i	−0.256109	−	1.45247i
$714$		0			0
$715$	−50.1662	+	18.2590i	−1.87611	+	0.682848i
$716$		0			0
$717$	7.85824	+	8.21527i	0.293471	+	0.306805i
$718$		0			0
$719$	−3.92880	+	6.80488i	−0.146520	+	0.253779i	−0.929939	−	0.367714i	$-0.880140\pi$
$719$	−3.92880	+	6.80488i	−0.146520	+	0.253779i	0.783419	+	0.621494i	$0.213474\pi$
$720$		0			0
$721$	10.8487	+	18.7905i	0.404026	+	0.699793i
$722$		0			0
$723$	−17.0620	−	8.42239i	−0.634544	−	0.313232i
$724$		0			0
$725$	−47.2733	−	39.6670i	−1.75568	−	1.47319i
$726$		0			0
$727$	−13.5158	−	4.91935i	−0.501273	−	0.182449i	0.0789933	−	0.996875i	$-0.474829\pi$
$727$	−13.5158	−	4.91935i	−0.501273	−	0.182449i	−0.580267	+	0.814427i	$0.697052\pi$
$728$		0			0
$729$	21.3818	+	16.4870i	0.791918	+	0.610628i
$730$		0			0
$731$	−0.286323	−	0.104213i	−0.0105900	−	0.00385445i
$732$		0			0
$733$	−11.0072	−	9.23615i	−0.406561	−	0.341145i	0.416462	−	0.909153i	$-0.363270\pi$
$733$	−11.0072	−	9.23615i	−0.406561	−	0.341145i	−0.823023	+	0.568008i	$0.807714\pi$
$734$		0			0
$735$	−45.7244	−	22.5711i	−1.68657	−	0.832547i
$736$		0			0
$737$	−13.5208	−	23.4187i	−0.498044	−	0.862638i
$738$		0			0
$739$	14.1659	−	24.5361i	0.521101	−	0.902574i	−0.478598	−	0.878034i	$-0.658855\pi$
$739$	14.1659	−	24.5361i	0.521101	−	0.902574i	0.999699	−	0.0245393i	$-0.00781189\pi$
$740$		0			0
$741$	2.73860	+	2.86303i	0.100605	+	0.105176i
$742$		0			0
$743$	34.6587	−	12.6147i	1.27150	−	0.462789i	0.383890	−	0.923379i	$-0.374584\pi$
$743$	34.6587	−	12.6147i	1.27150	−	0.462789i	0.887613	+	0.460590i	$0.152362\pi$
$744$		0			0
$745$	10.0805	+	57.1695i	0.369322	+	2.09453i
$746$		0			0
$747$	28.9844	+	18.4971i	1.06048	+	0.676774i
$748$		0			0
$749$	−10.4096	+	8.73472i	−0.380360	+	0.319160i
$750$		0			0
$751$	−4.88071	+	27.6799i	−0.178100	+	1.01005i	0.756406	+	0.654103i	$0.226954\pi$
$751$	−4.88071	+	27.6799i	−0.178100	+	1.01005i	−0.934505	+	0.355950i	$0.884157\pi$
$752$		0			0
$753$	−0.241222	−	0.548803i	−0.00879061	−	0.0199995i
$754$		0			0
$755$	12.1474			0.442088
$756$		0			0
$757$	−37.9840			−1.38055			−0.690276	−	0.723546i	$-0.742511\pi$
$757$	−37.9840			−1.38055			−0.690276	+	0.723546i	$0.742511\pi$
$758$		0			0
$759$	−13.7905	+	18.7925i	−0.500565	+	0.682123i
$760$		0			0
$761$	0.571817	−	3.24294i	0.0207284	−	0.117556i	−0.972688	−	0.232117i	$-0.925435\pi$
$761$	0.571817	−	3.24294i	0.0207284	−	0.117556i	0.993416	+	0.114560i	$0.0365460\pi$
$762$		0			0
$763$	−10.9954	+	9.22625i	−0.398061	+	0.334013i
$764$		0			0
$765$	−1.77865	−	2.32175i	−0.0643071	−	0.0839430i
$766$		0			0
$767$	−0.543160	−	3.08041i	−0.0196124	−	0.111227i
$768$		0			0
$769$	−33.2209	+	12.0914i	−1.19798	+	0.436028i	−0.862518	−	0.506027i	$-0.831114\pi$
$769$	−33.2209	+	12.0914i	−1.19798	+	0.436028i	−0.335459	+	0.942055i	$0.608891\pi$
$770$		0			0
$771$	−41.2009	+	10.0647i	−1.48382	+	0.362470i
$772$		0			0
$773$	5.46875	−	9.47216i	0.196697	−	0.340690i	−0.750758	−	0.660577i	$-0.770312\pi$
$773$	5.46875	−	9.47216i	0.196697	−	0.340690i	0.947456	+	0.319887i	$0.103645\pi$
$774$		0			0
$775$	54.9665	+	95.2049i	1.97446	+	3.41986i
$776$		0			0
$777$	4.87312	+	74.7993i	0.174822	+	2.68341i
$778$		0			0
$779$	2.66891	+	2.23948i	0.0956235	+	0.0802377i
$780$		0			0
$781$	13.1974	+	4.80345i	0.472239	+	0.171881i
$782$		0			0
$783$	24.2511	+	19.5105i	0.866662	+	0.697249i
$784$		0			0
$785$	−6.13343	−	2.23239i	−0.218912	−	0.0796773i
$786$		0			0
$787$	−21.4753	−	18.0199i	−0.765512	−	0.642341i	0.174043	−	0.984738i	$-0.444317\pi$
$787$	−21.4753	−	18.0199i	−0.765512	−	0.642341i	−0.939555	+	0.342397i	$0.888761\pi$
$788$		0			0
$789$	4.80776	−	3.20971i	0.171161	−	0.114269i
$790$		0			0
$791$	−12.0364	−	20.8477i	−0.427966	−	0.741259i
$792$		0			0
$793$	3.37336	−	5.84284i	0.119792	−	0.207485i
$794$		0			0
$795$	−9.33656	+	31.9856i	−0.331134	+	1.13441i
$796$		0			0
$797$	40.0807	−	14.5882i	1.41973	−	0.516740i	0.485761	−	0.874092i	$-0.338542\pi$
$797$	40.0807	−	14.5882i	1.41973	−	0.516740i	0.933970	+	0.357352i	$0.116320\pi$
$798$		0			0
$799$	−0.433743	−	2.45988i	−0.0153447	−	0.0870243i
$800$		0			0
$801$	12.9547	+	41.1997i	0.457731	+	1.45572i
$802$		0			0
$803$	8.44480	−	7.08603i	0.298010	−	0.250060i
$804$		0			0
$805$	9.55484	−	54.1882i	0.336764	−	1.90988i
$806$		0			0
$807$	21.7980	+	2.39593i	0.767326	+	0.0843406i
$808$		0			0
$809$	−2.97576			−0.104622			−0.0523110	−	0.998631i	$-0.516659\pi$
$809$	−2.97576			−0.104622			−0.0523110	+	0.998631i	$0.516659\pi$
$810$		0			0
$811$	−27.1093			−0.951935			−0.475968	−	0.879463i	$-0.657902\pi$
$811$	−27.1093			−0.951935			−0.475968	+	0.879463i	$0.657902\pi$
$812$		0			0
$813$	47.1996	+	5.18795i	1.65536	+	0.181949i
$814$		0			0
$815$	−3.95722	+	22.4425i	−0.138615	+	0.786126i
$816$		0			0
$817$	−0.572406	+	0.480306i	−0.0200260	+	0.0168038i
$818$		0			0
$819$	−28.9351	+	31.5274i	−1.01108	+	1.10166i
$820$		0			0
$821$	−5.42100	−	30.7440i	−0.189194	−	1.07297i	−0.920447	−	0.390867i	$-0.872175\pi$
$821$	−5.42100	−	30.7440i	−0.189194	−	1.07297i	0.731253	−	0.682106i	$-0.238936\pi$
$822$		0			0
$823$	−9.48319	+	3.45160i	−0.330563	+	0.120315i	−0.501970	−	0.864885i	$-0.667391\pi$
$823$	−9.48319	+	3.45160i	−0.330563	+	0.120315i	0.171406	+	0.985200i	$0.445169\pi$
$824$		0			0
$825$	18.2323	−	62.4608i	0.634766	−	2.17461i
$826$		0			0
$827$	13.7283	−	23.7782i	0.477381	−	0.826848i	−0.522283	−	0.852772i	$-0.674919\pi$
$827$	13.7283	−	23.7782i	0.477381	−	0.826848i	0.999664	+	0.0259240i	$0.00825280\pi$
$828$		0			0
$829$	−19.3456	−	33.5075i	−0.671900	−	1.16376i	−0.977365	−	0.211561i	$-0.932145\pi$
$829$	−19.3456	−	33.5075i	−0.671900	−	1.16376i	0.305465	−	0.952203i	$-0.401188\pi$
$830$		0			0
$831$	27.4431	−	18.3213i	0.951992	−	0.635560i
$832$		0			0
$833$	−1.43683	−	1.20564i	−0.0497832	−	0.0417730i
$834$		0			0
$835$	67.6401	+	24.6190i	2.34078	+	0.851976i
$836$		0			0
$837$	−28.7086	−	47.4361i	−0.992314	−	1.63963i
$838$		0			0
$839$	3.00278	+	1.09292i	0.103667	+	0.0377318i	0.393333	−	0.919396i	$-0.371322\pi$
$839$	3.00278	+	1.09292i	0.103667	+	0.0377318i	−0.289666	+	0.957128i	$0.593544\pi$
$840$		0			0
$841$	5.27079	+	4.42272i	0.181751	+	0.152508i
$842$		0			0
$843$	−1.04004	−	15.9640i	−0.0358210	−	0.549829i
$844$		0			0
$845$	−1.97012	−	3.41234i	−0.0677740	−	0.117388i
$846$		0			0
$847$	−4.37657	+	7.58044i	−0.150381	+	0.260467i
$848$		0			0
$849$	51.3186	−	12.5362i	1.76125	−	0.430242i
$850$		0			0
$851$	−39.3797	+	14.3331i	−1.34992	+	0.491331i
$852$		0			0
$853$	0.671445	+	3.80795i	0.0229898	+	0.130382i	0.994143	−	0.108076i	$-0.0344691\pi$
$853$	0.671445	+	3.80795i	0.0229898	+	0.130382i	−0.971153	+	0.238458i	$0.923358\pi$
$854$		0			0
$855$	−7.11183	+	0.930611i	−0.243219	+	0.0318262i
$856$		0			0
$857$	41.2228	−	34.5900i	1.40814	−	1.18157i	0.450798	−	0.892626i	$-0.351139\pi$
$857$	41.2228	−	34.5900i	1.40814	−	1.18157i	0.957345	−	0.288947i	$-0.0933050\pi$
$858$		0			0
$859$	−0.382790	+	2.17091i	−0.0130606	+	0.0740705i	−0.990641	−	0.136490i	$-0.956418\pi$
$859$	−0.382790	+	2.17091i	−0.0130606	+	0.0740705i	0.977581	+	0.210561i	$0.0675289\pi$
$860$		0			0
$861$	−22.2634	+	30.3384i	−0.758734	+	1.03393i
$862$		0			0
$863$	−1.88634			−0.0642118			−0.0321059	−	0.999484i	$-0.510221\pi$
$863$	−1.88634			−0.0642118			−0.0321059	+	0.999484i	$0.510221\pi$
$864$		0			0
$865$	−48.0737			−1.63455
$866$		0			0
$867$	11.8050	+	26.8574i	0.400917	+	0.912125i
$868$		0			0
$869$	−9.84573	+	55.8379i	−0.333994	+	1.89417i
$870$		0			0
$871$	21.2614	−	17.8404i	0.720415	−	0.604500i
$872$		0			0
$873$	0.486489	−	10.9453i	0.0164652	−	0.370441i
$874$		0			0
$875$	13.7272	+	77.8506i	0.464063	+	2.63183i
$876$		0			0
$877$	25.8738	−	9.41728i	0.873695	−	0.317999i	0.134033	−	0.990977i	$-0.457207\pi$
$877$	25.8738	−	9.41728i	0.873695	−	0.317999i	0.739663	+	0.672978i	$0.234985\pi$
$878$		0			0
$879$	−22.5790	−	23.6048i	−0.761570	−	0.796172i
$880$		0			0
$881$	15.5948	−	27.0109i	0.525401	−	0.910022i	−0.474161	−	0.880438i	$-0.657249\pi$
$881$	15.5948	−	27.0109i	0.525401	−	0.910022i	0.999562	−	0.0295835i	$-0.00941809\pi$
$882$		0			0
$883$	15.1096	+	26.1705i	0.508478	+	0.880709i	0.999952	+	0.00981694i	$0.00312488\pi$
$883$	15.1096	+	26.1705i	0.508478	+	0.880709i	−0.491474	+	0.870892i	$0.663542\pi$
$884$		0			0
$885$	5.07769	+	2.50652i	0.170685	+	0.0842556i
$886$		0			0
$887$	17.9560	+	15.0669i	0.602903	+	0.505896i	0.892377	−	0.451290i	$-0.149036\pi$
$887$	17.9560	+	15.0669i	0.602903	+	0.505896i	−0.289474	+	0.957186i	$0.593480\pi$
$888$		0			0
$889$	−55.3620	−	20.1501i	−1.85678	−	0.675813i
$890$		0			0
$891$	−8.54370	+	31.6865i	−0.286225	+	1.06154i
$892$		0			0
$893$	−5.75611	−	2.09505i	−0.192621	−	0.0701083i
$894$		0			0
$895$	2.49777	+	2.09588i	0.0834914	+	0.0700576i
$896$		0			0
$897$	−21.4529	−	10.5899i	−0.716293	−	0.353586i
$898$		0			0
$899$	−31.9592	−	55.3549i	−1.06590	−	1.84619i
$900$		0			0
$901$	−0.612816	+	1.06143i	−0.0204159	+	0.0353613i
$902$		0			0
$903$	−5.57875	−	5.83222i	−0.185649	−	0.194084i
$904$		0			0
$905$	−36.0810	+	13.1324i	−1.19937	+	0.436536i
$906$		0			0
$907$	1.25655	+	7.12625i	0.0417231	+	0.236623i	0.998537	−	0.0540789i	$-0.0172222\pi$
$907$	1.25655	+	7.12625i	0.0417231	+	0.236623i	−0.956814	+	0.290702i	$0.906111\pi$
$908$		0			0
$909$	−11.9230	+	6.19484i	−0.395462	+	0.205470i
$910$		0			0
$911$	5.80489	−	4.87088i	0.192325	−	0.161379i	−0.541541	−	0.840675i	$-0.682159\pi$
$911$	5.80489	−	4.87088i	0.192325	−	0.161379i	0.733865	+	0.679295i	$0.237714\pi$
$912$		0			0
$913$	−7.25725	+	41.1579i	−0.240180	+	1.36213i
$914$		0			0
$915$	4.91472	+	11.1815i	0.162476	+	0.369648i
$916$		0			0
$917$	35.7370			1.18014
$918$		0			0
$919$	−1.47958			−0.0488068			−0.0244034	−	0.999702i	$-0.507769\pi$
$919$	−1.47958			−0.0488068			−0.0244034	+	0.999702i	$0.507769\pi$
$920$		0			0
$921$	24.2682	−	33.0705i	0.799666	−	1.08971i
$922$		0			0
$923$	−2.50310	+	14.1958i	−0.0823904	+	0.467259i
$924$		0			0
$925$	89.6129	−	75.1941i	2.94645	−	2.47237i
$926$		0			0
$927$	−6.54813	+	15.7735i	−0.215069	+	0.518071i
$928$		0			0
$929$	7.38754	+	41.8968i	0.242377	+	1.37459i	0.826505	+	0.562929i	$0.190326\pi$
$929$	7.38754	+	41.8968i	0.242377	+	1.37459i	−0.584128	+	0.811662i	$0.698563\pi$
$930$		0			0
$931$	−4.32232	+	1.57320i	−0.141658	+	0.0515595i
$932$		0			0
$933$	54.5808	−	13.3331i	1.78689	−	0.436507i
$934$		0			0
$935$	1.77749	−	3.07870i	0.0581301	−	0.100684i
$936$		0			0
$937$	24.3077	+	42.1021i	0.794097	+	1.37542i	0.923411	+	0.383812i	$0.125389\pi$
$937$	24.3077	+	42.1021i	0.794097	+	1.37542i	−0.129315	+	0.991604i	$0.541278\pi$
$938$		0			0
$939$	2.24183	+	34.4106i	0.0731592	+	1.12295i
$940$		0			0
$941$	27.8859	+	23.3990i	0.909053	+	0.762786i	0.971939	−	0.235235i	$-0.0755859\pi$
$941$	27.8859	+	23.3990i	0.909053	+	0.762786i	−0.0628855	+	0.998021i	$0.520030\pi$
$942$		0			0
$943$	−19.7697	−	7.19557i	−0.643789	−	0.234320i
$944$		0			0
$945$	−15.0241	−	75.9989i	−0.488735	−	2.47225i
$946$		0			0
$947$	−11.2832	−	4.10675i	−0.366655	−	0.133451i	0.152121	−	0.988362i	$-0.451390\pi$
$947$	−11.2832	−	4.10675i	−0.366655	−	0.133451i	−0.518775	+	0.854911i	$0.673612\pi$
$948$		0			0
$949$	8.66753	+	7.27292i	0.281360	+	0.236089i
$950$		0			0
$951$	−2.29588	+	1.53275i	−0.0744489	+	0.0497029i
$952$		0			0
$953$	−1.29882	−	2.24961i	−0.0420727	−	0.0728721i	0.844222	−	0.535993i	$-0.180063\pi$
$953$	−1.29882	−	2.24961i	−0.0420727	−	0.0728721i	−0.886295	+	0.463121i	$0.846729\pi$
$954$		0			0
$955$	−20.6458	+	35.7596i	−0.668083	+	1.15715i
$956$		0			0
$957$	−10.6008	+	36.3166i	−0.342675	+	1.17395i
$958$		0			0
$959$	20.8315	−	7.58206i	0.672685	−	0.244837i
$960$		0			0
$961$	14.3895	+	81.6067i	0.464176	+	2.63247i
$962$		0			0
$963$	−10.4409	−	2.32328i	−0.336452	−	0.0748667i
$964$		0			0
$965$	−11.2882	+	9.47194i	−0.363380	+	0.304912i
$966$		0			0
$967$	2.90588	−	16.4801i	0.0934468	−	0.529963i	−0.901765	−	0.432226i	$-0.857728\pi$
$967$	2.90588	−	16.4801i	0.0934468	−	0.529963i	0.995212	−	0.0977374i	$-0.0311605\pi$
$968$		0			0
$969$	−0.262247	−	0.0288249i	−0.00842459	−	0.000925989i
$970$		0			0
$971$	23.6212			0.758039			0.379019	−	0.925389i	$-0.376261\pi$
$971$	23.6212			0.758039			0.379019	+	0.925389i	$0.376261\pi$
$972$		0			0
$973$	20.2114			0.647946
$974$		0			0
$975$	66.3838	+	7.29657i	2.12598	+	0.233677i
$976$		0			0
$977$	−0.669050	+	3.79437i	−0.0214048	+	0.121393i	−0.993638	−	0.112622i	$-0.964075\pi$
$977$	−0.669050	+	3.79437i	−0.0214048	+	0.121393i	0.972233	+	0.234014i	$0.0751863\pi$
$978$		0			0
$979$	−40.2134	+	33.7430i	−1.28523	+	1.07843i
$980$		0			0
$981$	−11.0284	−	2.45402i	−0.352109	−	0.0783508i
$982$		0			0
$983$	−5.22375	−	29.6254i	−0.166612	−	0.944903i	−0.947387	−	0.320091i	$-0.896287\pi$
$983$	−5.22375	−	29.6254i	−0.166612	−	0.944903i	0.780775	−	0.624812i	$-0.214824\pi$
$984$		0			0
$985$	−50.4225	+	18.3523i	−1.60660	+	0.584753i
$986$		0			0
$987$	18.5389	−	63.5114i	0.590100	−	2.02159i
$988$		0			0
$989$	2.25608	−	3.90764i	0.0717391	−	0.124256i
$990$		0			0
$991$	−19.9708	−	34.5904i	−0.634393	−	1.09880i	−0.986643	−	0.162896i	$-0.947917\pi$
$991$	−19.9708	−	34.5904i	−0.634393	−	1.09880i	0.352250	−	0.935906i	$-0.385417\pi$
$992$		0			0
$993$	−31.2364	+	20.8537i	−0.991256	+	0.661773i
$994$		0			0
$995$	−29.3912	−	24.6622i	−0.931764	−	0.781843i
$996$		0			0
$997$	−47.8060	−	17.4000i	−1.51403	−	0.551063i	−0.554383	−	0.832262i	$-0.687046\pi$
$997$	−47.8060	−	17.4000i	−1.51403	−	0.551063i	−0.959649	+	0.281199i	$0.909268\pi$
$998$		0			0
$999$	−44.4058	+	38.8504i	−1.40494	+	1.22917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.193.10	yes	60
4.3	odd	2	inner	864.2.y.d.193.1	✓	60
27.7	even	9	inner	864.2.y.d.385.10	yes	60
108.7	odd	18	inner	864.2.y.d.385.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.193.1	✓	60	4.3	odd	2	inner
864.2.y.d.193.10	yes	60	1.1	even	1	trivial
864.2.y.d.385.1	yes	60	108.7	odd	18	inner
864.2.y.d.385.10	yes	60	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72168 + 0.189239i) q^{3} +(0.679279 - 3.85238i) q^{5} +(2.91962 - 2.44985i) q^{7} +(2.92838 + 0.651618i) q^{9} +O(q^{10})\)	\(q+(1.72168 + 0.189239i) q^{3} +(0.679279 - 3.85238i) q^{5} +(2.91962 - 2.44985i) q^{7} +(2.92838 + 0.651618i) q^{9} +(0.633200 + 3.59106i) q^{11} +(-3.51692 + 1.28005i) q^{13} +(1.89852 - 6.50403i) q^{15} +(0.124612 - 0.215834i) q^{17} +(-0.305590 - 0.529297i) q^{19} +(5.49027 - 3.66536i) q^{21} +(2.82720 + 2.37230i) q^{23} +(-9.68095 - 3.52358i) q^{25} +(4.91842 + 1.67604i) q^{27} +(5.62879 + 2.04871i) q^{29} +(-8.17429 - 6.85905i) q^{31} +(0.410602 + 6.30248i) q^{33} +(-7.45453 - 12.9116i) q^{35} +(-5.67746 + 9.83365i) q^{37} +(-6.29725 + 1.53831i) q^{39} +(-5.35669 + 1.94967i) q^{41} +(-0.212301 - 1.20402i) q^{43} +(4.49946 - 10.8386i) q^{45} +(7.67765 - 6.44231i) q^{47} +(1.30687 - 7.41164i) q^{49} +(0.255386 - 0.348016i) q^{51} -4.91781 q^{53} +14.2642 q^{55} +(-0.425965 - 0.969111i) q^{57} +(-0.145128 + 0.823062i) q^{59} +(-1.38093 + 1.15873i) q^{61} +(10.1461 - 5.27162i) q^{63} +(2.54229 + 14.4180i) q^{65} +(-6.96862 + 2.53637i) q^{67} +(4.41861 + 4.61937i) q^{69} +(1.92575 - 3.33550i) q^{71} +(-1.51159 - 2.61815i) q^{73} +(-16.0007 - 7.89849i) q^{75} +(10.6463 + 8.93328i) q^{77} +(14.6114 + 5.31813i) q^{79} +(8.15079 + 3.81637i) q^{81} +(10.7700 + 3.91997i) q^{83} +(-0.746827 - 0.626662i) q^{85} +(9.30329 + 4.59242i) q^{87} +(7.19807 + 12.4674i) q^{89} +(-7.13213 + 12.3532i) q^{91} +(-12.7755 - 13.3560i) q^{93} +(-2.24663 + 0.817708i) q^{95} +(-0.634167 - 3.59654i) q^{97} +(-0.485747 + 10.9286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more