LMFDB - Embedded newform 216.3.p.b.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.564251 + 1.91875i) q^{2} +(-3.36324 + 2.16532i) q^{4} +(-5.15803 + 2.97799i) q^{5} +(-4.09037 - 2.36158i) q^{7} +(-6.05243 - 5.23145i) q^{8} +O(q^{10})$	\(q+(0.564251 + 1.91875i) q^{2} +(-3.36324 + 2.16532i) q^{4} +(-5.15803 + 2.97799i) q^{5} +(-4.09037 - 2.36158i) q^{7} +(-6.05243 - 5.23145i) q^{8} +(-8.62446 - 8.21666i) q^{10} +(6.94921 - 12.0364i) q^{11} +(4.03163 - 2.32766i) q^{13} +(2.22329 - 9.18095i) q^{14} +(6.62277 - 14.5650i) q^{16} -21.5221 q^{17} +3.83672 q^{19} +(10.8994 - 21.1845i) q^{20} +(27.0160 + 6.54228i) q^{22} +(-30.0178 + 17.3308i) q^{23} +(5.23684 - 9.07047i) q^{25} +(6.74106 + 6.42232i) q^{26} +(18.8705 - 0.914414i) q^{28} +(-39.3950 - 22.7447i) q^{29} +(-31.8750 + 18.4030i) q^{31} +(31.6836 + 4.48916i) q^{32} +(-12.1439 - 41.2956i) q^{34} +28.1310 q^{35} +36.0613i q^{37} +(2.16488 + 7.36173i) q^{38} +(46.7978 + 8.95988i) q^{40} +(10.2409 + 17.7377i) q^{41} +(3.50522 - 6.07122i) q^{43} +(2.69077 + 55.5285i) q^{44} +(-50.1912 - 47.8179i) q^{46} +(53.1514 + 30.6870i) q^{47} +(-13.3459 - 23.1158i) q^{49} +(20.3589 + 4.93018i) q^{50} +(-8.51920 + 16.5582i) q^{52} -58.7545i q^{53} +82.7787i q^{55} +(12.4022 + 35.6919i) q^{56} +(21.4128 - 88.4230i) q^{58} +(-11.0410 - 19.1235i) q^{59} +(-47.1047 - 27.1959i) q^{61} +(-53.2964 - 50.7763i) q^{62} +(9.26389 + 63.3260i) q^{64} +(-13.8635 + 24.0123i) q^{65} +(56.9612 + 98.6596i) q^{67} +(72.3839 - 46.6022i) q^{68} +(15.8730 + 53.9765i) q^{70} -8.30318i q^{71} -114.051 q^{73} +(-69.1928 + 20.3476i) q^{74} +(-12.9038 + 8.30773i) q^{76} +(-56.8497 + 32.8222i) q^{77} +(47.5352 + 27.4445i) q^{79} +(9.21392 + 94.8492i) q^{80} +(-28.2559 + 29.6582i) q^{82} +(-15.6347 + 27.0802i) q^{83} +(111.011 - 64.0925i) q^{85} +(13.6270 + 3.29996i) q^{86} +(-105.027 + 36.4950i) q^{88} -47.7407 q^{89} -21.9878 q^{91} +(63.4304 - 123.286i) q^{92} +(-28.8900 + 119.300i) q^{94} +(-19.7899 + 11.4257i) q^{95} +(-28.7623 + 49.8177i) q^{97} +(36.8231 - 38.6506i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.564251	+	1.91875i	0.282126	+	0.959377i
$2$	0.564251	+	1.91875i	0.282126	+	0.959377i
$3$		0			0
$3$		0			0
$4$	−3.36324	+	2.16532i	−0.840810	+	0.541330i
$5$	−5.15803	+	2.97799i	−1.03161	+	0.595598i	−0.917444	−	0.397864i	$-0.869751\pi$
$5$	−5.15803	+	2.97799i	−1.03161	+	0.595598i	−0.114161	+	0.993462i	$0.536418\pi$
$6$		0			0
$7$	−4.09037	−	2.36158i	−0.584339	−	0.337368i	0.178517	−	0.983937i	$-0.442870\pi$
$7$	−4.09037	−	2.36158i	−0.584339	−	0.337368i	−0.762856	+	0.646569i	$0.776203\pi$
$8$	−6.05243	−	5.23145i	−0.756554	−	0.653931i
$9$		0			0
$10$	−8.62446	−	8.21666i	−0.862446	−	0.821666i
$11$	6.94921	−	12.0364i	0.631746	−	1.09422i	−0.355448	−	0.934696i	$-0.615672\pi$
$11$	6.94921	−	12.0364i	0.631746	−	1.09422i	0.987195	−	0.159521i	$-0.0509948\pi$
$12$		0			0
$13$	4.03163	−	2.32766i	0.310125	−	0.179051i	−0.336857	−	0.941556i	$-0.609364\pi$
$13$	4.03163	−	2.32766i	0.310125	−	0.179051i	0.646982	+	0.762505i	$0.276031\pi$
$14$	2.22329	−	9.18095i	0.158806	−	0.655782i
$15$		0			0
$16$	6.62277	−	14.5650i	0.413923	−	0.910312i
$17$	−21.5221			−1.26600			−0.633002	−	0.774150i	$-0.718178\pi$
$17$	−21.5221			−1.26600			−0.633002	+	0.774150i	$0.718178\pi$
$18$		0			0
$19$	3.83672			0.201933			0.100966	−	0.994890i	$-0.467807\pi$
$19$	3.83672			0.201933			0.100966	+	0.994890i	$0.467807\pi$
$20$	10.8994	−	21.1845i	0.544969	−	1.05922i
$21$		0			0
$22$	27.0160	+	6.54228i	1.22800	+	0.297376i
$23$	−30.0178	+	17.3308i	−1.30512	+	0.753513i	−0.981278	−	0.192597i	$-0.938309\pi$
$23$	−30.0178	+	17.3308i	−1.30512	+	0.753513i	−0.323845	+	0.946110i	$0.604976\pi$
$24$		0			0
$25$	5.23684	−	9.07047i	0.209474	−	0.362819i
$26$	6.74106	+	6.42232i	0.259272	+	0.247012i
$27$		0			0
$28$	18.8705	−	0.914414i	0.673946	−	0.0326577i
$29$	−39.3950	−	22.7447i	−1.35845	−	0.784300i	−0.369033	−	0.929416i	$-0.620311\pi$
$29$	−39.3950	−	22.7447i	−1.35845	−	0.784300i	−0.989415	+	0.145116i	$0.953644\pi$
$30$		0			0
$31$	−31.8750	+	18.4030i	−1.02822	+	0.593646i	−0.916476	−	0.400091i	$-0.868979\pi$
$31$	−31.8750	+	18.4030i	−1.02822	+	0.593646i	−0.111749	+	0.993736i	$0.535645\pi$
$32$	31.6836	+	4.48916i	0.990111	+	0.140286i
$33$		0			0
$34$	−12.1439	−	41.2956i	−0.357172	−	1.21458i
$35$	28.1310			0.803743
$36$		0			0
$37$			36.0613i			0.974630i	0.873226	+	0.487315i	$0.162024\pi$
$37$			36.0613i			0.974630i	−0.873226	+	0.487315i	$0.837976\pi$
$38$	2.16488	+	7.36173i	0.0569704	+	0.193730i
$39$		0			0
$40$	46.7978	+	8.95988i	1.16995	+	0.223997i
$41$	10.2409	+	17.7377i	0.249777	+	0.432627i	0.963464	−	0.267838i	$-0.0863093\pi$
$41$	10.2409	+	17.7377i	0.249777	+	0.432627i	−0.713687	+	0.700465i	$0.752976\pi$
$42$		0			0
$43$	3.50522	−	6.07122i	0.0815167	−	0.141191i	−0.822385	−	0.568932i	$-0.807357\pi$
$43$	3.50522	−	6.07122i	0.0815167	−	0.141191i	0.903902	+	0.427740i	$0.140690\pi$
$44$	2.69077	+	55.5285i	0.0611538	+	1.26201i
$45$		0			0
$46$	−50.1912	−	47.8179i	−1.09111	−	1.03952i
$47$	53.1514	+	30.6870i	1.13088	+	0.652914i	0.944156	−	0.329499i	$-0.106880\pi$
$47$	53.1514	+	30.6870i	1.13088	+	0.652914i	0.186724	+	0.982412i	$0.440213\pi$
$48$		0			0
$49$	−13.3459	−	23.1158i	−0.272365	−	0.471750i
$50$	20.3589	+	4.93018i	0.407178	+	0.0986037i
$51$		0			0
$52$	−8.51920	+	16.5582i	−0.163831	+	0.318428i
$53$		−	58.7545i		−	1.10858i	−0.832325	−	0.554288i	$-0.812991\pi$
$53$		−	58.7545i		−	1.10858i	0.832325	−	0.554288i	$-0.187009\pi$
$54$		0			0
$55$			82.7787i			1.50507i
$56$	12.4022	+	35.6919i	0.221468	+	0.637355i
$57$		0			0
$58$	21.4128	−	88.4230i	0.369187	−	1.52454i
$59$	−11.0410	−	19.1235i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$59$	−11.0410	−	19.1235i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$60$		0			0
$61$	−47.1047	−	27.1959i	−0.772209	−	0.445835i	0.0614532	−	0.998110i	$-0.480427\pi$
$61$	−47.1047	−	27.1959i	−0.772209	−	0.445835i	−0.833662	+	0.552275i	$0.813760\pi$
$62$	−53.2964	−	50.7763i	−0.859619	−	0.818973i
$63$		0			0
$64$	9.26389	+	63.3260i	0.144748	+	0.989469i
$65$	−13.8635	+	24.0123i	−0.213285	+	0.369420i
$66$		0			0
$67$	56.9612	+	98.6596i	0.850167	+	1.47253i	0.881058	+	0.473009i	$0.156832\pi$
$67$	56.9612	+	98.6596i	0.850167	+	1.47253i	−0.0308908	+	0.999523i	$0.509834\pi$
$68$	72.3839	−	46.6022i	1.06447	−	0.685326i
$69$		0			0
$70$	15.8730	+	53.9765i	0.226757	+	0.771093i
$71$		−	8.30318i		−	0.116946i	−0.998289	−	0.0584731i	$-0.981377\pi$
$71$		−	8.30318i		−	0.116946i	0.998289	−	0.0584731i	$-0.0186232\pi$
$72$		0			0
$73$	−114.051			−1.56234			−0.781172	−	0.624316i	$-0.785378\pi$
$73$	−114.051			−1.56234			−0.781172	+	0.624316i	$0.785378\pi$
$74$	−69.1928	+	20.3476i	−0.935038	+	0.274968i
$75$		0			0
$76$	−12.9038	+	8.30773i	−0.169787	+	0.109312i
$77$	−56.8497	+	32.8222i	−0.738308	+	0.426262i
$78$		0			0
$79$	47.5352	+	27.4445i	0.601712	+	0.347399i	0.769715	−	0.638388i	$-0.220398\pi$
$79$	47.5352	+	27.4445i	0.601712	+	0.347399i	−0.168003	+	0.985787i	$0.553732\pi$
$80$	9.21392	+	94.8492i	0.115174	+	1.18561i
$81$		0			0
$82$	−28.2559	+	29.6582i	−0.344584	+	0.361686i
$83$	−15.6347	+	27.0802i	−0.188370	+	0.326267i	−0.944707	−	0.327916i	$-0.893654\pi$
$83$	−15.6347	+	27.0802i	−0.188370	+	0.326267i	0.756337	+	0.654183i	$0.226987\pi$
$84$		0			0
$85$	111.011	−	64.0925i	1.30602	−	0.754029i
$86$	13.6270	+	3.29996i	0.158454	+	0.0383717i
$87$		0			0
$88$	−105.027	+	36.4950i	−1.19349	+	0.414715i
$89$	−47.7407			−0.536413			−0.268206	−	0.963361i	$-0.586431\pi$
$89$	−47.7407			−0.536413			−0.268206	+	0.963361i	$0.586431\pi$
$90$		0			0
$91$	−21.9878			−0.241624
$92$	63.4304	−	123.286i	0.689461	−	1.34006i
$93$		0			0
$94$	−28.8900	+	119.300i	−0.307340	+	1.26914i
$95$	−19.7899	+	11.4257i	−0.208315	+	0.120271i
$96$		0			0
$97$	−28.7623	+	49.8177i	−0.296518	+	0.513585i	−0.975337	−	0.220721i	$-0.929159\pi$
$97$	−28.7623	+	49.8177i	−0.296518	+	0.513585i	0.678819	+	0.734306i	$0.262492\pi$
$98$	36.8231	−	38.6506i	0.375745	−	0.394394i
$99$		0			0
$100$	2.02773	+	41.8456i	0.0202773	+	0.418456i
$101$	114.007	+	65.8222i	1.12879	+	0.651705i	0.943629	−	0.331004i	$-0.107387\pi$
$101$	114.007	+	65.8222i	1.12879	+	0.651705i	0.185157	+	0.982709i	$0.440721\pi$
$102$		0			0
$103$	−37.1176	+	21.4299i	−0.360365	+	0.208057i	−0.669241	−	0.743045i	$-0.733381\pi$
$103$	−37.1176	+	21.4299i	−0.360365	+	0.208057i	0.308876	+	0.951102i	$0.400047\pi$
$104$	−36.5782	−	7.00324i	−0.351713	−	0.0673388i
$105$		0			0
$106$	112.735	−	33.1523i	1.06354	−	0.312758i
$107$	91.6085			0.856154			0.428077	−	0.903742i	$-0.359191\pi$
$107$	91.6085			0.856154			0.428077	+	0.903742i	$0.359191\pi$
$108$		0			0
$109$		−	152.712i		−	1.40102i	−0.713641	−	0.700512i	$-0.752955\pi$
$109$		−	152.712i		−	1.40102i	0.713641	−	0.700512i	$-0.247045\pi$
$110$	−158.832	+	46.7080i	−1.44393	+	0.424618i
$111$		0			0
$112$	−61.4860	+	43.9360i	−0.548982	+	0.392286i
$113$	−8.45762	−	14.6490i	−0.0748462	−	0.129637i	0.826173	−	0.563416i	$-0.190513\pi$
$113$	−8.45762	−	14.6490i	−0.0748462	−	0.129637i	−0.901019	+	0.433779i	$0.857180\pi$
$114$		0			0
$115$	103.222	−	178.786i	0.897582	−	1.55466i
$116$	181.744	−	8.80686i	1.56676	−	0.0759212i
$117$		0			0
$118$	30.4634	−	31.9754i	0.258165	−	0.270978i
$119$	88.0333	+	50.8261i	0.739776	+	0.427110i
$120$		0			0
$121$	−36.0830	−	62.4976i	−0.298206	−	0.516509i
$122$	25.6034	−	105.728i	0.209864	−	0.866621i
$123$		0			0
$124$	67.3547	−	130.913i	0.543183	−	1.05575i
$125$		−	86.5185i		−	0.692148i
$126$		0			0
$127$		−	144.231i		−	1.13568i	−0.823140	−	0.567839i	$-0.807780\pi$
$127$		−	144.231i		−	1.13568i	0.823140	−	0.567839i	$-0.192220\pi$
$128$	−116.280	+	53.5069i	−0.908437	+	0.418023i
$129$		0			0
$130$	−53.8962	−	13.0517i	−0.414586	−	0.100398i
$131$	−8.71188	−	15.0894i	−0.0665029	−	0.115186i	0.830857	−	0.556486i	$-0.187851\pi$
$131$	−8.71188	−	15.0894i	−0.0665029	−	0.115186i	−0.897360	+	0.441300i	$0.854518\pi$
$132$		0			0
$133$	−15.6936	−	9.06072i	−0.117997	−	0.0681257i
$134$	−157.163	+	164.963i	−1.17286	+	1.23107i
$135$		0			0
$136$	130.261	+	112.592i	0.957801	+	0.827879i
$137$	−46.5748	+	80.6699i	−0.339962	+	0.588831i	−0.984425	−	0.175804i	$-0.943748\pi$
$137$	−46.5748	+	80.6699i	−0.339962	+	0.588831i	0.644463	+	0.764635i	$0.277081\pi$
$138$		0			0
$139$	22.0873	+	38.2563i	0.158902	+	0.275226i	0.934473	−	0.356034i	$-0.115871\pi$
$139$	22.0873	+	38.2563i	0.158902	+	0.275226i	−0.775571	+	0.631260i	$0.782538\pi$
$140$	−94.6114	+	60.9127i	−0.675796	+	0.435091i
$141$		0			0
$142$	15.9318	−	4.68508i	0.112196	−	0.0329935i
$143$		−	64.7016i		−	0.452459i
$144$		0			0
$145$	270.934			1.86851
$146$	−64.3535	−	218.836i	−0.440777	−	1.49888i
$147$		0			0
$148$	−78.0843	−	121.283i	−0.527596	−	0.819478i
$149$	27.3905	−	15.8139i	0.183829	−	0.106134i	−0.405261	−	0.914201i	$-0.632820\pi$
$149$	27.3905	−	15.8139i	0.183829	−	0.106134i	0.589090	+	0.808067i	$0.299486\pi$
$150$		0			0
$151$	−15.3552	−	8.86531i	−0.101690	−	0.0587106i	0.448293	−	0.893887i	$-0.352032\pi$
$151$	−15.3552	−	8.86531i	−0.101690	−	0.0587106i	−0.549982	+	0.835176i	$0.685366\pi$
$152$	−23.2215	−	20.0716i	−0.152773	−	0.132050i
$153$		0			0
$154$	−95.0553	−	90.5607i	−0.617242	−	0.588056i
$155$	109.608	−	189.847i	0.707148	−	1.22482i
$156$		0			0
$157$	76.4244	−	44.1236i	0.486780	−	0.281042i	−0.236458	−	0.971642i	$-0.575987\pi$
$157$	76.4244	−	44.1236i	0.486780	−	0.281042i	0.723237	+	0.690599i	$0.242653\pi$
$158$	−25.8374	+	106.694i	−0.163528	+	0.675279i
$159$		0			0
$160$	−176.793	+	71.1980i	−1.10496	+	0.444988i
$161$	163.712			1.01685
$162$		0			0
$163$	33.8559			0.207705			0.103852	−	0.994593i	$-0.466883\pi$
$163$	33.8559			0.207705			0.103852	+	0.994593i	$0.466883\pi$
$164$	−72.8503	−	37.4814i	−0.444209	−	0.228545i
$165$		0			0
$166$	−60.7821	−	14.7192i	−0.366157	−	0.0886699i
$167$	50.0218	−	28.8801i	0.299531	−	0.172935i	−0.342701	−	0.939445i	$-0.611342\pi$
$167$	50.0218	−	28.8801i	0.299531	−	0.172935i	0.642232	+	0.766510i	$0.278008\pi$
$168$		0			0
$169$	−73.6640	+	127.590i	−0.435882	+	0.754969i
$170$	185.616	+	176.839i	1.09186	+	1.04023i
$171$		0			0
$172$	1.35724	+	28.0089i	0.00789092	+	0.162842i
$173$	15.6471	+	9.03387i	0.0904458	+	0.0522189i	0.544541	−	0.838734i	$-0.316704\pi$
$173$	15.6471	+	9.03387i	0.0904458	+	0.0522189i	−0.454095	+	0.890953i	$0.650037\pi$
$174$		0			0
$175$	−42.8413	+	24.7344i	−0.244807	+	0.141340i
$176$	−129.287	−	180.929i	−0.734584	−	1.02801i
$177$		0			0
$178$	−26.9378	−	91.6028i	−0.151336	−	0.514622i
$179$	−264.511			−1.47771			−0.738857	−	0.673862i	$-0.764634\pi$
$179$	−264.511			−1.47771			−0.738857	+	0.673862i	$0.764634\pi$
$180$		0			0
$181$			185.479i			1.02475i	0.858762	+	0.512374i	$0.171234\pi$
$181$			185.479i			1.02475i	−0.858762	+	0.512374i	$0.828766\pi$
$182$	−12.4067	−	42.1892i	−0.0681684	−	0.231809i
$183$		0			0
$184$	272.346	+	52.1432i	1.48014	+	0.283387i
$185$	−107.390	−	186.005i	−0.580487	−	1.00543i
$186$		0			0
$187$	−149.561	+	259.048i	−0.799793	+	1.38528i
$188$	−245.208	+	11.8821i	−1.30430	+	0.0632028i
$189$		0			0
$190$	−33.0896	−	31.5250i	−0.174156	−	0.165921i
$191$	79.8243	+	46.0866i	0.417928	+	0.241291i	0.694191	−	0.719791i	$-0.255763\pi$
$191$	79.8243	+	46.0866i	0.417928	+	0.241291i	−0.276262	+	0.961082i	$0.589096\pi$
$192$		0			0
$193$	−135.169	−	234.120i	−0.700359	−	1.21306i	−0.968341	−	0.249633i	$-0.919690\pi$
$193$	−135.169	−	234.120i	−0.700359	−	1.21306i	0.267982	−	0.963424i	$-0.413643\pi$
$194$	−111.817	−	27.0780i	−0.576377	−	0.139578i
$195$		0			0
$196$	94.9385	+	48.8457i	0.484380	+	0.249213i
$197$		−	140.218i		−	0.711765i	−0.934531	−	0.355883i	$-0.884180\pi$
$197$		−	140.218i		−	0.711765i	0.934531	−	0.355883i	$-0.115820\pi$
$198$		0			0
$199$		−	272.949i		−	1.37160i	−0.727788	−	0.685802i	$-0.759452\pi$
$199$		−	272.949i		−	1.37160i	0.727788	−	0.685802i	$-0.240548\pi$
$200$	−79.1473	+	27.5022i	−0.395737	+	0.137511i
$201$		0			0
$202$	−61.9678	+	255.893i	−0.306771	+	1.26679i
$203$	107.427	+	186.069i	0.529196	+	0.916594i
$204$		0			0
$205$	−105.645	−	60.9944i	−0.515343	−	0.297533i
$206$	−62.0623	−	59.1278i	−0.301273	−	0.287028i
$207$		0			0
$208$	−7.20180	−	74.1361i	−0.0346240	−	0.356424i
$209$	26.6622	−	46.1802i	0.127570	−	0.220958i
$210$		0			0
$211$	−64.2535	−	111.290i	−0.304519	−	0.527443i	0.672635	−	0.739974i	$-0.265162\pi$
$211$	−64.2535	−	111.290i	−0.304519	−	0.527443i	−0.977154	+	0.212532i	$0.931829\pi$
$212$	127.222	+	197.606i	0.600105	+	0.932102i
$213$		0			0
$214$	51.6902	+	175.774i	0.241543	+	0.821375i
$215$			41.7540i			0.194205i
$216$		0			0
$217$	173.841			0.801109
$218$	293.016	−	86.1677i	1.34411	−	0.395265i
$219$		0			0
$220$	−179.242	−	278.405i	−0.814738	−	1.26548i
$221$	−86.7689	+	50.0961i	−0.392620	+	0.226679i
$222$		0			0
$223$	251.240	+	145.054i	1.12664	+	0.650465i	0.943087	−	0.332546i	$-0.107908\pi$
$223$	251.240	+	145.054i	1.12664	+	0.650465i	0.183551	+	0.983010i	$0.441241\pi$
$224$	−118.996	−	93.1855i	−0.531232	−	0.416007i
$225$		0			0
$226$	23.3357	−	24.4938i	0.103255	−	0.108380i
$227$	−132.263	+	229.086i	−0.582656	+	1.00919i	0.412507	+	0.910954i	$0.364653\pi$
$227$	−132.263	+	229.086i	−0.582656	+	1.00919i	−0.995163	+	0.0982354i	$0.968680\pi$
$228$		0			0
$229$	−143.260	+	82.7110i	−0.625588	+	0.361183i	−0.779041	−	0.626973i	$-0.784294\pi$
$229$	−143.260	+	82.7110i	−0.625588	+	0.361183i	0.153454	+	0.988156i	$0.450960\pi$
$230$	401.289	+	97.1775i	1.74473	+	0.422511i
$231$		0			0
$232$	119.448	+	343.754i	0.514861	+	1.48170i
$233$	−163.520			−0.701803			−0.350902	−	0.936412i	$-0.614125\pi$
$233$	−163.520			−0.701803			−0.350902	+	0.936412i	$0.614125\pi$
$234$		0			0
$235$	−365.542			−1.55550
$236$	78.5419	+	40.4097i	0.332805	+	0.171228i
$237$		0			0
$238$	−47.8498	+	197.593i	−0.201050	+	0.830223i
$239$	−79.7160	+	46.0240i	−0.333540	+	0.192569i	−0.657412	−	0.753532i	$-0.728349\pi$
$239$	−79.7160	+	46.0240i	−0.333540	+	0.192569i	0.323872	+	0.946101i	$0.395015\pi$
$240$		0			0
$241$	16.0255	−	27.7570i	0.0664958	−	0.115174i	−0.830861	−	0.556480i	$-0.812151\pi$
$241$	16.0255	−	27.7570i	0.0664958	−	0.115174i	0.897357	+	0.441306i	$0.145485\pi$
$242$	99.5576	−	104.499i	0.411395	−	0.431813i
$243$		0			0
$244$	217.312	−	10.5304i	0.890625	−	0.0431573i
$245$	137.677	+	79.4879i	0.561947	+	0.324440i
$246$		0			0
$247$	15.4682	−	8.93058i	0.0626244	−	0.0361562i
$248$	289.196	+	55.3692i	1.16611	+	0.223263i
$249$		0			0
$250$	166.008	−	48.8182i	0.664031	−	0.195273i
$251$	108.956			0.434088			0.217044	−	0.976162i	$-0.430359\pi$
$251$	108.956			0.434088			0.217044	+	0.976162i	$0.430359\pi$
$252$		0			0
$253$			481.741i			1.90412i
$254$	276.744	−	81.3826i	1.08954	−	0.320404i
$255$		0			0
$256$	−168.278	−	192.921i	−0.657335	−	0.753599i
$257$	244.729	+	423.883i	0.952252	+	1.64935i	0.740535	+	0.672018i	$0.234572\pi$
$257$	244.729	+	423.883i	0.952252	+	1.64935i	0.211717	+	0.977331i	$0.432094\pi$
$258$		0			0
$259$	85.1616	−	147.504i	0.328809	−	0.569514i
$260$	−5.36801	−	110.778i	−0.0206462	−	0.426069i
$261$		0			0
$262$	24.0372	−	25.2302i	0.0917451	−	0.0962984i
$263$	−341.950	−	197.425i	−1.30019	−	0.750666i	−0.319755	−	0.947500i	$-0.603600\pi$
$263$	−341.950	−	197.425i	−1.30019	−	0.750666i	−0.980437	+	0.196835i	$0.936934\pi$
$264$		0			0
$265$	174.970	+	303.057i	0.660265	+	1.14361i
$266$	8.53015	−	35.2247i	0.0320682	−	0.132424i
$267$		0			0
$268$	−405.204	−	208.477i	−1.51195	−	0.777899i
$269$			359.184i			1.33526i	0.744494	+	0.667629i	$0.232691\pi$
$269$			359.184i			1.33526i	−0.744494	+	0.667629i	$0.767309\pi$
$270$		0			0
$271$		−	223.217i		−	0.823680i	−0.911256	−	0.411840i	$-0.864886\pi$
$271$		−	223.217i		−	0.823680i	0.911256	−	0.411840i	$-0.135114\pi$
$272$	−142.536	+	313.469i	−0.524029	+	1.15246i
$273$		0			0
$274$	−181.066	−	43.8475i	−0.660824	−	0.160027i
$275$	−72.7838	−	126.065i	−0.264668	−	0.458419i
$276$		0			0
$277$	111.426	+	64.3319i	0.402260	+	0.232245i	0.687459	−	0.726223i	$-0.258726\pi$
$277$	111.426	+	64.3319i	0.402260	+	0.232245i	−0.285198	+	0.958468i	$0.592060\pi$
$278$	−60.9418	+	63.9663i	−0.219215	+	0.230095i
$279$		0			0
$280$	−170.261	−	147.166i	−0.608075	−	0.525593i
$281$	169.623	−	293.796i	0.603642	−	1.04554i	−0.388622	−	0.921397i	$-0.627049\pi$
$281$	169.623	−	293.796i	0.603642	−	1.04554i	0.992264	−	0.124142i	$-0.0396178\pi$
$282$		0			0
$283$	8.66907	+	15.0153i	0.0306327	+	0.0530575i	0.880935	−	0.473237i	$-0.156914\pi$
$283$	8.66907	+	15.0153i	0.0306327	+	0.0530575i	−0.850303	+	0.526294i	$0.823581\pi$
$284$	17.9790	+	27.9256i	0.0633065	+	0.0983295i
$285$		0			0
$286$	124.146	−	36.5080i	0.434079	−	0.127650i
$287$		−	96.7384i		−	0.337068i
$288$		0			0
$289$	174.199			0.602766
$290$	152.875	+	519.856i	0.527155	+	1.79261i
$291$		0			0
$292$	383.581	−	246.957i	1.31363	−	0.845744i
$293$	−136.021	+	78.5318i	−0.464235	+	0.268026i	−0.713824	−	0.700326i	$-0.753038\pi$
$293$	−136.021	+	78.5318i	−0.464235	+	0.268026i	0.249588	+	0.968352i	$0.419705\pi$
$294$		0			0
$295$	113.899	+	65.7597i	0.386099	+	0.222914i
$296$	188.653	−	218.259i	0.637341	−	0.737360i
$297$		0			0
$298$	45.7982	+	43.6327i	0.153685	+	0.146418i
$299$	−80.6804	+	139.743i	−0.269834	+	0.467367i
$300$		0			0
$301$	−28.6753	+	16.5557i	−0.0952668	+	0.0550023i
$302$	8.34618	−	34.4651i	0.0276364	−	0.114123i
$303$		0			0
$304$	25.4097	−	55.8818i	0.0835846	−	0.183822i
$305$	323.957			1.06215
$306$		0			0
$307$	−41.8176			−0.136214			−0.0681069	−	0.997678i	$-0.521696\pi$
$307$	−41.8176			−0.136214			−0.0681069	+	0.997678i	$0.521696\pi$
$308$	120.129	−	233.487i	0.390028	−	0.758074i
$309$		0			0
$310$	426.116	+	103.190i	1.37457	+	0.332870i
$311$	−40.6974	+	23.4966i	−0.130860	+	0.0755519i	−0.564001	−	0.825774i	$-0.690739\pi$
$311$	−40.6974	+	23.4966i	−0.130860	+	0.0755519i	0.433141	+	0.901326i	$0.357405\pi$
$312$		0			0
$313$	−183.527	+	317.878i	−0.586349	+	1.01559i	0.408357	+	0.912822i	$0.366102\pi$
$313$	−183.527	+	317.878i	−0.586349	+	1.01559i	−0.994706	+	0.102763i	$0.967232\pi$
$314$	127.785	+	121.743i	0.406959	+	0.387716i
$315$		0			0
$316$	−219.299	+	10.6266i	−0.693983	+	0.0336286i
$317$	−67.3034	−	38.8576i	−0.212313	−	0.122579i	0.390073	−	0.920784i	$-0.372450\pi$
$317$	−67.3034	−	38.8576i	−0.212313	−	0.122579i	−0.602386	+	0.798205i	$0.705783\pi$
$318$		0			0
$319$	−547.528	+	316.115i	−1.71639	+	0.990957i
$320$	−236.367	−	299.049i	−0.738648	−	0.934530i
$321$		0			0
$322$	92.3748	+	314.124i	0.286878	+	0.975539i
$323$	−82.5742			−0.255648
$324$		0			0
$325$		−	48.7583i		−	0.150026i
$326$	19.1032	+	64.9611i	0.0585988	+	0.199267i
$327$		0			0
$328$	30.8117	−	160.931i	0.0939381	−	0.490643i
$329$	−144.939	−	251.042i	−0.440545	−	0.763046i
$330$		0			0
$331$	251.153	−	435.010i	0.758771	−	1.31423i	−0.184707	−	0.982794i	$-0.559134\pi$
$331$	251.153	−	435.010i	0.758771	−	1.31423i	0.943478	−	0.331436i	$-0.107533\pi$
$332$	−6.05384	−	124.931i	−0.0182345	−	0.376299i
$333$		0			0
$334$	83.6386	+	79.6839i	0.250415	+	0.238574i
$335$	−587.615	−	339.259i	−1.75407	−	1.01271i
$336$		0			0
$337$	23.0951	+	40.0018i	0.0685314	+	0.118700i	0.898255	−	0.439475i	$-0.144835\pi$
$337$	23.0951	+	40.0018i	0.0685314	+	0.118700i	−0.829724	+	0.558174i	$0.811502\pi$
$338$	−286.379	−	69.3504i	−0.847274	−	0.205179i
$339$		0			0
$340$	−234.577	+	455.934i	−0.689934	+	1.34098i
$341$			511.546i			1.50013i
$342$		0			0
$343$			357.504i			1.04229i
$344$	−52.9764	+	18.4083i	−0.154001	+	0.0535124i
$345$		0			0
$346$	−8.50487	+	35.1204i	−0.0245805	+	0.101504i
$347$	−127.082	−	220.112i	−0.366230	−	0.634329i	0.622743	−	0.782427i	$-0.286018\pi$
$347$	−127.082	−	220.112i	−0.366230	−	0.634329i	−0.988973	+	0.148097i	$0.952685\pi$
$348$		0			0
$349$	−213.501	−	123.265i	−0.611750	−	0.353194i	0.161900	−	0.986807i	$-0.448238\pi$
$349$	−213.501	−	123.265i	−0.611750	−	0.353194i	−0.773650	+	0.633613i	$0.781571\pi$
$350$	−71.6325	−	68.2454i	−0.204664	−	0.194987i
$351$		0			0
$352$	274.209	−	350.159i	0.779002	−	0.994770i
$353$	76.3516	−	132.245i	0.216293	−	0.374631i	−0.737379	−	0.675480i	$-0.763937\pi$
$353$	76.3516	−	132.245i	0.216293	−	0.374631i	0.953672	+	0.300849i	$0.0972699\pi$
$354$		0			0
$355$	24.7268	+	42.8280i	0.0696529	+	0.120642i
$356$	160.564	−	103.374i	0.451021	−	0.290376i
$357$		0			0
$358$	−149.251	−	507.532i	−0.416901	−	1.41769i
$359$		−	343.066i		−	0.955615i	−0.878465	−	0.477807i	$-0.841432\pi$
$359$		−	343.066i		−	0.955615i	0.878465	−	0.477807i	$-0.158568\pi$
$360$		0			0
$361$	−346.280			−0.959223
$362$	−355.889	+	104.657i	−0.983120	+	0.289108i
$363$		0			0
$364$	73.9503	−	47.6106i	0.203160	−	0.130798i
$365$	588.279	−	339.643i	1.61172	−	0.930529i
$366$		0			0
$367$	−35.7464	−	20.6382i	−0.0974016	−	0.0562348i	0.450508	−	0.892772i	$-0.351243\pi$
$367$	−35.7464	−	20.6382i	−0.0974016	−	0.0562348i	−0.547910	+	0.836538i	$0.684576\pi$
$368$	53.6216	+	551.987i	0.145711	+	1.49997i
$369$		0			0
$370$	296.303	−	311.009i	0.800820	−	0.840565i
$371$	−138.753	+	240.328i	−0.373998	+	0.647784i
$372$		0			0
$373$	−93.5900	+	54.0342i	−0.250911	+	0.144864i	−0.620182	−	0.784458i	$-0.712941\pi$
$373$	−93.5900	+	54.0342i	−0.250911	+	0.144864i	0.369270	+	0.929322i	$0.379608\pi$
$374$	−581.439	−	140.803i	−1.55465	−	0.376480i
$375$		0			0
$376$	−161.158	−	463.789i	−0.428611	−	1.23348i
$377$	−211.768			−0.561718
$378$		0			0
$379$	−290.232			−0.765783			−0.382891	−	0.923793i	$-0.625072\pi$
$379$	−290.232			−0.765783			−0.382891	+	0.923793i	$0.625072\pi$
$380$	41.8179	−	81.2789i	0.110047	−	0.213892i
$381$		0			0
$382$	−43.3879	+	179.168i	−0.113581	+	0.469025i
$383$	39.2004	−	22.6324i	0.102351	−	0.0590924i	−0.447951	−	0.894058i	$-0.647846\pi$
$383$	39.2004	−	22.6324i	0.102351	−	0.0590924i	0.550302	+	0.834966i	$0.314513\pi$
$384$		0			0
$385$	195.488	−	338.596i	0.507762	−	0.879469i
$386$	372.949	−	391.459i	0.966190	−	1.01414i
$387$		0			0
$388$	−11.1369	−	229.829i	−0.0287033	−	0.592342i
$389$	−473.733	−	273.510i	−1.21782	−	0.703110i	−0.253371	−	0.967369i	$-0.581539\pi$
$389$	−473.733	−	273.510i	−1.21782	−	0.703110i	−0.964452	+	0.264259i	$0.914873\pi$
$390$		0			0
$391$	646.046	−	372.995i	1.65229	−	0.953951i
$392$	−40.1538	+	209.725i	−0.102433	+	0.535013i
$393$		0			0
$394$	269.043	−	79.1180i	0.682851	−	0.200807i
$395$	−326.918			−0.827639
$396$		0			0
$397$			360.883i			0.909026i	0.890740	+	0.454513i	$0.150187\pi$
$397$			360.883i			0.909026i	−0.890740	+	0.454513i	$0.849813\pi$
$398$	523.723	−	154.012i	1.31589	−	0.386965i
$399$		0			0
$400$	−97.4289	−	136.346i	−0.243572	−	0.340865i
$401$	−64.5497	−	111.803i	−0.160972	−	0.278812i	0.774246	−	0.632885i	$-0.218130\pi$
$401$	−64.5497	−	111.803i	−0.160972	−	0.278812i	−0.935218	+	0.354074i	$0.884796\pi$
$402$		0			0
$403$	−85.6720	+	148.388i	−0.212585	+	0.368209i
$404$	−525.961	+	25.4867i	−1.30188	+	0.0630858i
$405$		0			0
$406$	−296.404	+	311.115i	−0.730060	+	0.766294i
$407$	434.047	+	250.597i	1.06646	+	0.615718i
$408$		0			0
$409$	−201.124	−	348.356i	−0.491745	−	0.851727i	0.508210	−	0.861233i	$-0.330307\pi$
$409$	−201.124	−	348.356i	−0.491745	−	0.851727i	−0.999955	+	0.00950593i	$0.996974\pi$
$410$	57.4227	−	237.124i	0.140055	−	0.578350i
$411$		0			0
$412$	78.4329	−	152.445i	0.190371	−	0.370013i
$413$			104.296i			0.252534i
$414$		0			0
$415$		−	186.240i		−	0.448772i
$416$	138.185	−	55.6499i	0.332177	−	0.133774i
$417$		0			0
$418$	103.653	+	25.1009i	0.247973	+	0.0600500i
$419$	35.6383	+	61.7274i	0.0850557	+	0.147321i	0.905415	−	0.424528i	$-0.139560\pi$
$419$	35.6383	+	61.7274i	0.0850557	+	0.147321i	−0.820359	+	0.571848i	$0.806227\pi$
$420$		0			0
$421$	−594.980	−	343.512i	−1.41326	−	0.815943i	−0.417562	−	0.908649i	$-0.637115\pi$
$421$	−594.980	−	343.512i	−1.41326	−	0.815943i	−0.995694	+	0.0927053i	$0.970449\pi$
$422$	177.284	−	186.083i	0.420104	−	0.440954i
$423$		0			0
$424$	−307.371	+	355.608i	−0.724932	+	0.838697i
$425$	−112.708	+	195.215i	−0.265194	+	0.459330i
$426$		0			0
$427$	128.451	+	222.483i	0.300821	+	0.521038i
$428$	−308.101	+	198.362i	−0.719863	+	0.463462i
$429$		0			0
$430$	−80.1157	+	23.5598i	−0.186316	+	0.0547902i
$431$			411.731i			0.955292i	0.878552	+	0.477646i	$0.158510\pi$
$431$			411.731i			0.955292i	−0.878552	+	0.477646i	$0.841490\pi$
$432$		0			0
$433$	812.833			1.87721			0.938606	−	0.344992i	$-0.112118\pi$
$433$	812.833			1.87721			0.938606	+	0.344992i	$0.112118\pi$
$434$	98.0899	+	333.558i	0.226014	+	0.768566i
$435$		0			0
$436$	330.670	+	513.606i	0.758416	+	1.17799i
$437$	−115.170	+	66.4935i	−0.263547	+	0.152159i
$438$		0			0
$439$	−436.189	−	251.834i	−0.993597	−	0.573653i	−0.0872494	−	0.996186i	$-0.527808\pi$
$439$	−436.189	−	251.834i	−0.993597	−	0.573653i	−0.906348	+	0.422533i	$0.861141\pi$
$440$	433.052	−	501.012i	0.984210	−	1.13866i
$441$		0			0
$442$	−145.082	−	138.222i	−0.328239	−	0.312718i
$443$	163.387	−	282.994i	0.368819	−	0.638813i	−0.620562	−	0.784157i	$-0.713096\pi$
$443$	163.387	−	282.994i	0.368819	−	0.638813i	0.989381	+	0.145344i	$0.0464289\pi$
$444$		0			0
$445$	246.248	−	142.171i	0.553366	−	0.319486i
$446$	−136.560	+	563.915i	−0.306188	+	1.26438i
$447$		0			0
$448$	111.657	−	280.904i	0.249233	−	0.627019i
$449$	482.106			1.07373			0.536866	−	0.843667i	$-0.319608\pi$
$449$	482.106			1.07373			0.536866	+	0.843667i	$0.319608\pi$
$450$		0			0
$451$	284.664			0.631183
$452$	60.1648	+	30.9547i	0.133108	+	0.0684839i
$453$		0			0
$454$	−514.190	−	124.518i	−1.13258	−	0.274269i
$455$	113.414	−	65.4794i	0.249261	−	0.143911i
$456$		0			0
$457$	−128.853	+	223.180i	−0.281954	+	0.488359i	−0.971866	−	0.235534i	$-0.924316\pi$
$457$	−128.853	+	223.180i	−0.281954	+	0.488359i	0.689912	+	0.723893i	$0.257649\pi$
$458$	−239.536	−	228.210i	−0.523005	−	0.498276i
$459$		0			0
$460$	39.9680	+	824.807i	0.0868870	+	1.79306i
$461$	−102.474	−	59.1634i	−0.222286	−	0.128337i	0.384722	−	0.923032i	$-0.374297\pi$
$461$	−102.474	−	59.1634i	−0.222286	−	0.128337i	−0.607008	+	0.794695i	$0.707631\pi$
$462$		0			0
$463$	332.975	−	192.243i	0.719168	−	0.415212i	−0.0952784	−	0.995451i	$-0.530374\pi$
$463$	332.975	−	192.243i	0.719168	−	0.415212i	0.814446	+	0.580239i	$0.197041\pi$
$464$	−592.180	+	423.154i	−1.27625	+	0.911971i
$465$		0			0
$466$	−92.2665	−	313.755i	−0.197997	−	0.673294i
$467$	881.059			1.88664			0.943318	−	0.331891i	$-0.107686\pi$
$467$	881.059			1.88664			0.943318	+	0.331891i	$0.107686\pi$
$468$		0			0
$469$		−	538.073i		−	1.14728i
$470$	−206.257	−	701.385i	−0.438846	−	1.49231i
$471$		0			0
$472$	−33.2190	+	173.504i	−0.0703791	+	0.367593i
$473$	−48.7170	−	84.3803i	−0.102996	−	0.178394i
$474$		0			0
$475$	20.0923	−	34.8009i	0.0422996	−	0.0732650i
$476$	−406.132	+	19.6801i	−0.853218	+	0.0413447i
$477$		0			0
$478$	−133.289	−	126.986i	−0.278847	−	0.265662i
$479$	410.614	+	237.068i	0.857232	+	0.494923i	0.863084	−	0.505060i	$-0.168530\pi$
$479$	410.614	+	237.068i	0.857232	+	0.494923i	−0.00585234	+	0.999983i	$0.501863\pi$
$480$		0			0
$481$	83.9384	+	145.386i	0.174508	+	0.302257i
$482$	62.3012	+	15.0871i	0.129256	+	0.0313010i
$483$		0			0
$484$	256.683	+	132.063i	0.530337	+	0.272858i
$485$		−	342.615i		−	0.706423i
$486$		0			0
$487$		−	67.4929i		−	0.138589i	−0.997596	−	0.0692945i	$-0.977925\pi$
$487$		−	67.4929i		−	0.138589i	0.997596	−	0.0692945i	$-0.0220748\pi$
$488$	142.824	+	411.028i	0.292672	+	0.842270i
$489$		0			0
$490$	−74.8333	+	309.020i	−0.152721	+	0.630652i
$491$	103.521	+	179.303i	0.210837	+	0.365180i	0.951977	−	0.306171i	$-0.0990478\pi$
$491$	103.521	+	179.303i	0.210837	+	0.365180i	−0.741140	+	0.671351i	$0.765714\pi$
$492$		0			0
$493$	847.862	+	489.513i	1.71980	+	0.992927i
$494$	25.8636	+	24.6406i	0.0523554	+	0.0498798i
$495$		0			0
$496$	56.9391	+	586.138i	0.114797	+	1.18173i
$497$	−19.6086	+	33.9631i	−0.0394539	+	0.0683362i
$498$		0			0
$499$	136.696	+	236.765i	0.273940	+	0.474479i	0.969867	−	0.243634i	$-0.0783396\pi$
$499$	136.696	+	236.765i	0.273940	+	0.474479i	−0.695927	+	0.718113i	$0.745006\pi$
$500$	187.340	+	290.982i	0.374680	+	0.581965i
$501$		0			0
$502$	61.4786	+	209.060i	0.122467	+	0.416454i
$503$			801.394i			1.59323i	0.604488	+	0.796615i	$0.293378\pi$
$503$			801.394i			1.59323i	−0.604488	+	0.796615i	$0.706622\pi$
$504$		0			0
$505$	−784.071			−1.55262
$506$	−924.344	+	271.823i	−1.82677	+	0.537200i
$507$		0			0
$508$	312.307	+	485.084i	0.614777	+	0.954890i
$509$	456.038	−	263.294i	0.895950	−	0.517277i	0.0200657	−	0.999799i	$-0.493612\pi$
$509$	456.038	−	263.294i	0.895950	−	0.517277i	0.875884	+	0.482522i	$0.160279\pi$
$510$		0			0
$511$	466.512	+	269.341i	0.912939	+	0.527085i
$512$	275.218	−	431.740i	0.537534	−	0.843242i
$513$		0			0
$514$	−675.238	+	708.751i	−1.31369	+	1.37889i
$515$	127.636	−	221.072i	0.247837	−	0.429265i
$516$		0			0
$517$	738.720	−	426.500i	1.42886	−	0.824952i
$518$	331.077	+	80.1747i	0.639145	+	0.154777i
$519$		0			0
$520$	209.527	−	72.8065i	0.402936	−	0.140013i
$521$	−860.976			−1.65255			−0.826273	−	0.563270i	$-0.809543\pi$
$521$	−860.976			−1.65255			−0.826273	+	0.563270i	$0.809543\pi$
$522$		0			0
$523$	233.126			0.445747			0.222873	−	0.974847i	$-0.428456\pi$
$523$	233.126			0.445747			0.222873	+	0.974847i	$0.428456\pi$
$524$	61.9736	+	31.8853i	0.118270	+	0.0608499i
$525$		0			0
$526$	185.864	−	767.516i	0.353354	−	1.45916i
$527$	686.015	−	396.071i	1.30174	−	0.751558i
$528$		0			0
$529$	336.213	−	582.339i	0.635564	−	1.10083i
$530$	−482.766	+	506.726i	−0.910879	+	0.956086i
$531$		0			0
$532$	72.4008	−	3.50835i	0.136092	−	0.00659465i
$533$	82.5746	+	47.6745i	0.154924	+	0.0894456i
$534$		0			0
$535$	−472.519	+	272.809i	−0.883213	+	0.509923i
$536$	171.379	−	895.120i	0.319737	−	1.67000i
$537$		0			0
$538$	−689.187	+	202.670i	−1.28102	+	0.376711i
$539$	−370.974			−0.688263
$540$		0			0
$541$		−	735.170i		−	1.35891i	−0.733718	−	0.679455i	$-0.762216\pi$
$541$		−	735.170i		−	1.35891i	0.733718	−	0.679455i	$-0.237784\pi$
$542$	428.299	−	125.951i	0.790220	−	0.232381i
$543$		0			0
$544$	−681.896	−	96.6161i	−1.25348	−	0.177603i
$545$	454.773	+	787.691i	0.834447	+	1.44530i
$546$		0			0
$547$	−252.906	+	438.046i	−0.462351	+	0.800816i	−0.999078	−	0.0429407i	$-0.986327\pi$
$547$	−252.906	+	438.046i	−0.462351	+	0.800816i	0.536727	+	0.843756i	$0.319661\pi$
$548$	−18.0340	−	372.162i	−0.0329087	−	0.679127i
$549$		0			0
$550$	200.820	−	210.787i	0.365127	−	0.383249i
$551$	−151.148	−	87.2651i	−0.274315	−	0.158376i
$552$		0			0
$553$	−129.625	−	224.516i	−0.234403	−	0.405997i
$554$	−60.5648	+	250.099i	−0.109323	+	0.451442i
$555$		0			0
$556$	−157.122	−	80.8392i	−0.282594	−	0.145394i
$557$		−	240.438i		−	0.431666i	−0.976430	−	0.215833i	$-0.930753\pi$
$557$		−	240.438i		−	0.431666i	0.976430	−	0.215833i	$-0.0692467\pi$
$558$		0			0
$559$		−	32.6358i		−	0.0583825i
$560$	186.305	−	409.728i	0.332688	−	0.731657i
$561$		0			0
$562$	659.434	+	159.691i	1.17337	+	0.284147i
$563$	−71.8708	−	124.484i	−0.127657	−	0.221108i	0.795112	−	0.606463i	$-0.207412\pi$
$563$	−71.8708	−	124.484i	−0.127657	−	0.221108i	−0.922768	+	0.385355i	$0.874079\pi$
$564$		0			0
$565$	87.2493	+	50.3734i	0.154423	+	0.0891564i
$566$	−23.9191	+	25.1062i	−0.0422599	+	0.0443572i
$567$		0			0
$568$	−43.4376	+	50.2544i	−0.0764747	+	0.0884761i
$569$	−468.006	+	810.610i	−0.822506	+	1.42462i	0.0813051	+	0.996689i	$0.474091\pi$
$569$	−468.006	+	810.610i	−0.822506	+	1.42462i	−0.903811	+	0.427932i	$0.859242\pi$
$570$		0			0
$571$	−104.431	−	180.879i	−0.182891	−	0.316776i	0.759973	−	0.649955i	$-0.225212\pi$
$571$	−104.431	−	180.879i	−0.182891	−	0.316776i	−0.942864	+	0.333179i	$0.891879\pi$
$572$	140.100	+	217.607i	0.244929	+	0.380432i
$573$		0			0
$574$	185.617	−	54.5848i	0.323375	−	0.0950954i
$575$			363.035i			0.631364i
$576$		0			0
$577$	−707.574			−1.22630			−0.613149	−	0.789967i	$-0.710097\pi$
$577$	−707.574			−1.22630			−0.613149	+	0.789967i	$0.710097\pi$
$578$	98.2923	+	334.246i	0.170056	+	0.578280i
$579$		0			0
$580$	−911.216	+	586.659i	−1.57106	+	1.01148i
$581$	127.904	−	73.8453i	0.220144	−	0.127100i
$582$		0			0
$583$	−707.192	−	408.297i	−1.21302	−	0.700338i
$584$	690.287	+	596.652i	1.18200	+	1.02167i
$585$		0			0
$586$	−227.433	−	216.679i	−0.388111	−	0.369760i
$587$	172.823	−	299.339i	0.294418	−	0.509947i	−0.680431	−	0.732812i	$-0.738208\pi$
$587$	172.823	−	299.339i	0.294418	−	0.509947i	0.974849	+	0.222865i	$0.0715409\pi$
$588$		0			0
$589$	−122.295	+	70.6073i	−0.207632	+	0.119876i
$590$	−61.9090	+	255.650i	−0.104930	+	0.433304i
$591$		0			0
$592$	525.232	+	238.826i	0.887217	+	0.403422i
$593$	−577.178			−0.973318			−0.486659	−	0.873592i	$-0.661785\pi$
$593$	−577.178			−0.973318			−0.486659	+	0.873592i	$0.661785\pi$
$594$		0			0
$595$	−605.438			−1.01754
$596$	−57.8787	+	112.495i	−0.0971119	+	0.188750i
$597$		0			0
$598$	−313.656	−	75.9560i	−0.524508	−	0.127017i
$599$	580.291	−	335.031i	0.968766	−	0.559317i	0.0699059	−	0.997554i	$-0.477730\pi$
$599$	580.291	−	335.031i	0.968766	−	0.559317i	0.898860	+	0.438237i	$0.144397\pi$
$600$		0			0
$601$	−474.923	+	822.591i	−0.790221	+	1.36870i	0.135609	+	0.990762i	$0.456701\pi$
$601$	−474.923	+	822.591i	−0.790221	+	1.36870i	−0.925830	+	0.377941i	$0.876632\pi$
$602$	−47.9464	−	45.6793i	−0.0796452	−	0.0758793i
$603$		0			0
$604$	70.8393	−	3.43269i	0.117284	−	0.00568326i
$605$	372.234	+	214.909i	0.615263	+	0.355222i
$606$		0			0
$607$	−247.947	+	143.152i	−0.408479	+	0.235835i	−0.690136	−	0.723680i	$-0.742449\pi$
$607$	−247.947	+	143.152i	−0.408479	+	0.235835i	0.281657	+	0.959515i	$0.409116\pi$
$608$	121.561	+	17.2237i	0.199936	+	0.0283284i
$609$		0			0
$610$	182.793	+	621.594i	0.299661	+	1.01901i
$611$	285.715			0.467619
$612$		0			0
$613$			461.893i			0.753496i	0.926316	+	0.376748i	$0.122958\pi$
$613$			461.893i			0.753496i	−0.926316	+	0.376748i	$0.877042\pi$
$614$	−23.5957	−	80.2378i	−0.0384294	−	0.130680i
$615$		0			0
$616$	515.787	+	98.7522i	0.837316	+	0.160312i
$617$	−307.736	−	533.015i	−0.498763	−	0.863882i	0.501236	−	0.865310i	$-0.332879\pi$
$617$	−307.736	−	533.015i	−0.498763	−	0.863882i	−0.999999	+	0.00142829i	$0.999545\pi$
$618$		0			0
$619$	121.945	−	211.215i	0.197003	−	0.341219i	−0.750552	−	0.660811i	$-0.770212\pi$
$619$	121.945	−	211.215i	0.197003	−	0.341219i	0.947555	+	0.319592i	$0.103546\pi$
$620$	42.4407	+	875.836i	0.0684528	+	1.41264i
$621$		0			0
$622$	−68.0478	−	64.8302i	−0.109402	−	0.104229i
$623$	195.277	+	112.743i	0.313447	+	0.180969i
$624$		0			0
$625$	388.572	+	673.026i	0.621715	+	1.07684i
$626$	−713.486	−	172.780i	−1.13975	−	0.276007i
$627$		0			0
$628$	−161.492	+	313.882i	−0.257152	+	0.499812i
$629$		−	776.114i		−	1.23388i
$630$		0			0
$631$			1132.71i			1.79510i	0.440912	+	0.897550i	$0.354655\pi$
$631$			1132.71i			1.79510i	−0.440912	+	0.897550i	$0.645345\pi$
$632$	−144.129	−	414.784i	−0.228053	−	0.656304i
$633$		0			0
$634$	36.5822	−	151.064i	0.0577007	−	0.238272i
$635$	429.519	+	743.948i	0.676408	+	1.17157i
$636$		0			0
$637$	−107.611	−	62.1294i	−0.168935	−	0.0975344i
$638$	−915.491	−	872.203i	−1.43494	−	1.36709i
$639$		0			0
$640$	440.432	−	622.270i	0.688175	−	0.972297i
$641$	−104.496	+	180.992i	−0.163020	+	0.282359i	−0.935950	−	0.352132i	$-0.885457\pi$
$641$	−104.496	+	180.992i	−0.163020	+	0.282359i	0.772930	+	0.634491i	$0.218790\pi$
$642$		0			0
$643$	−88.2601	−	152.871i	−0.137263	−	0.237746i	0.789197	−	0.614141i	$-0.210497\pi$
$643$	−88.2601	−	152.871i	−0.137263	−	0.237746i	−0.926460	+	0.376394i	$0.877164\pi$
$644$	−550.603	+	354.489i	−0.854974	+	0.550449i
$645$		0			0
$646$	−46.5926	−	158.440i	−0.0721248	−	0.245263i
$647$		−	186.463i		−	0.288196i	−0.989563	−	0.144098i	$-0.953972\pi$
$647$		−	186.463i		−	0.288196i	0.989563	−	0.144098i	$-0.0460281\pi$
$648$		0			0
$649$	−306.904			−0.472887
$650$	93.5553	−	27.5120i	0.143931	−	0.0423261i
$651$		0			0
$652$	−113.865	+	73.3088i	−0.174640	+	0.112437i
$653$	−757.512	+	437.350i	−1.16005	+	0.669754i	−0.951316	−	0.308218i	$-0.900267\pi$
$653$	−757.512	+	437.350i	−1.16005	+	0.669754i	−0.208733	+	0.977973i	$0.566934\pi$
$654$		0			0
$655$	89.8723	+	51.8878i	0.137210	+	0.0792180i
$656$	326.172	−	31.6853i	0.497214	−	0.0483008i
$657$		0			0
$658$	399.906	−	419.754i	0.607760	−	0.637924i
$659$	431.297	−	747.028i	0.654472	−	1.13358i	−0.327554	−	0.944833i	$-0.606224\pi$
$659$	431.297	−	747.028i	0.654472	−	1.13358i	0.982026	−	0.188746i	$-0.0604424\pi$
$660$		0			0
$661$	−361.406	+	208.658i	−0.546757	+	0.315670i	−0.747813	−	0.663910i	$-0.768896\pi$
$661$	−361.406	+	208.658i	−0.546757	+	0.315670i	0.201056	+	0.979580i	$0.435563\pi$
$662$	976.391	+	236.446i	1.47491	+	0.357170i
$663$		0			0
$664$	236.297	−	82.1085i	0.355869	−	0.123657i
$665$	107.931			0.162302
$666$		0			0
$667$	1576.74			2.36392
$668$	−105.701	+	205.444i	−0.158234	+	0.307551i
$669$		0			0
$670$	319.393	−	1318.92i	0.476706	−	1.96853i
$671$	−654.681	+	377.980i	−0.975680	+	0.563309i
$672$		0			0
$673$	651.368	−	1128.20i	0.967857	−	1.67638i	0.266121	−	0.963940i	$-0.414258\pi$
$673$	651.368	−	1128.20i	0.967857	−	1.67638i	0.701736	−	0.712438i	$-0.252409\pi$
$674$	−63.7223	+	66.8849i	−0.0945435	+	0.0992357i
$675$		0			0
$676$	−28.5230	−	588.621i	−0.0421939	−	0.870742i
$677$	−408.374	−	235.775i	−0.603211	−	0.348264i	0.167093	−	0.985941i	$-0.446562\pi$
$677$	−408.374	−	235.775i	−0.603211	−	0.348264i	−0.770304	+	0.637677i	$0.779895\pi$
$678$		0			0
$679$	235.297	−	135.849i	0.346535	−	0.200072i
$680$	−1007.19	−	192.835i	−1.48116	−	0.283581i
$681$		0			0
$682$	−981.531	+	288.640i	−1.43919	+	0.423226i
$683$	−316.113			−0.462830			−0.231415	−	0.972855i	$-0.574336\pi$
$683$	−316.113			−0.462830			−0.231415	+	0.972855i	$0.574336\pi$
$684$		0			0
$685$		−	554.797i		−	0.809922i
$686$	−685.963	+	201.722i	−0.999946	+	0.294056i
$687$		0			0
$688$	−65.2129	−	91.2618i	−0.0947863	−	0.132648i
$689$	−136.761	−	236.876i	−0.198491	−	0.343797i
$690$		0			0
$691$	14.4746	−	25.0708i	0.0209473	−	0.0362819i	−0.855362	−	0.518031i	$-0.826665\pi$
$691$	14.4746	−	25.0708i	0.0209473	−	0.0362819i	0.876309	+	0.481749i	$0.159998\pi$
$692$	−72.1862	+	3.49796i	−0.104315	+	0.00505485i
$693$		0			0
$694$	350.635	−	368.038i	0.505238	−	0.530314i
$695$	−227.854	−	131.552i	−0.327847	−	0.189283i
$696$		0			0
$697$	−220.405	−	381.752i	−0.316219	−	0.547707i
$698$	116.047	−	479.208i	0.166256	−	0.686544i
$699$		0			0
$700$	90.5275	−	175.953i	0.129325	−	0.251361i
$701$		−	181.322i		−	0.258662i	−0.991601	−	0.129331i	$-0.958717\pi$
$701$		−	181.322i		−	0.258662i	0.991601	−	0.129331i	$-0.0412830\pi$
$702$		0			0
$703$			138.357i			0.196810i
$704$	826.592	+	328.562i	1.17414	+	0.466707i
$705$		0			0
$706$	296.827	+	71.8806i	0.420435	+	0.101814i
$707$	−310.889	−	538.475i	−0.439729	−	0.761633i
$708$		0			0
$709$	−56.7386	−	32.7581i	−0.0800262	−	0.0462032i	0.459453	−	0.888202i	$-0.348045\pi$
$709$	−56.7386	−	32.7581i	−0.0800262	−	0.0462032i	−0.539479	+	0.841999i	$0.681379\pi$
$710$	−68.2244	+	71.6104i	−0.0960907	+	0.100860i
$711$		0			0
$712$	288.948	+	249.753i	0.405825	+	0.350777i
$713$	637.878	−	1104.84i	0.894640	−	1.54956i
$714$		0			0
$715$	192.681	+	333.733i	0.269483	+	0.466759i
$716$	889.614	−	572.751i	1.24248	−	0.799932i
$717$		0			0
$718$	658.259	−	193.575i	0.916795	−	0.269604i
$719$		−	583.213i		−	0.811144i	−0.914063	−	0.405572i	$-0.867072\pi$
$719$		−	583.213i		−	0.811144i	0.914063	−	0.405572i	$-0.132928\pi$
$720$		0			0
$721$	202.433			0.280767
$722$	−195.389	−	664.426i	−0.270622	−	0.920257i
$723$		0			0
$724$	−401.622	−	623.812i	−0.554727	−	0.861618i
$725$	−412.610	+	238.221i	−0.569118	+	0.328580i
$726$		0			0
$727$	870.370	+	502.508i	1.19721	+	0.691208i	0.959932	−	0.280234i	$-0.0904122\pi$
$727$	870.370	+	502.508i	1.19721	+	0.691208i	0.237276	+	0.971442i	$0.423746\pi$
$728$	133.080	+	115.028i	0.182802	+	0.158006i
$729$		0			0
$730$	983.629	+	937.119i	1.34744	+	1.28372i
$731$	−75.4396	+	130.665i	−0.103201	+	0.178749i
$732$		0			0
$733$	−487.340	+	281.366i	−0.664857	+	0.383855i	−0.794125	−	0.607755i	$-0.792070\pi$
$733$	−487.340	+	281.366i	−0.664857	+	0.383855i	0.129268	+	0.991610i	$0.458737\pi$
$734$	19.4297	−	80.2337i	0.0264709	−	0.109310i
$735$		0			0
$736$	−1028.87	+	414.346i	−1.39792	+	0.562971i
$737$	1583.34			2.14836
$738$		0			0
$739$	786.903			1.06482			0.532411	−	0.846486i	$-0.321286\pi$
$739$	786.903			1.06482			0.532411	+	0.846486i	$0.321286\pi$
$740$	763.940	+	393.046i	1.03235	+	0.531143i
$741$		0			0
$742$	−539.422	−	130.628i	−0.726984	−	0.176049i
$743$	−1259.40	+	727.115i	−1.69502	+	0.978620i	−0.744672	+	0.667430i	$0.767394\pi$
$743$	−1259.40	+	727.115i	−1.69502	+	0.978620i	−0.950348	+	0.311190i	$0.899272\pi$
$744$		0			0
$745$	−94.1874	+	163.137i	−0.126426	+	0.218976i
$746$	−156.487	−	149.087i	−0.209768	−	0.199849i
$747$		0			0
$748$	−57.9109	−	1195.09i	−0.0774209	−	1.59771i
$749$	−374.713	−	216.341i	−0.500284	−	0.288839i
$750$		0			0
$751$	−298.356	+	172.256i	−0.397279	+	0.229369i	−0.685309	−	0.728252i	$-0.740333\pi$
$751$	−298.356	+	172.256i	−0.397279	+	0.229369i	0.288031	+	0.957621i	$0.407000\pi$
$752$	798.965	−	570.916i	1.06245	−	0.759197i
$753$		0			0
$754$	−119.490	−	406.330i	−0.158475	−	0.538900i
$755$	105.603			0.139872
$756$		0			0
$757$		−	1091.69i		−	1.44212i	−0.692870	−	0.721062i	$-0.743654\pi$
$757$		−	1091.69i		−	1.44212i	0.692870	−	0.721062i	$-0.256346\pi$
$758$	−163.764	−	556.883i	−0.216047	−	0.734675i
$759$		0			0
$760$	179.550	+	34.3766i	0.236250	+	0.0452323i
$761$	−133.134	−	230.595i	−0.174946	−	0.303015i	0.765197	−	0.643797i	$-0.222642\pi$
$761$	−133.134	−	230.595i	−0.174946	−	0.303015i	−0.940143	+	0.340781i	$0.889308\pi$
$762$		0			0
$763$	−360.640	+	624.647i	−0.472661	+	0.818673i
$764$	−368.261	+	17.8449i	−0.482016	+	0.0233572i
$765$		0			0
$766$	65.5449	+	62.4457i	0.0855678	+	0.0815218i
$767$	−89.0260	−	51.3992i	−0.116070	−	0.0670133i
$768$		0			0
$769$	−426.068	−	737.971i	−0.554054	−	0.959650i	−0.997976	−	0.0635850i	$-0.979747\pi$
$769$	−426.068	−	737.971i	−0.554054	−	0.959650i	0.443922	−	0.896065i	$-0.353587\pi$
$770$	759.987	+	184.041i	0.986996	+	0.239014i
$771$		0			0
$772$	961.551	+	494.717i	1.24553	+	0.640825i
$773$			1203.58i			1.55702i	0.627630	+	0.778512i	$0.284025\pi$
$773$			1203.58i			1.55702i	−0.627630	+	0.778512i	$0.715975\pi$
$774$		0			0
$775$			385.495i			0.497412i
$776$	434.701	−	151.050i	0.560181	−	0.194652i
$777$		0			0
$778$	257.494	−	1063.31i	0.330969	−	1.36672i
$779$	39.2913	+	68.0546i	0.0504382	+	0.0873615i
$780$		0			0
$781$	−99.9402	−	57.7005i	−0.127964	−	0.0738803i
$782$	1080.22	+	1029.14i	1.38135	+	1.31604i
$783$		0			0
$784$	−425.068	+	41.2923i	−0.542178	+	0.0526687i
$785$	−262.799	+	455.182i	−0.334776	+	0.579850i
$786$		0			0
$787$	−353.524	−	612.322i	−0.449205	−	0.778046i	0.549130	−	0.835737i	$-0.314959\pi$
$787$	−353.524	−	612.322i	−0.449205	−	0.778046i	−0.998334	+	0.0576915i	$0.981626\pi$
$788$	303.616	+	471.586i	0.385300	+	0.598459i
$789$		0			0
$790$	−184.464	−	627.275i	−0.233498	−	0.794019i
$791$			79.8933i			0.101003i
$792$		0			0
$793$	−253.212			−0.319308
$794$	−692.447	+	203.629i	−0.872099	+	0.256460i
$795$		0			0
$796$	591.022	+	917.994i	0.742491	+	1.15326i
$797$	−802.601	+	463.382i	−1.00703	+	0.581408i	−0.910320	−	0.413905i	$-0.864165\pi$
$797$	−802.601	+	463.382i	−1.00703	+	0.581408i	−0.0967079	+	0.995313i	$0.530831\pi$
$798$		0			0
$799$	−1143.93	−	660.447i	−1.43170	−	0.826592i
$800$	206.641	−	263.876i	0.258301	−	0.329845i
$801$		0			0
$802$	178.101	−	186.940i	0.222071	−	0.233093i
$803$	−792.565	+	1372.76i	−0.987005	+	1.70954i
$804$		0			0
$805$	−844.432	+	487.533i	−1.04898	+	0.605631i
$806$	−333.061	−	80.6552i	−0.413227	−	0.100069i
$807$		0			0
$808$	−345.677	−	994.808i	−0.427818	−	1.23120i
$809$	−804.591			−0.994551			−0.497275	−	0.867593i	$-0.665666\pi$
$809$	−804.591			−0.994551			−0.497275	+	0.867593i	$0.665666\pi$
$810$		0			0
$811$	652.228			0.804227			0.402113	−	0.915590i	$-0.368276\pi$
$811$	652.228			0.804227			0.402113	+	0.915590i	$0.368276\pi$
$812$	−764.200	−	393.180i	−0.941134	−	0.484212i
$813$		0			0
$814$	−235.923	+	974.231i	−0.289832	+	1.19684i
$815$	−174.629	+	100.822i	−0.214269	+	0.123708i
$816$		0			0
$817$	13.4485	−	23.2936i	0.0164609	−	0.0285111i
$818$	554.926	−	582.468i	0.678394	−	0.712063i
$819$		0			0
$820$	487.383	−	23.6173i	0.594369	−	0.0288016i
$821$	162.159	+	93.6225i	0.197514	+	0.114035i	0.595495	−	0.803359i	$-0.296956\pi$
$821$	162.159	+	93.6225i	0.197514	+	0.114035i	−0.397981	+	0.917393i	$0.630289\pi$
$822$		0			0
$823$	−260.354	+	150.315i	−0.316347	+	0.182643i	−0.649763	−	0.760137i	$-0.725132\pi$
$823$	−260.354	+	150.315i	−0.316347	+	0.182643i	0.333416	+	0.942780i	$0.391799\pi$
$824$	336.761	+	64.4761i	0.408691	+	0.0782477i
$825$		0			0
$826$	−200.119	+	58.8494i	−0.242275	+	0.0712462i
$827$	−755.962			−0.914101			−0.457051	−	0.889441i	$-0.651094\pi$
$827$	−755.962			−0.914101			−0.457051	+	0.889441i	$0.651094\pi$
$828$		0			0
$829$			205.363i			0.247724i	0.992299	+	0.123862i	$0.0395280\pi$
$829$			205.363i			0.247724i	−0.992299	+	0.123862i	$0.960472\pi$
$830$	357.350	−	105.086i	0.430542	−	0.126610i
$831$		0			0
$832$	184.750	+	233.743i	0.222055	+	0.280942i
$833$	287.231	+	497.499i	0.344815	+	0.597238i
$834$		0			0
$835$	−172.009	+	297.929i	−0.205999	+	0.356801i
$836$	10.3237	+	213.047i	0.0123489	+	0.254841i
$837$		0			0
$838$	−98.3308	+	103.211i	−0.117340	+	0.123163i
$839$	249.008	+	143.765i	0.296791	+	0.171352i	0.641000	−	0.767541i	$-0.278520\pi$
$839$	249.008	+	143.765i	0.296791	+	0.171352i	−0.344209	+	0.938893i	$0.611853\pi$
$840$		0			0
$841$	614.143	+	1063.73i	0.730253	+	1.26484i
$842$	323.397	−	1335.45i	0.384082	−	1.58604i
$843$		0			0
$844$	457.080	+	235.167i	0.541563	+	0.278634i
$845$		−	877.482i		−	1.03844i
$846$		0			0
$847$			340.851i			0.402422i
$848$	−855.759	−	389.118i	−1.00915	−	0.458865i
$849$		0			0
$850$	−438.166	−	106.108i	−0.515489	−	0.124833i
$851$	−624.971	−	1082.48i	−0.734396	−	1.27201i
$852$		0			0
$853$	1224.79	+	707.134i	1.43586	+	0.828997i	0.997559	−	0.0698290i	$-0.0222454\pi$
$853$	1224.79	+	707.134i	1.43586	+	0.828997i	0.438306	+	0.898826i	$0.355579\pi$
$854$	−354.412	+	372.002i	−0.415002	+	0.435599i
$855$		0			0
$856$	−554.454	−	479.245i	−0.647727	−	0.559866i
$857$	−214.812	+	372.065i	−0.250656	+	0.434149i	−0.963707	−	0.266964i	$-0.913980\pi$
$857$	−214.812	+	372.065i	−0.250656	+	0.434149i	0.713051	+	0.701113i	$0.247313\pi$
$858$		0			0
$859$	−820.973	−	1421.97i	−0.955731	−	1.65537i	−0.732687	−	0.680566i	$-0.761734\pi$
$859$	−820.973	−	1421.97i	−0.955731	−	1.65537i	−0.223043	−	0.974809i	$-0.571599\pi$
$860$	−90.4109	−	140.429i	−0.105129	−	0.163289i
$861$		0			0
$862$	−790.011	+	232.320i	−0.916486	+	0.269512i
$863$		−	343.475i		−	0.398001i	−0.979999	−	0.199000i	$-0.936231\pi$
$863$		−	343.475i		−	0.398001i	0.979999	−	0.199000i	$-0.0637695\pi$
$864$		0			0
$865$	−107.611			−0.124406
$866$	458.642	+	1559.63i	0.529610	+	1.80095i
$867$		0			0
$868$	−584.668	+	376.421i	−0.673581	+	0.433665i
$869$	660.665	−	381.435i	0.760259	−	0.438935i
$870$		0			0
$871$	459.292	+	265.172i	0.527316	+	0.304446i
$872$	−798.903	+	924.277i	−0.916173	+	1.05995i
$873$		0			0
$874$	−192.569	−	183.464i	−0.220331	−	0.209913i
$875$	−204.320	+	353.893i	−0.233509	+	0.404449i
$876$		0			0
$877$	−322.495	+	186.193i	−0.367725	+	0.212306i	−0.672464	−	0.740130i	$-0.734764\pi$
$877$	−322.495	+	186.193i	−0.367725	+	0.212306i	0.304739	+	0.952436i	$0.401431\pi$
$878$	237.087	−	979.038i	0.270031	−	1.11508i
$879$		0			0
$880$	1205.67	+	548.224i	1.37008	+	0.622982i
$881$	526.956			0.598134			0.299067	−	0.954232i	$-0.403325\pi$
$881$	526.956			0.598134			0.299067	+	0.954232i	$0.403325\pi$
$882$		0			0
$883$	−1534.59			−1.73792			−0.868962	−	0.494879i	$-0.835212\pi$
$883$	−1534.59			−1.73792			−0.868962	+	0.494879i	$0.835212\pi$
$884$	183.351	−	356.368i	0.207410	−	0.403131i
$885$		0			0
$886$	635.188	+	153.819i	0.716916	+	0.173611i
$887$	−525.057	+	303.142i	−0.591946	+	0.341760i	−0.765867	−	0.642999i	$-0.777690\pi$
$887$	−525.057	+	303.142i	−0.591946	+	0.341760i	0.173920	+	0.984760i	$0.444356\pi$
$888$		0			0
$889$	−340.613	+	589.959i	−0.383142	+	0.663621i
$890$	411.738	+	392.269i	0.462627	+	0.440752i
$891$		0			0
$892$	−1159.07	+	56.1654i	−1.29940	+	0.0629657i
$893$	203.927	+	117.737i	0.228362	+	0.131845i
$894$		0			0
$895$	1364.36	−	787.711i	1.52442	−	0.880124i
$896$	601.989	+	55.7408i	0.671863	+	0.0622107i
$897$		0			0
$898$	272.029	+	925.043i	0.302927	+	1.03011i
$899$	1674.28			1.86239
$900$		0			0
$901$			1264.52i			1.40346i
$902$	160.622	+	546.200i	0.178073	+	0.605543i
$903$		0			0
$904$	−25.4464	+	132.908i	−0.0281487	+	0.147022i
$905$	−552.355	−	956.708i	−0.610338	−	1.05714i
$906$		0			0
$907$	−297.755	+	515.726i	−0.328285	+	0.568606i	−0.982172	−	0.187986i	$-0.939804\pi$
$907$	−297.755	+	515.726i	−0.328285	+	0.568606i	0.653887	+	0.756593i	$0.273137\pi$
$908$	−51.2128	−	1056.86i	−0.0564018	−	1.16395i
$909$		0			0
$910$	189.633	+	180.666i	0.208388	+	0.198534i
$911$	335.426	+	193.658i	0.368195	+	0.212578i	0.672670	−	0.739943i	$-0.265148\pi$
$911$	335.426	+	193.658i	0.368195	+	0.212578i	−0.304475	+	0.952520i	$0.598481\pi$
$912$		0			0
$913$	217.298	+	376.371i	0.238004	+	0.412236i
$914$	−500.933	−	121.308i	−0.548067	−	0.132722i
$915$		0			0
$916$	302.721	−	588.380i	0.330481	−	0.642336i
$917$			82.2952i			0.0897439i
$918$		0			0
$919$		−	1508.26i		−	1.64119i	−0.571508	−	0.820597i	$-0.693641\pi$
$919$		−	1508.26i		−	1.64119i	0.571508	−	0.820597i	$-0.306359\pi$
$920$	−1560.05	+	542.088i	−1.69571	+	0.589226i
$921$		0			0
$922$	55.6989	−	230.005i	0.0604110	−	0.249464i
$923$	−19.3270	−	33.4753i	−0.0209393	−	0.0362679i
$924$		0			0
$925$	327.093	+	188.847i	0.353614	+	0.204159i
$926$	556.749	+	530.424i	0.601241	+	0.572812i
$927$		0			0
$928$	−1146.07	−	897.483i	−1.23499	−	0.967116i
$929$	346.221	−	599.672i	0.372681	−	0.645503i	−0.617296	−	0.786731i	$-0.711772\pi$
$929$	346.221	−	599.672i	0.372681	−	0.645503i	0.989977	+	0.141228i	$0.0451052\pi$
$930$		0			0
$931$	−51.2045	−	88.6887i	−0.0549994	−	0.0952618i
$932$	549.958	−	354.074i	0.590083	−	0.379907i
$933$		0			0
$934$	497.139	+	1690.54i	0.532269	+	1.81000i
$935$		−	1781.57i		−	1.90542i
$936$		0			0
$937$	735.537			0.784991			0.392496	−	0.919754i	$-0.371612\pi$
$937$	735.537			0.784991			0.392496	+	0.919754i	$0.371612\pi$
$938$	1032.43	−	303.609i	1.10067	−	0.323676i
$939$		0			0
$940$	1229.40	−	791.515i	1.30788	−	0.842037i
$941$	−246.674	+	142.418i	−0.262141	+	0.151347i	−0.625311	−	0.780376i	$-0.715028\pi$
$941$	−246.674	+	142.418i	−0.262141	+	0.151347i	0.363170	+	0.931723i	$0.381694\pi$
$942$		0			0
$943$	−614.817	−	354.965i	−0.651980	−	0.376421i
$944$	−351.655	+	34.1608i	−0.372516	+	0.0361873i
$945$		0			0
$946$	134.417	−	141.088i	0.142089	−	0.149141i
$947$	327.212	−	566.748i	0.345525	−	0.598466i	−0.639924	−	0.768438i	$-0.721034\pi$
$947$	327.212	−	566.748i	0.345525	−	0.598466i	0.985449	+	0.169972i	$0.0543676\pi$
$948$		0			0
$949$	−459.811	+	265.472i	−0.484522	+	0.279739i
$950$	78.1114	+	18.9157i	0.0822226	+	0.0199113i
$951$		0			0
$952$	−266.922	−	768.163i	−0.280380	−	0.806894i
$953$	−883.663			−0.927243			−0.463622	−	0.886033i	$-0.653450\pi$
$953$	−883.663			−0.927243			−0.463622	+	0.886033i	$0.653450\pi$
$954$		0			0
$955$	−548.981			−0.574850
$956$	168.447	−	327.401i	0.176200	−	0.342469i
$957$		0			0
$958$	−223.186	+	921.634i	−0.232971	+	0.962040i
$959$	381.017	−	219.980i	0.397306	−	0.229385i
$960$		0			0
$961$	196.842	−	340.941i	0.204831	−	0.354777i
$962$	−231.597	+	243.091i	−0.240745	+	0.252694i
$963$		0			0
$964$	6.20514	+	128.054i	0.00643687	+	0.132836i
$965$	1394.41	+	805.065i	1.44499	+	0.834264i
$966$		0			0
$967$	−93.5260	+	53.9973i	−0.0967177	+	0.0558400i	−0.547579	−	0.836754i	$-0.684450\pi$
$967$	−93.5260	+	53.9973i	−0.0967177	+	0.0558400i	0.450861	+	0.892594i	$0.351117\pi$
$968$	−108.563	+	567.029i	−0.112152	+	0.585773i
$969$		0			0
$970$	657.394	−	193.321i	0.677726	−	0.199300i
$971$	−384.915			−0.396411			−0.198206	−	0.980160i	$-0.563511\pi$
$971$	−384.915			−0.396411			−0.198206	+	0.980160i	$0.563511\pi$
$972$		0			0
$973$		−	208.644i		−	0.214433i
$974$	129.502	−	38.0830i	0.132959	−	0.0390995i
$975$		0			0
$976$	−708.072	+	505.967i	−0.725484	+	0.518409i
$977$	791.946	+	1371.69i	0.810589	+	1.40398i	0.912452	+	0.409183i	$0.134186\pi$
$977$	791.946	+	1371.69i	0.810589	+	1.40398i	−0.101863	+	0.994798i	$0.532480\pi$
$978$		0			0
$979$	−331.760	+	574.626i	−0.338877	+	0.586952i
$980$	−635.158	+	30.7781i	−0.648120	+	0.0314062i
$981$		0			0
$982$	−285.628	+	299.803i	−0.290863	+	0.305299i
$983$	−48.2339	−	27.8478i	−0.0490680	−	0.0283294i	0.475265	−	0.879843i	$-0.342352\pi$
$983$	−48.2339	−	27.8478i	−0.0490680	−	0.0283294i	−0.524333	+	0.851513i	$0.675685\pi$
$984$		0			0
$985$	417.567	+	723.247i	0.423926	+	0.734261i
$986$	−460.848	+	1903.05i	−0.467392	+	1.93007i
$987$		0			0
$988$	−32.6858	+	63.5294i	−0.0330828	+	0.0643010i
$989$			242.993i			0.245696i
$990$		0			0
$991$			1622.31i			1.63704i	0.574477	+	0.818521i	$0.305205\pi$
$991$			1622.31i			1.63704i	−0.574477	+	0.818521i	$0.694795\pi$
$992$	−1092.53	+	439.981i	−1.10134	+	0.443529i
$993$		0			0
$994$	−76.2310	−	18.4604i	−0.0766912	−	0.0185718i
$995$	812.840	+	1407.88i	0.816924	+	1.41495i
$996$		0			0
$997$	1233.43	+	712.120i	1.23714	+	0.714263i	0.968508	−	0.248981i	$-0.0800956\pi$
$997$	1233.43	+	712.120i	1.23714	+	0.714263i	0.268631	+	0.963243i	$0.413429\pi$
$998$	−377.163	+	395.882i	−0.377919	+	0.396675i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.12		40
3.2	odd	2		72.3.p.b.43.9	✓	40
4.3	odd	2		864.3.t.b.559.5		40
8.3	odd	2	inner	216.3.p.b.19.2		40
8.5	even	2		864.3.t.b.559.16		40
9.2	odd	6		648.3.b.f.163.4		20
9.4	even	3	inner	216.3.p.b.91.2		40
9.5	odd	6		72.3.p.b.67.19	yes	40
9.7	even	3		648.3.b.e.163.17		20
12.11	even	2		288.3.t.b.79.8		40
24.5	odd	2		288.3.t.b.79.7		40
24.11	even	2		72.3.p.b.43.19	yes	40
36.7	odd	6		2592.3.b.f.1135.5		20
36.11	even	6		2592.3.b.e.1135.16		20
36.23	even	6		288.3.t.b.175.7		40
36.31	odd	6		864.3.t.b.847.16		40
72.5	odd	6		288.3.t.b.175.8		40
72.11	even	6		648.3.b.f.163.3		20
72.13	even	6		864.3.t.b.847.5		40
72.29	odd	6		2592.3.b.e.1135.5		20
72.43	odd	6		648.3.b.e.163.18		20
72.59	even	6		72.3.p.b.67.9	yes	40
72.61	even	6		2592.3.b.f.1135.16		20
72.67	odd	6	inner	216.3.p.b.91.12		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.9	✓	40	3.2	odd	2
72.3.p.b.43.19	yes	40	24.11	even	2
72.3.p.b.67.9	yes	40	72.59	even	6
72.3.p.b.67.19	yes	40	9.5	odd	6
216.3.p.b.19.2		40	8.3	odd	2	inner
216.3.p.b.19.12		40	1.1	even	1	trivial
216.3.p.b.91.2		40	9.4	even	3	inner
216.3.p.b.91.12		40	72.67	odd	6	inner
288.3.t.b.79.7		40	24.5	odd	2
288.3.t.b.79.8		40	12.11	even	2
288.3.t.b.175.7		40	36.23	even	6
288.3.t.b.175.8		40	72.5	odd	6
648.3.b.e.163.17		20	9.7	even	3
648.3.b.e.163.18		20	72.43	odd	6
648.3.b.f.163.3		20	72.11	even	6
648.3.b.f.163.4		20	9.2	odd	6
864.3.t.b.559.5		40	4.3	odd	2
864.3.t.b.559.16		40	8.5	even	2
864.3.t.b.847.5		40	72.13	even	6
864.3.t.b.847.16		40	36.31	odd	6
2592.3.b.e.1135.5		20	72.29	odd	6
2592.3.b.e.1135.16		20	36.11	even	6
2592.3.b.f.1135.5		20	36.7	odd	6
2592.3.b.f.1135.16		20	72.61	even	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.564251 + 1.91875i) q^{2} +(-3.36324 + 2.16532i) q^{4} +(-5.15803 + 2.97799i) q^{5} +(-4.09037 - 2.36158i) q^{7} +(-6.05243 - 5.23145i) q^{8} +O(q^{10})\)	\(q+(0.564251 + 1.91875i) q^{2} +(-3.36324 + 2.16532i) q^{4} +(-5.15803 + 2.97799i) q^{5} +(-4.09037 - 2.36158i) q^{7} +(-6.05243 - 5.23145i) q^{8} +(-8.62446 - 8.21666i) q^{10} +(6.94921 - 12.0364i) q^{11} +(4.03163 - 2.32766i) q^{13} +(2.22329 - 9.18095i) q^{14} +(6.62277 - 14.5650i) q^{16} -21.5221 q^{17} +3.83672 q^{19} +(10.8994 - 21.1845i) q^{20} +(27.0160 + 6.54228i) q^{22} +(-30.0178 + 17.3308i) q^{23} +(5.23684 - 9.07047i) q^{25} +(6.74106 + 6.42232i) q^{26} +(18.8705 - 0.914414i) q^{28} +(-39.3950 - 22.7447i) q^{29} +(-31.8750 + 18.4030i) q^{31} +(31.6836 + 4.48916i) q^{32} +(-12.1439 - 41.2956i) q^{34} +28.1310 q^{35} +36.0613i q^{37} +(2.16488 + 7.36173i) q^{38} +(46.7978 + 8.95988i) q^{40} +(10.2409 + 17.7377i) q^{41} +(3.50522 - 6.07122i) q^{43} +(2.69077 + 55.5285i) q^{44} +(-50.1912 - 47.8179i) q^{46} +(53.1514 + 30.6870i) q^{47} +(-13.3459 - 23.1158i) q^{49} +(20.3589 + 4.93018i) q^{50} +(-8.51920 + 16.5582i) q^{52} -58.7545i q^{53} +82.7787i q^{55} +(12.4022 + 35.6919i) q^{56} +(21.4128 - 88.4230i) q^{58} +(-11.0410 - 19.1235i) q^{59} +(-47.1047 - 27.1959i) q^{61} +(-53.2964 - 50.7763i) q^{62} +(9.26389 + 63.3260i) q^{64} +(-13.8635 + 24.0123i) q^{65} +(56.9612 + 98.6596i) q^{67} +(72.3839 - 46.6022i) q^{68} +(15.8730 + 53.9765i) q^{70} -8.30318i q^{71} -114.051 q^{73} +(-69.1928 + 20.3476i) q^{74} +(-12.9038 + 8.30773i) q^{76} +(-56.8497 + 32.8222i) q^{77} +(47.5352 + 27.4445i) q^{79} +(9.21392 + 94.8492i) q^{80} +(-28.2559 + 29.6582i) q^{82} +(-15.6347 + 27.0802i) q^{83} +(111.011 - 64.0925i) q^{85} +(13.6270 + 3.29996i) q^{86} +(-105.027 + 36.4950i) q^{88} -47.7407 q^{89} -21.9878 q^{91} +(63.4304 - 123.286i) q^{92} +(-28.8900 + 119.300i) q^{94} +(-19.7899 + 11.4257i) q^{95} +(-28.7623 + 49.8177i) q^{97} +(36.8231 - 38.6506i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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