LMFDB - Embedded newform 27.5.d.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,5,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.d (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:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.39400128.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 $ x^6 - x^5 + 11x^4 + 14x^3 + 98x^2 + 20x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.2
Root			$-0.102534 - 0.177594i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.5.d.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.307601 - 0.177594i) q^{2} +(-7.93692 - 13.7472i) q^{4} +(30.0804 - 17.3669i) q^{5} +(15.6054 - 27.0294i) q^{7} +11.3212i q^{8} -12.3370 q^{10} +(-49.9968 - 28.8657i) q^{11} +(36.6478 + 63.4758i) q^{13} +(-9.60051 + 5.54285i) q^{14} +(-124.980 + 216.472i) q^{16} +386.985i q^{17} +115.791 q^{19} +(-477.491 - 275.679i) q^{20} +(10.2527 + 17.7583i) q^{22} +(474.852 - 274.156i) q^{23} +(290.719 - 503.539i) q^{25} -26.0337i q^{26} -495.436 q^{28} +(680.082 + 392.645i) q^{29} +(-272.367 - 471.753i) q^{31} +(233.759 - 134.961i) q^{32} +(68.7261 - 119.037i) q^{34} -1084.07i q^{35} +898.827 q^{37} +(-35.6175 - 20.5637i) q^{38} +(196.614 + 340.546i) q^{40} +(-2242.01 + 1294.43i) q^{41} +(-1000.05 + 1732.14i) q^{43} +916.419i q^{44} -194.753 q^{46} +(702.646 + 405.673i) q^{47} +(713.441 + 1235.72i) q^{49} +(-178.851 + 103.260i) q^{50} +(581.741 - 1007.61i) q^{52} -2221.00i q^{53} -2005.23 q^{55} +(306.005 + 176.672i) q^{56} +(-139.463 - 241.557i) q^{58} +(-1309.65 + 756.128i) q^{59} +(951.281 - 1647.67i) q^{61} +193.483i q^{62} +3903.49 q^{64} +(2204.76 + 1272.92i) q^{65} +(-2253.55 - 3903.26i) q^{67} +(5319.94 - 3071.47i) q^{68} +(-192.524 + 333.462i) q^{70} -3993.54i q^{71} -3436.70 q^{73} +(-276.480 - 159.626i) q^{74} +(-919.023 - 1591.80i) q^{76} +(-1560.44 + 900.923i) q^{77} +(-601.388 + 1041.63i) q^{79} +8682.07i q^{80} +919.529 q^{82} +(-8016.22 - 4628.17i) q^{83} +(6720.72 + 11640.6i) q^{85} +(615.236 - 355.207i) q^{86} +(326.794 - 566.024i) q^{88} +8929.99i q^{89} +2287.62 q^{91} +(-7537.72 - 4351.91i) q^{92} +(-144.090 - 249.571i) q^{94} +(3483.03 - 2010.93i) q^{95} +(-3335.14 + 5776.64i) q^{97} -506.811i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29}+ \cdots - 28959 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.307601	−	0.177594i	−0.0769004	−	0.0443984i	0.461057	−	0.887371i	$-0.347470\pi$
$2$	−0.307601	−	0.177594i	−0.0769004	−	0.0443984i	−0.537957	+	0.842972i	$0.680804\pi$
$3$		0			0
$3$		0			0
$4$	−7.93692	−	13.7472i	−0.496058	−	0.859197i
$5$	30.0804	−	17.3669i	1.20321	−	0.694676i	0.241946	−	0.970290i	$-0.422214\pi$
$5$	30.0804	−	17.3669i	1.20321	−	0.694676i	0.961268	+	0.275614i	$0.0888811\pi$
$6$		0			0
$7$	15.6054	−	27.0294i	0.318478	−	0.551620i	−0.661693	−	0.749775i	$-0.730162\pi$
$7$	15.6054	−	27.0294i	0.318478	−	0.551620i	0.980171	+	0.198155i	$0.0634949\pi$
$8$			11.3212i			0.176894i
$9$		0			0
$10$	−12.3370			−0.123370
$11$	−49.9968	−	28.8657i	−0.413197	−	0.238559i	0.278965	−	0.960301i	$-0.410009\pi$
$11$	−49.9968	−	28.8657i	−0.413197	−	0.238559i	−0.692162	+	0.721742i	$0.743342\pi$
$12$		0			0
$13$	36.6478	+	63.4758i	0.216851	+	0.375597i	0.953844	−	0.300304i	$-0.0970882\pi$
$13$	36.6478	+	63.4758i	0.216851	+	0.375597i	−0.736993	+	0.675901i	$0.763755\pi$
$14$	−9.60051	+	5.54285i	−0.0489822	+	0.0282799i
$15$		0			0
$16$	−124.980	+	216.472i	−0.488204	+	0.845594i
$17$			386.985i			1.33905i	0.742791	+	0.669524i	$0.233502\pi$
$17$			386.985i			1.33905i	−0.742791	+	0.669524i	$0.766498\pi$
$18$		0			0
$19$	115.791			0.320750			0.160375	−	0.987056i	$-0.448730\pi$
$19$	115.791			0.320750			0.160375	+	0.987056i	$0.448730\pi$
$20$	−477.491	−	275.679i	−1.19373	−	0.689199i
$21$		0			0
$22$	10.2527	+	17.7583i	0.0211833	+	0.0366906i
$23$	474.852	−	274.156i	0.897641	−	0.518253i	0.0212066	−	0.999775i	$-0.493249\pi$
$23$	474.852	−	274.156i	0.897641	−	0.518253i	0.876434	+	0.481522i	$0.159916\pi$
$24$		0			0
$25$	290.719	−	503.539i	0.465150	−	0.805663i
$26$		−	26.0337i		−	0.0385113i
$27$		0			0
$28$	−495.436			−0.631934
$29$	680.082	+	392.645i	0.808658	+	0.466879i	0.846490	−	0.532405i	$-0.178712\pi$
$29$	680.082	+	392.645i	0.808658	+	0.466879i	−0.0378313	+	0.999284i	$0.512045\pi$
$30$		0			0
$31$	−272.367	−	471.753i	−0.283420	−	0.490898i	0.688805	−	0.724947i	$-0.258136\pi$
$31$	−272.367	−	471.753i	−0.283420	−	0.490898i	−0.972225	+	0.234049i	$0.924802\pi$
$32$	233.759	−	134.961i	0.228280	−	0.131798i
$33$		0			0
$34$	68.7261	−	119.037i	0.0594516	−	0.102973i
$35$		−	1084.07i		−	0.884957i
$36$		0			0
$37$	898.827			0.656557			0.328279	−	0.944581i	$-0.393532\pi$
$37$	898.827			0.656557			0.328279	+	0.944581i	$0.393532\pi$
$38$	−35.6175	−	20.5637i	−0.0246658	−	0.0142408i
$39$		0			0
$40$	196.614	+	340.546i	0.122884	+	0.212841i
$41$	−2242.01	+	1294.43i	−1.33374	+	0.770034i	−0.985870	−	0.167510i	$-0.946427\pi$
$41$	−2242.01	+	1294.43i	−1.33374	+	0.770034i	−0.347867	+	0.937544i	$0.613094\pi$
$42$		0			0
$43$	−1000.05	+	1732.14i	−0.540862	+	0.936801i	0.457993	+	0.888956i	$0.348569\pi$
$43$	−1000.05	+	1732.14i	−0.540862	+	0.936801i	−0.998855	+	0.0478447i	$0.984765\pi$
$44$			916.419i			0.473357i
$45$		0			0
$46$	−194.753			−0.0920385
$47$	702.646	+	405.673i	0.318083	+	0.183645i	0.650538	−	0.759474i	$-0.274544\pi$
$47$	702.646	+	405.673i	0.318083	+	0.183645i	−0.332455	+	0.943119i	$0.607877\pi$
$48$		0			0
$49$	713.441	+	1235.72i	0.297143	+	0.514667i
$50$	−178.851	+	103.260i	−0.0715404	+	0.0413039i
$51$		0			0
$52$	581.741	−	1007.61i	0.215141	−	0.372635i
$53$		−	2221.00i		−	0.790672i	−0.918537	−	0.395336i	$-0.870628\pi$
$53$		−	2221.00i		−	0.790672i	0.918537	−	0.395336i	$-0.129372\pi$
$54$		0			0
$55$	−2005.23			−0.662886
$56$	306.005	+	176.672i	0.0975781	+	0.0563368i
$57$		0			0
$58$	−139.463	−	241.557i	−0.0414574	−	0.0718064i
$59$	−1309.65	+	756.128i	−0.376229	+	0.217216i	−0.676176	−	0.736740i	$-0.736364\pi$
$59$	−1309.65	+	756.128i	−0.376229	+	0.217216i	0.299947	+	0.953956i	$0.403031\pi$
$60$		0			0
$61$	951.281	−	1647.67i	0.255652	−	0.442802i	−0.709420	−	0.704786i	$-0.751043\pi$
$61$	951.281	−	1647.67i	0.255652	−	0.442802i	0.965072	+	0.261983i	$0.0843765\pi$
$62$			193.483i			0.0503337i
$63$		0			0
$64$	3903.49			0.953001
$65$	2204.76	+	1272.92i	0.521836	+	0.301282i
$66$		0			0
$67$	−2253.55	−	3903.26i	−0.502015	−	0.869516i	−0.999997	−	0.00232883i	$-0.999259\pi$
$67$	−2253.55	−	3903.26i	−0.502015	−	0.869516i	0.497982	−	0.867187i	$-0.334075\pi$
$68$	5319.94	−	3071.47i	1.15051	−	0.664244i
$69$		0			0
$70$	−192.524	+	333.462i	−0.0392907	+	0.0680535i
$71$		−	3993.54i		−	0.792213i	−0.918205	−	0.396106i	$-0.870361\pi$
$71$		−	3993.54i		−	0.792213i	0.918205	−	0.396106i	$-0.129639\pi$
$72$		0			0
$73$	−3436.70			−0.644905			−0.322452	−	0.946586i	$-0.604507\pi$
$73$	−3436.70			−0.644905			−0.322452	+	0.946586i	$0.604507\pi$
$74$	−276.480	−	159.626i	−0.0504895	−	0.0291501i
$75$		0			0
$76$	−919.023	−	1591.80i	−0.159111	−	0.275588i
$77$	−1560.44	+	900.923i	−0.263188	+	0.151952i
$78$		0			0
$79$	−601.388	+	1041.63i	−0.0963608	+	0.166902i	−0.910176	−	0.414222i	$-0.864054\pi$
$79$	−601.388	+	1041.63i	−0.0963608	+	0.166902i	0.813815	+	0.581124i	$0.197387\pi$
$80$			8682.07i			1.35657i
$81$		0			0
$82$	919.529			0.136753
$83$	−8016.22	−	4628.17i	−1.16363	−	0.671820i	−0.211456	−	0.977387i	$-0.567821\pi$
$83$	−8016.22	−	4628.17i	−1.16363	−	0.671820i	−0.952170	+	0.305567i	$0.901154\pi$
$84$		0			0
$85$	6720.72	+	11640.6i	0.930204	+	1.61116i
$86$	615.236	−	355.207i	0.0831850	−	0.0480269i
$87$		0			0
$88$	326.794	−	566.024i	0.0421996	−	0.0730919i
$89$			8929.99i			1.12738i	0.825986	+	0.563691i	$0.190619\pi$
$89$			8929.99i			1.12738i	−0.825986	+	0.563691i	$0.809381\pi$
$90$		0			0
$91$	2287.62			0.276249
$92$	−7537.72	−	4351.91i	−0.890563	−	0.514167i
$93$		0			0
$94$	−144.090	−	249.571i	−0.0163071	−	0.0282448i
$95$	3483.03	−	2010.93i	0.385932	−	0.222818i
$96$		0			0
$97$	−3335.14	+	5776.64i	−0.354463	+	0.613948i	−0.987026	−	0.160561i	$-0.948670\pi$
$97$	−3335.14	+	5776.64i	−0.354463	+	0.613948i	0.632563	+	0.774509i	$0.282003\pi$
$98$		−	506.811i		−	0.0527708i
$99$		0			0
$100$	−9229.64			−0.922964
$101$	7924.19	+	4575.03i	0.776805	+	0.448489i	0.835297	−	0.549799i	$-0.185296\pi$
$101$	7924.19	+	4575.03i	0.776805	+	0.448489i	−0.0584918	+	0.998288i	$0.518629\pi$
$102$		0			0
$103$	−7656.20	−	13260.9i	−0.721670	−	1.24997i	−0.960330	−	0.278866i	$-0.910041\pi$
$103$	−7656.20	−	13260.9i	−0.721670	−	1.24997i	0.238660	−	0.971103i	$-0.423292\pi$
$104$	−718.622	+	414.897i	−0.0664406	+	0.0383595i
$105$		0			0
$106$	−394.435	+	683.182i	−0.0351046	+	0.0608029i
$107$		−	6099.28i		−	0.532735i	−0.963872	−	0.266367i	$-0.914177\pi$
$107$		−	6099.28i		−	0.532735i	0.963872	−	0.266367i	$-0.0858234\pi$
$108$		0			0
$109$	15169.5			1.27679			0.638393	−	0.769710i	$-0.279599\pi$
$109$	15169.5			1.27679			0.638393	+	0.769710i	$0.279599\pi$
$110$	616.812	+	356.116i	0.0509762	+	0.0294311i
$111$		0			0
$112$	3900.74	+	6756.28i	0.310964	+	0.538606i
$113$	1189.11	−	686.532i	0.0931246	−	0.0537655i	−0.452714	−	0.891656i	$-0.649544\pi$
$113$	1189.11	−	686.532i	0.0931246	−	0.0537655i	0.545839	+	0.837890i	$0.316211\pi$
$114$		0			0
$115$	9522.48	−	16493.4i	0.720036	−	1.24714i
$116$		−	12465.6i		−	0.926396i
$117$		0			0
$118$	537.135			0.0385762
$119$	10460.0	+	6039.06i	0.738646	+	0.426457i
$120$		0			0
$121$	−5654.04	−	9793.09i	−0.386179	−	0.668881i
$122$	−585.231	+	337.883i	−0.0393195	+	0.0227011i
$123$		0			0
$124$	−4323.51	+	7488.53i	−0.281185	+	0.487027i
$125$			1513.10i			0.0968386i
$126$		0			0
$127$	−19152.4			−1.18745			−0.593726	−	0.804667i	$-0.702344\pi$
$127$	−19152.4			−1.18745			−0.593726	+	0.804667i	$0.702344\pi$
$128$	−4940.87	−	2852.61i	−0.301567	−	0.174110i
$129$		0			0
$130$	−452.124	−	783.102i	−0.0267529	−	0.0463374i
$131$	2615.39	−	1510.00i	0.152403	−	0.0879902i	−0.421859	−	0.906661i	$-0.638622\pi$
$131$	2615.39	−	1510.00i	0.152403	−	0.0879902i	0.574262	+	0.818671i	$0.305289\pi$
$132$		0			0
$133$	1806.97	−	3129.76i	0.102152	−	0.176932i
$134$			1600.86i			0.0891548i
$135$		0			0
$136$	−4381.13			−0.236869
$137$	8788.30	+	5073.93i	0.468235	+	0.270336i	0.715501	−	0.698612i	$-0.246199\pi$
$137$	8788.30	+	5073.93i	0.468235	+	0.270336i	−0.247266	+	0.968948i	$0.579532\pi$
$138$		0			0
$139$	17563.2	+	30420.3i	0.909021	+	1.57447i	0.815427	+	0.578860i	$0.196502\pi$
$139$	17563.2	+	30420.3i	0.909021	+	1.57447i	0.0935938	+	0.995610i	$0.470165\pi$
$140$	−14902.9	+	8604.19i	−0.760352	+	0.438989i
$141$		0			0
$142$	−709.229	+	1228.42i	−0.0351730	+	0.0609214i
$143$		−	4231.45i		−	0.206927i
$144$		0			0
$145$	27276.1			1.29732
$146$	1057.13	+	610.336i	0.0495934	+	0.0286328i
$147$		0			0
$148$	−7133.92	−	12356.3i	−0.325690	−	0.564112i
$149$	−32373.7	+	18691.0i	−1.45821	+	0.841899i	−0.998923	−	0.0463890i	$-0.985229\pi$
$149$	−32373.7	+	18691.0i	−1.45821	+	0.841899i	−0.459288	+	0.888288i	$0.651895\pi$
$150$		0			0
$151$	−16635.0	+	28812.7i	−0.729573	+	1.26366i	0.227490	+	0.973780i	$0.426948\pi$
$151$	−16635.0	+	28812.7i	−0.729573	+	1.26366i	−0.957064	+	0.289878i	$0.906385\pi$
$152$			1310.89i			0.0567387i
$153$		0			0
$154$	639.993			0.0269857
$155$	−16385.8	−	9460.33i	−0.682030	−	0.393770i
$156$		0			0
$157$	−4040.16	−	6997.77i	−0.163908	−	0.283897i	0.772359	−	0.635186i	$-0.219077\pi$
$157$	−4040.16	−	6997.77i	−0.163908	−	0.283897i	−0.936267	+	0.351289i	$0.885743\pi$
$158$	369.975	−	213.605i	0.0148204	−	0.00855654i
$159$		0			0
$160$	4687.71	−	8119.35i	0.183114	−	0.317162i
$161$		−	17113.3i		−	0.660209i
$162$		0			0
$163$	−25427.1			−0.957022			−0.478511	−	0.878081i	$-0.658823\pi$
$163$	−25427.1			−0.957022			−0.478511	+	0.878081i	$0.658823\pi$
$164$	35589.4	+	20547.5i	1.32322	+	0.763962i
$165$		0			0
$166$	1643.87	+	2847.26i	0.0596555	+	0.103326i
$167$	30356.6	−	17526.4i	1.08848	−	0.628434i	0.155309	−	0.987866i	$-0.450363\pi$
$167$	30356.6	−	17526.4i	1.08848	−	0.628434i	0.933171	+	0.359432i	$0.117029\pi$
$168$		0			0
$169$	11594.4	−	20082.1i	0.405951	−	0.703129i
$170$		−	4774.24i		−	0.165198i
$171$		0			0
$172$	31749.4			1.07319
$173$	−12731.0	−	7350.23i	−0.425372	−	0.245589i	0.272001	−	0.962297i	$-0.412315\pi$
$173$	−12731.0	−	7350.23i	−0.425372	−	0.245589i	−0.697373	+	0.716708i	$0.745648\pi$
$174$		0			0
$175$	−9073.58	−	15715.9i	−0.296280	−	0.513172i
$176$	12497.2	−	7215.28i	0.403449	−	0.232931i
$177$		0			0
$178$	1585.91	−	2746.88i	0.0500540	−	0.0866960i
$179$			37052.5i			1.15641i	0.815892	+	0.578205i	$0.196247\pi$
$179$			37052.5i			1.15641i	−0.815892	+	0.578205i	$0.803753\pi$
$180$		0			0
$181$	−39664.7			−1.21073			−0.605365	−	0.795948i	$-0.706973\pi$
$181$	−39664.7			−1.21073			−0.605365	+	0.795948i	$0.706973\pi$
$182$	−703.674	−	406.267i	−0.0212436	−	0.0122650i
$183$		0			0
$184$	3103.77	+	5375.89i	0.0916757	+	0.158787i
$185$	27037.0	−	15609.8i	0.789979	−	0.456094i
$186$		0			0
$187$	11170.6	−	19348.0i	0.319442	−	0.553290i
$188$		−	12879.2i		−	0.364395i
$189$		0			0
$190$	−1428.51			−0.0395710
$191$	−49915.1	−	28818.5i	−1.36825	−	0.789959i	−0.377545	−	0.925991i	$-0.623232\pi$
$191$	−49915.1	−	28818.5i	−1.36825	−	0.789959i	−0.990704	+	0.136032i	$0.956565\pi$
$192$		0			0
$193$	−2089.81	−	3619.67i	−0.0561039	−	0.0971748i	0.836609	−	0.547800i	$-0.184534\pi$
$193$	−2089.81	−	3619.67i	−0.0561039	−	0.0971748i	−0.892713	+	0.450625i	$0.851201\pi$
$194$	2051.79	−	1184.60i	0.0545167	−	0.0314752i
$195$		0			0
$196$	11325.1	−	19615.6i	0.294800	−	0.510609i
$197$			22191.5i			0.571812i	0.958258	+	0.285906i	$0.0922945\pi$
$197$			22191.5i			0.571812i	−0.958258	+	0.285906i	$0.907705\pi$
$198$		0			0
$199$	50608.7			1.27797			0.638983	−	0.769221i	$-0.279355\pi$
$199$	50608.7			1.27797			0.638983	+	0.769221i	$0.279355\pi$
$200$	5700.67	+	3291.28i	0.142517	+	0.0822820i
$201$		0			0
$202$	−1624.99	−	2814.57i	−0.0398244	−	0.0689779i
$203$	21225.9	−	12254.8i	0.515080	−	0.297382i
$204$		0			0
$205$	−44960.4	+	77873.6i	−1.06985	+	1.85303i
$206$			5438.77i			0.128164i
$207$		0			0
$208$	−18321.0			−0.423469
$209$	−5789.18	−	3342.38i	−0.132533	−	0.0765180i
$210$		0			0
$211$	4459.02	+	7723.26i	0.100156	+	0.173474i	0.911749	−	0.410749i	$-0.134733\pi$
$211$	4459.02	+	7723.26i	0.100156	+	0.173474i	−0.811593	+	0.584223i	$0.801399\pi$
$212$	−30532.4	+	17627.9i	−0.679343	+	0.392219i
$213$		0			0
$214$	−1083.19	+	1876.15i	−0.0236526	+	0.0409675i
$215$			69471.4i			1.50290i
$216$		0			0
$217$	−17001.6			−0.361052
$218$	−4666.16	−	2694.01i	−0.0981853	−	0.0566873i
$219$		0			0
$220$	15915.4	+	27566.2i	0.328830	+	0.569550i
$221$	−24564.2	+	14182.1i	−0.502941	+	0.290373i
$222$		0			0
$223$	4248.76	−	7359.07i	0.0854384	−	0.147984i	−0.820140	−	0.572164i	$-0.806104\pi$
$223$	4248.76	−	7359.07i	0.0854384	−	0.147984i	0.905578	+	0.424180i	$0.139438\pi$
$224$		−	8424.49i		−	0.167899i
$225$		0			0
$226$	−487.695			−0.00954842
$227$	−16543.5	−	9551.40i	−0.321052	−	0.185360i	0.330809	−	0.943698i	$-0.392678\pi$
$227$	−16543.5	−	9551.40i	−0.321052	−	0.185360i	−0.651862	+	0.758338i	$0.726012\pi$
$228$		0			0
$229$	5361.51	+	9286.40i	0.102239	+	0.177083i	0.912607	−	0.408839i	$-0.134066\pi$
$229$	5361.51	+	9286.40i	0.102239	+	0.177083i	−0.810368	+	0.585921i	$0.800733\pi$
$230$	−5858.25	+	3382.26i	−0.110742	+	0.0639370i
$231$		0			0
$232$	−4445.21	+	7699.34i	−0.0825880	+	0.143047i
$233$		−	102200.i		−	1.88251i	−0.337694	−	0.941256i	$-0.609647\pi$
$233$		−	102200.i		−	1.88251i	0.337694	−	0.941256i	$-0.390353\pi$
$234$		0			0
$235$	28181.1			0.510296
$236$	20789.2	+	12002.7i	0.373262	+	0.215503i
$237$		0			0
$238$	−2145.00	−	3715.25i	−0.0378681	−	0.0655894i
$239$	−13440.9	+	7760.09i	−0.235305	+	0.135854i	−0.613017	−	0.790070i	$-0.710044\pi$
$239$	−13440.9	+	7760.09i	−0.235305	+	0.135854i	0.377712	+	0.925923i	$0.376711\pi$
$240$		0			0
$241$	35978.9	−	62317.3i	0.619461	−	1.07294i	−0.370123	−	0.928983i	$-0.620685\pi$
$241$	35978.9	−	62317.3i	0.619461	−	1.07294i	0.989584	−	0.143955i	$-0.0459820\pi$
$242$			4016.49i			0.0685830i
$243$		0			0
$244$	−30201.0			−0.507272
$245$	42921.1	+	24780.5i	0.715054	+	0.412837i
$246$		0			0
$247$	4243.48	+	7349.92i	0.0695550	+	0.120473i
$248$	5340.81	−	3083.52i	0.0868368	−	0.0501352i
$249$		0			0
$250$	268.718	−	465.433i	0.00429948	−	0.00744692i
$251$			41487.8i			0.658526i	0.944238	+	0.329263i	$0.106800\pi$
$251$			41487.8i			0.658526i	−0.944238	+	0.329263i	$0.893200\pi$
$252$		0			0
$253$	−31654.8			−0.494537
$254$	5891.31	+	3401.35i	0.0913155	+	0.0527210i
$255$		0			0
$256$	−30214.7	−	52333.4i	−0.461040	−	0.798545i
$257$	62812.2	−	36264.6i	0.950994	−	0.549057i	0.0576045	−	0.998339i	$-0.481654\pi$
$257$	62812.2	−	36264.6i	0.950994	−	0.549057i	0.893390	+	0.449283i	$0.148320\pi$
$258$		0			0
$259$	14026.6	−	24294.7i	0.209099	−	0.362170i
$260$		−	40412.2i		−	0.597813i
$261$		0			0
$262$	−1072.67			−0.0156265
$263$	74383.1	+	42945.1i	1.07538	+	0.620872i	0.929647	−	0.368451i	$-0.120112\pi$
$263$	74383.1	+	42945.1i	1.07538	+	0.620872i	0.145735	+	0.989324i	$0.453445\pi$
$264$		0			0
$265$	−38571.8	−	66808.4i	−0.549261	−	0.951347i
$266$	−1111.65	+	641.812i	−0.0157111	+	0.00907078i
$267$		0			0
$268$	−35772.5	+	61959.7i	−0.498057	+	0.862660i
$269$		−	88967.6i		−	1.22950i	−0.788724	−	0.614748i	$-0.789258\pi$
$269$		−	88967.6i		−	1.22950i	0.788724	−	0.614748i	$-0.210742\pi$
$270$		0			0
$271$	96541.6			1.31455			0.657273	−	0.753652i	$-0.271710\pi$
$271$	96541.6			1.31455			0.657273	+	0.753652i	$0.271710\pi$
$272$	−83771.3	−	48365.4i	−1.13229	−	0.653728i
$273$		0			0
$274$	−1802.20	−	3121.49i	−0.0240050	−	0.0415778i
$275$	−29070.0	+	16783.6i	−0.384397	+	0.221932i
$276$		0			0
$277$	11770.8	−	20387.6i	0.153407	−	0.265710i	−0.779071	−	0.626936i	$-0.784309\pi$
$277$	11770.8	−	20387.6i	0.153407	−	0.265710i	0.932478	+	0.361227i	$0.117642\pi$
$278$		−	12476.5i		−	0.161436i
$279$		0			0
$280$	12273.0			0.156543
$281$	50584.4	+	29204.9i	0.640626	+	0.369865i	0.784855	−	0.619679i	$-0.212737\pi$
$281$	50584.4	+	29204.9i	0.640626	+	0.369865i	−0.144230	+	0.989544i	$0.546070\pi$
$282$		0			0
$283$	38058.6	+	65919.5i	0.475204	+	0.823078i	0.999597	−	0.0283989i	$-0.00904087\pi$
$283$	38058.6	+	65919.5i	0.475204	+	0.823078i	−0.524393	+	0.851477i	$0.675708\pi$
$284$	−54899.9	+	31696.4i	−0.680667	+	0.392983i
$285$		0			0
$286$	−751.480	+	1301.60i	−0.00918724	+	0.0159128i
$287$			80800.3i			0.980956i
$288$		0			0
$289$	−66236.1			−0.793047
$290$	−8390.18	−	4844.07i	−0.0997643	−	0.0575990i
$291$		0			0
$292$	27276.8	+	47244.8i	0.319910	+	0.554100i
$293$	−121166.	+	69955.5i	−1.41139	+	0.814866i	−0.995519	−	0.0945573i	$-0.969856\pi$
$293$	−121166.	+	69955.5i	−1.41139	+	0.814866i	−0.415871	+	0.909424i	$0.636523\pi$
$294$		0			0
$295$	−26263.2	+	45489.2i	−0.301789	+	0.522714i
$296$			10175.8i			0.116141i
$297$		0			0
$298$	13277.6			0.149516
$299$	34804.5	+	20094.4i	0.389308	+	0.224767i
$300$		0			0
$301$	31212.5	+	54061.7i	0.344505	+	0.596701i
$302$	10233.9	−	5908.55i	0.112209	−	0.0647838i
$303$		0			0
$304$	−14471.6	+	25065.5i	−0.156592	+	0.271225i
$305$		−	66083.2i		−	0.710381i
$306$		0			0
$307$	−81796.8			−0.867880			−0.433940	−	0.900942i	$-0.642877\pi$
$307$	−81796.8			−0.867880			−0.433940	+	0.900942i	$0.642877\pi$
$308$	24770.2	+	14301.1i	0.261113	+	0.150754i
$309$		0			0
$310$	3360.19	+	5820.03i	0.0349656	+	0.0605622i
$311$	1474.59	−	851.354i	0.0152458	−	0.00880216i	−0.492358	−	0.870393i	$-0.663865\pi$
$311$	1474.59	−	851.354i	0.0152458	−	0.00880216i	0.507604	+	0.861591i	$0.330531\pi$
$312$		0			0
$313$	34980.1	−	60587.3i	0.357052	−	0.618433i	−0.630415	−	0.776259i	$-0.717115\pi$
$313$	34980.1	−	60587.3i	0.357052	−	0.618433i	0.987467	+	0.157826i	$0.0504484\pi$
$314$			2870.03i			0.0291090i
$315$		0			0
$316$	19092.7			0.191202
$317$	−101004.	−	58314.7i	−1.00512	−	0.580309i	−0.0953639	−	0.995442i	$-0.530401\pi$
$317$	−101004.	−	58314.7i	−1.00512	−	0.580309i	−0.909760	+	0.415134i	$0.863735\pi$
$318$		0			0
$319$	−22668.0	−	39262.1i	−0.222757	−	0.385826i
$320$	117418.	−	67791.6i	1.14666	−	0.662027i
$321$		0			0
$322$	−3039.21	+	5264.07i	−0.0293123	+	0.0507703i
$323$			44809.3i			0.429500i
$324$		0			0
$325$	42616.8			0.403472
$326$	7821.42	+	4515.70i	0.0735954	+	0.0424903i
$327$		0			0
$328$	−14654.5	−	25382.3i	−0.136214	−	0.235930i
$329$	21930.2	−	12661.4i	0.202605	−	0.116974i
$330$		0			0
$331$	−50418.1	+	87326.8i	−0.460183	+	0.797061i	−0.998970	−	0.0453817i	$-0.985550\pi$
$331$	−50418.1	+	87326.8i	−0.460183	+	0.797061i	0.538787	+	0.842442i	$0.318883\pi$
$332$			146934.i			1.33305i
$333$		0			0
$334$	−12450.3			−0.111606
$335$	−135575.	−	78274.3i	−1.20806	−	0.697476i
$336$		0			0
$337$	−20047.2	−	34722.8i	−0.176520	−	0.305742i	0.764166	−	0.645020i	$-0.223151\pi$
$337$	−20047.2	−	34722.8i	−0.176520	−	0.305742i	−0.940686	+	0.339277i	$0.889817\pi$
$338$	−7132.90	+	4118.18i	−0.0624356	+	0.0360472i
$339$		0			0
$340$	106684.	−	184782.i	0.922869	−	1.59846i
$341$			31448.2i			0.270450i
$342$		0			0
$343$	119471.			1.01549
$344$	−19609.9	−	11321.8i	−0.165714	−	0.0956751i
$345$		0			0
$346$	2610.71	+	4521.88i	0.0218075	+	0.0377717i
$347$	196035.	−	113181.i	1.62808	−	0.939971i	0.643412	−	0.765520i	$-0.277518\pi$
$347$	196035.	−	113181.i	1.62808	−	0.939971i	0.984666	−	0.174451i	$-0.0558150\pi$
$348$		0			0
$349$	−39799.1	+	68934.1i	−0.326755	+	0.565957i	−0.981866	−	0.189576i	$-0.939289\pi$
$349$	−39799.1	+	68934.1i	−0.326755	+	0.565957i	0.655111	+	0.755533i	$0.272622\pi$
$350$			6445.64i			0.0526175i
$351$		0			0
$352$	−15583.0			−0.125766
$353$	121173.	+	69959.4i	0.972427	+	0.561431i	0.899975	−	0.435941i	$-0.143584\pi$
$353$	121173.	+	69959.4i	0.972427	+	0.561431i	0.0724520	+	0.997372i	$0.476918\pi$
$354$		0			0
$355$	−69355.5	−	120127.i	−0.550331	−	0.953202i
$356$	122762.	−	70876.6i	0.968642	−	0.559246i
$357$		0			0
$358$	6580.30	−	11397.4i	0.0513428	−	0.0889283i
$359$		−	211616.i		−	1.64195i	−0.570963	−	0.820976i	$-0.693430\pi$
$359$		−	211616.i		−	1.64195i	0.570963	−	0.820976i	$-0.306570\pi$
$360$		0			0
$361$	−116913.			−0.897119
$362$	12200.9	+	7044.20i	0.0931055	+	0.0537545i
$363$		0			0
$364$	−18156.6	−	31448.2i	−0.137035	−	0.237352i
$365$	−103377.	+	59684.8i	−0.775959	+	0.448000i
$366$		0			0
$367$	15996.8	−	27707.3i	0.118769	−	0.205713i	−0.800511	−	0.599318i	$-0.795439\pi$
$367$	15996.8	−	27707.3i	0.118769	−	0.205713i	0.919280	+	0.393604i	$0.128772\pi$
$368$			137056.i			1.01205i
$369$		0			0
$370$	−11088.8			−0.0809995
$371$	−60032.2	−	34659.6i	−0.436151	−	0.251812i
$372$		0			0
$373$	61573.9	+	106649.i	0.442567	+	0.766548i	0.997879	−	0.0650938i	$-0.0207347\pi$
$373$	61573.9	+	106649.i	0.442567	+	0.766548i	−0.555312	+	0.831642i	$0.687401\pi$
$374$	−6872.17	+	3967.65i	−0.0491305	+	0.0283655i
$375$		0			0
$376$	−4592.70	+	7954.79i	−0.0324857	+	0.0562669i
$377$			57558.3i			0.404972i
$378$		0			0
$379$	−116524.			−0.811218			−0.405609	−	0.914047i	$-0.632941\pi$
$379$	−116524.			−0.811218			−0.405609	+	0.914047i	$0.632941\pi$
$380$	−55289.1	−	31921.2i	−0.382889	−	0.221061i
$381$		0			0
$382$	10236.0	+	17729.2i	0.0701459	+	0.121496i
$383$	−156848.	+	90556.2i	−1.06925	+	0.617334i	−0.927978	−	0.372636i	$-0.878454\pi$
$383$	−156848.	+	90556.2i	−1.06925	+	0.617334i	−0.141277	+	0.989970i	$0.545121\pi$
$384$		0			0
$385$	−31292.5	+	54200.2i	−0.211115	+	0.365661i
$386$			1484.55i			0.00996371i
$387$		0			0
$388$	105883.			0.703336
$389$	44017.9	+	25413.7i	0.290891	+	0.167946i	0.638343	−	0.769752i	$-0.279620\pi$
$389$	44017.9	+	25413.7i	0.290891	+	0.167946i	−0.347453	+	0.937697i	$0.612953\pi$
$390$		0			0
$391$	106094.	+	183760.i	0.693965	+	1.20198i
$392$	−13989.8	+	8077.01i	−0.0910414	+	0.0525628i
$393$		0			0
$394$	3941.06	−	6826.12i	0.0253876	−	0.0439726i
$395$			41777.0i			0.267758i
$396$		0			0
$397$	228710.			1.45112			0.725561	−	0.688158i	$-0.241580\pi$
$397$	228710.			1.45112			0.725561	+	0.688158i	$0.241580\pi$
$398$	−15567.3	−	8987.80i	−0.0982761	−	0.0567397i
$399$		0			0
$400$	72668.1	+	125865.i	0.454176	+	0.786655i
$401$	−163618.	+	94464.9i	−1.01752	+	0.587465i	−0.913384	−	0.407099i	$-0.866541\pi$
$401$	−163618.	+	94464.9i	−1.01752	+	0.587465i	−0.104134	+	0.994563i	$0.533207\pi$
$402$		0			0
$403$	19963.3	−	34577.4i	0.122920	−	0.212903i
$404$		−	145247.i		−	0.889904i
$405$		0			0
$406$	−8705.50			−0.0528131
$407$	−44938.5	−	25945.2i	−0.271287	−	0.156628i
$408$		0			0
$409$	−138713.	−	240258.i	−0.829223	−	1.43626i	−0.898649	−	0.438669i	$-0.855450\pi$
$409$	−138713.	−	240258.i	−0.829223	−	1.43626i	0.0694256	−	0.997587i	$-0.477883\pi$
$410$	27659.7	−	15969.4i	0.164543	−	0.0949992i
$411$		0			0
$412$	−121533.	+	210502.i	−0.715980	+	1.24011i
$413$			47198.8i			0.276714i
$414$		0			0
$415$	−321508.			−1.86679
$416$	17133.5	+	9892.04i	0.0990056	+	0.0571609i
$417$		0			0
$418$	1187.17	+	2056.24i	0.00679456	+	0.0117685i
$419$	88699.9	−	51210.9i	0.505237	−	0.291699i	−0.225637	−	0.974212i	$-0.572446\pi$
$419$	88699.9	−	51210.9i	0.505237	−	0.291699i	0.730874	+	0.682513i	$0.239113\pi$
$420$		0			0
$421$	−23567.9	+	40820.8i	−0.132971	+	0.230312i	−0.924821	−	0.380404i	$-0.875785\pi$
$421$	−23567.9	+	40820.8i	−0.132971	+	0.230312i	0.791850	+	0.610716i	$0.209118\pi$
$422$		−	3167.58i		−	0.0177870i
$423$		0			0
$424$	25144.3			0.139865
$425$	194862.	+	112504.i	1.07882	+	0.622857i
$426$		0			0
$427$	−29690.3	−	51425.1i	−0.162839	−	0.282046i
$428$	−83847.7	+	48409.5i	−0.457724	+	0.264267i
$429$		0			0
$430$	12337.7	−	21369.5i	0.0667262	−	0.115573i
$431$		−	45556.1i		−	0.245240i	−0.992454	−	0.122620i	$-0.960870\pi$
$431$		−	45556.1i		−	0.245240i	0.992454	−	0.122620i	$-0.0391297\pi$
$432$		0			0
$433$	209599.			1.11793			0.558965	−	0.829192i	$-0.311199\pi$
$433$	209599.			1.11793			0.558965	+	0.829192i	$0.311199\pi$
$434$	5229.72	+	3019.38i	0.0277651	+	0.0160302i
$435$		0			0
$436$	−120399.	−	208537.i	−0.633360	−	1.09701i
$437$	54983.5	−	31744.8i	0.287919	−	0.166230i
$438$		0			0
$439$	91842.1	−	159075.i	0.476555	−	0.825417i	−0.523084	−	0.852281i	$-0.675219\pi$
$439$	91842.1	−	159075.i	0.476555	−	0.825417i	0.999639	+	0.0268637i	$0.00855202\pi$
$440$		−	22701.6i		−	0.117260i
$441$		0			0
$442$	10074.6			0.0515685
$443$	100410.	+	57971.5i	0.511644	+	0.295398i	0.733509	−	0.679680i	$-0.237881\pi$
$443$	100410.	+	57971.5i	0.511644	+	0.295398i	−0.221865	+	0.975077i	$0.571215\pi$
$444$		0			0
$445$	155086.	+	268617.i	0.783165	+	1.35648i
$446$	−2613.85	+	1509.11i	−0.0131405	+	0.00758666i
$447$		0			0
$448$	60915.7	−	105509.i	0.303510	−	0.525695i
$449$		−	328940.i		−	1.63164i	−0.578305	−	0.815820i	$-0.696286\pi$
$449$		−	328940.i		−	1.63164i	0.578305	−	0.815820i	$-0.303714\pi$
$450$		0			0
$451$	149458.			0.734795
$452$	−18875.7	−	10897.9i	−0.0923903	−	0.0533416i
$453$		0			0
$454$	3392.54	+	5876.05i	0.0164594	+	0.0285084i
$455$	68812.3	−	39728.8i	0.332387	−	0.191904i
$456$		0			0
$457$	106369.	−	184236.i	0.509308	−	0.882148i	−0.490634	−	0.871366i	$-0.663235\pi$
$457$	106369.	−	184236.i	0.509308	−	0.882148i	0.999942	−	0.0107819i	$-0.00343204\pi$
$458$		−	3808.68i		−	0.0181570i
$459$		0			0
$460$	−302317.			−1.42872
$461$	41957.2	+	24224.0i	0.197426	+	0.113984i	0.595454	−	0.803389i	$-0.296972\pi$
$461$	41957.2	+	24224.0i	0.197426	+	0.113984i	−0.398028	+	0.917373i	$0.630305\pi$
$462$		0			0
$463$	−84550.6	−	146446.i	−0.394416	−	0.683149i	0.598610	−	0.801040i	$-0.295720\pi$
$463$	−84550.6	−	146446.i	−0.394416	−	0.683149i	−0.993026	+	0.117892i	$0.962386\pi$
$464$	−169993.	+	98145.8i	−0.789580	+	0.455864i
$465$		0			0
$466$	−18150.0	+	31436.8i	−0.0835806	+	0.144766i
$467$			54646.4i			0.250569i	0.992121	+	0.125285i	$0.0399844\pi$
$467$			54646.4i			0.250569i	−0.992121	+	0.125285i	$0.960016\pi$
$468$		0			0
$469$	−140670.			−0.639524
$470$	−8668.55	−	5004.79i	−0.0392420	−	0.0226564i
$471$		0			0
$472$	−8560.28	−	14826.8i	−0.0384241	−	0.0665525i
$473$	99999.1	−	57734.5i	0.446965	−	0.258055i
$474$		0			0
$475$	33662.6	−	58305.3i	0.149197	−	0.258417i
$476$		−	191726.i		−	0.846189i
$477$		0			0
$478$	5512.58			0.0241268
$479$	120011.	+	69288.6i	0.523060	+	0.301989i	0.738186	−	0.674597i	$-0.235683\pi$
$479$	120011.	+	69288.6i	0.523060	+	0.301989i	−0.215126	+	0.976586i	$0.569016\pi$
$480$		0			0
$481$	32940.0	+	57053.7i	0.142375	+	0.246601i
$482$	−22134.3	+	12779.3i	−0.0952735	+	0.0550062i
$483$		0			0
$484$	−89751.4	+	155454.i	−0.383134	+	0.663607i
$485$			231684.i			0.984948i
$486$		0			0
$487$	23464.1			0.0989340			0.0494670	−	0.998776i	$-0.484248\pi$
$487$	23464.1			0.0989340			0.0494670	+	0.998776i	$0.484248\pi$
$488$	18653.6	+	10769.6i	0.0783289	+	0.0452232i
$489$		0			0
$490$	−8801.74	−	15245.1i	−0.0366586	−	0.0634946i
$491$	−64368.8	+	37163.4i	−0.267001	+	0.154153i	−0.627524	−	0.778597i	$-0.715932\pi$
$491$	−64368.8	+	37163.4i	−0.267001	+	0.154153i	0.360523	+	0.932750i	$0.382598\pi$
$492$		0			0
$493$	−151948.	+	263181.i	−0.625173	+	1.08283i
$494$		−	3014.46i		−	0.0123525i
$495$		0			0
$496$	136162.			0.553467
$497$	−107943.	−	62321.0i	−0.437001	−	0.252302i
$498$		0			0
$499$	9486.01	+	16430.2i	0.0380963	+	0.0659847i	0.884445	−	0.466645i	$-0.154537\pi$
$499$	9486.01	+	16430.2i	0.0380963	+	0.0659847i	−0.846349	+	0.532629i	$0.821204\pi$
$500$	20800.9	−	12009.4i	0.0832034	−	0.0480375i
$501$		0			0
$502$	7367.97	−	12761.7i	0.0292375	−	0.0506409i
$503$			117856.i			0.465818i	0.972498	+	0.232909i	$0.0748245\pi$
$503$			117856.i			0.465818i	−0.972498	+	0.232909i	$0.925175\pi$
$504$		0			0
$505$	317816.			1.24622
$506$	9737.06	+	5621.69i	0.0380300	+	0.0219567i
$507$		0			0
$508$	152011.	+	263291.i	0.589045	+	1.02026i
$509$	−158881.	+	91730.2i	−0.613250	+	0.354060i	−0.774236	−	0.632897i	$-0.781866\pi$
$509$	−158881.	+	91730.2i	−0.613250	+	0.354060i	0.160986	+	0.986957i	$0.448532\pi$
$510$		0			0
$511$	−53631.2	+	92891.9i	−0.205388	+	0.355743i
$512$			112747.i			0.430097i
$513$		0			0
$514$	−25761.5			−0.0975091
$515$	−460602.	−	265929.i	−1.73665	−	1.00265i
$516$		0			0
$517$	−23420.0	−	40564.7i	−0.0876207	−	0.151763i
$518$	−8629.19	+	4982.06i	−0.0321596	+	0.0185673i
$519$		0			0
$520$	−14410.9	+	24960.5i	−0.0532949	+	0.0923094i
$521$			409498.i			1.50861i	0.656526	+	0.754303i	$0.272025\pi$
$521$			409498.i			1.50861i	−0.656526	+	0.754303i	$0.727975\pi$
$522$		0			0
$523$	−211852.			−0.774513			−0.387256	−	0.921972i	$-0.626577\pi$
$523$	−211852.			−0.774513			−0.387256	+	0.921972i	$0.626577\pi$
$524$	−41516.4	−	23969.5i	−0.151202	−	0.0872964i
$525$		0			0
$526$	−15253.6	−	26420.0i	−0.0551315	−	0.0954906i
$527$	182561.	−	105402.i	0.657336	−	0.379513i
$528$		0			0
$529$	10402.4	−	18017.4i	0.0371724	−	0.0643845i
$530$			27400.5i			0.0975453i
$531$		0			0
$532$	−57367.0			−0.202693
$533$	−164330.	−	94875.7i	−0.578444	−	0.333965i
$534$		0			0
$535$	−105926.	−	183468.i	−0.370078	−	0.640994i
$536$	44189.5	−	25512.8i	0.153812	−	0.0888033i
$537$		0			0
$538$	−15800.1	+	27366.6i	−0.0545877	+	0.0945487i
$539$		−	82375.9i		−	0.283545i
$540$		0			0
$541$	44016.5			0.150391			0.0751954	−	0.997169i	$-0.476042\pi$
$541$	44016.5			0.150391			0.0751954	+	0.997169i	$0.476042\pi$
$542$	−29696.3	−	17145.2i	−0.101089	−	0.0583638i
$543$		0			0
$544$	52227.8	+	90461.2i	0.176483	+	0.305678i
$545$	456304.	−	263447.i	1.53625	−	0.886953i
$546$		0			0
$547$	21429.6	−	37117.1i	0.0716207	−	0.124051i	−0.827991	−	0.560741i	$-0.810516\pi$
$547$	21429.6	−	37117.1i	0.0716207	−	0.124051i	0.899612	+	0.436691i	$0.143850\pi$
$548$		−	161085.i		−	0.536408i
$549$		0			0
$550$	11922.6			0.0394137
$551$	78747.3	+	45464.8i	0.259378	+	0.149752i
$552$		0			0
$553$	18769.8	+	32510.3i	0.0613776	+	0.106309i
$554$	−7241.43	+	4180.84i	−0.0235942	+	0.0136221i
$555$		0			0
$556$	278795.	−	482888.i	0.901853	−	1.56206i
$557$			311007.i			1.00244i	0.865319	+	0.501222i	$0.167116\pi$
$557$			311007.i			1.00244i	−0.865319	+	0.501222i	$0.832884\pi$
$558$		0			0
$559$	−146599.			−0.469145
$560$	234671.	+	135487.i	0.748314	+	0.432039i
$561$		0			0
$562$	−10373.2	−	17967.0i	−0.0328429	−	0.0568856i
$563$	247482.	−	142884.i	0.780777	−	0.450782i	−0.0559288	−	0.998435i	$-0.517812\pi$
$563$	247482.	−	142884.i	0.780777	−	0.450782i	0.836705	+	0.547653i	$0.184479\pi$
$564$		0			0
$565$	23845.9	−	41302.2i	0.0746992	−	0.129383i
$566$		−	27035.9i		−	0.0843933i
$567$		0			0
$568$	45211.7			0.140137
$569$	118371.	+	68341.3i	0.365611	+	0.211086i	0.671539	−	0.740969i	$-0.265633\pi$
$569$	118371.	+	68341.3i	0.365611	+	0.211086i	−0.305928	+	0.952055i	$0.598967\pi$
$570$		0			0
$571$	14255.0	+	24690.4i	0.0437215	+	0.0757279i	0.887058	−	0.461658i	$-0.152745\pi$
$571$	14255.0	+	24690.4i	0.0437215	+	0.0757279i	−0.843337	+	0.537386i	$0.819412\pi$
$572$	−58170.4	+	33584.7i	−0.177791	+	0.102648i
$573$		0			0
$574$	14349.6	−	24854.3i	0.0435529	−	0.0754358i
$575$		−	318809.i		−	0.964261i
$576$		0			0
$577$	−293742.			−0.882297			−0.441149	−	0.897434i	$-0.645429\pi$
$577$	−293742.			−0.882297			−0.441149	+	0.897434i	$0.645429\pi$
$578$	20374.3	+	11763.1i	0.0609856	+	0.0352101i
$579$		0			0
$580$	−216489.	−	374969.i	−0.643545	−	1.11465i
$581$	−250193.	+	144449.i	−0.741179	+	0.427920i
$582$		0			0
$583$	−64110.6	+	111043.i	−0.188622	+	0.326703i
$584$		−	38907.5i		−	0.114080i
$585$		0			0
$586$	49694.6			0.144715
$587$	−334334.	−	193028.i	−0.970295	−	0.560200i	−0.0709687	−	0.997479i	$-0.522609\pi$
$587$	−334334.	−	193028.i	−0.970295	−	0.560200i	−0.899326	+	0.437279i	$0.855942\pi$
$588$		0			0
$589$	−31537.6	−	54624.7i	−0.0909072	−	0.157456i
$590$	16157.2	−	9328.37i	0.0464154	−	0.0267980i
$591$		0			0
$592$	−112335.	+	194571.i	−0.320534	+	0.555180i
$593$		−	305581.i		−	0.868995i	−0.900673	−	0.434497i	$-0.856926\pi$
$593$		−	305581.i		−	0.868995i	0.900673	−	0.434497i	$-0.143074\pi$
$594$		0			0
$595$	419519.			1.18500
$596$	513896.	+	296698.i	1.44671	+	0.835260i
$597$		0			0
$598$	−7137.28	−	12362.1i	−0.0199586	−	0.0345693i
$599$	−229270.	+	132369.i	−0.638988	+	0.368920i	−0.784225	−	0.620477i	$-0.786939\pi$
$599$	−229270.	+	132369.i	−0.638988	+	0.368920i	0.145236	+	0.989397i	$0.453606\pi$
$600$		0			0
$601$	66101.5	−	114491.i	0.183005	−	0.316973i	−0.759898	−	0.650043i	$-0.774751\pi$
$601$	66101.5	−	114491.i	0.183005	−	0.316973i	0.942902	+	0.333069i	$0.108084\pi$
$602$		−	22172.6i		−	0.0611820i
$603$		0			0
$604$	528123.			1.44764
$605$	−340151.	−	196386.i	−0.929312	−	0.536538i
$606$		0			0
$607$	127073.	+	220097.i	0.344886	+	0.597360i	0.985333	−	0.170642i	$-0.0545843\pi$
$607$	127073.	+	220097.i	0.344886	+	0.597360i	−0.640447	+	0.768002i	$0.721251\pi$
$608$	27067.2	−	15627.3i	0.0732211	−	0.0422742i
$609$		0			0
$610$	−11736.0	+	20327.3i	−0.0315398	+	0.0546286i
$611$			59468.0i			0.159295i
$612$		0			0
$613$	−492878.			−1.31165			−0.655826	−	0.754912i	$-0.727680\pi$
$613$	−492878.			−1.31165			−0.655826	+	0.754912i	$0.727680\pi$
$614$	25160.8	+	14526.6i	0.0667403	+	0.0385325i
$615$		0			0
$616$	−10199.5	−	17666.1i	−0.0268793	−	0.0465564i
$617$	105029.	−	60638.8i	0.275893	−	0.159287i	−0.355670	−	0.934612i	$-0.615747\pi$
$617$	105029.	−	60638.8i	0.275893	−	0.159287i	0.631563	+	0.775325i	$0.282414\pi$
$618$		0			0
$619$	−153682.	+	266185.i	−0.401090	+	0.694709i	−0.993858	−	0.110665i	$-0.964702\pi$
$619$	−153682.	+	266185.i	−0.401090	+	0.694709i	0.592768	+	0.805374i	$0.298035\pi$
$620$			300344.i			0.781331i
$621$		0			0
$622$	−604.780			−0.00156321
$623$	241372.	+	139356.i	0.621886	+	0.359046i
$624$		0			0
$625$	207977.	+	360227.i	0.532421	+	0.922181i
$626$	−21519.8	+	12424.5i	−0.0549149	+	0.0317051i
$627$		0			0
$628$	−64132.9	+	111081.i	−0.162615	+	0.281658i
$629$			347832.i			0.879161i
$630$		0			0
$631$	−254196.			−0.638425			−0.319212	−	0.947683i	$-0.603418\pi$
$631$	−254196.			−0.638425			−0.319212	+	0.947683i	$0.603418\pi$
$632$	−11792.5	−	6808.43i	−0.0295239	−	0.0170456i
$633$		0			0
$634$	20712.6	+	35875.3i	0.0515296	+	0.0892519i
$635$	−576112.	+	332618.i	−1.42876	+	0.824895i
$636$		0			0
$637$	−52292.1	+	90572.5i	−0.128872	+	0.223212i
$638$			16102.8i			0.0395602i
$639$		0			0
$640$	−198164.			−0.483799
$641$	−316954.	−	182993.i	−0.771400	−	0.445368i	0.0619737	−	0.998078i	$-0.480261\pi$
$641$	−316954.	−	182993.i	−0.771400	−	0.445368i	−0.833374	+	0.552710i	$0.813594\pi$
$642$		0			0
$643$	−115391.	−	199864.i	−0.279094	−	0.483406i	0.692066	−	0.721835i	$-0.256701\pi$
$643$	−115391.	−	199864.i	−0.279094	−	0.483406i	−0.971160	+	0.238429i	$0.923368\pi$
$644$	−235259.	+	135827.i	−0.567250	+	0.327502i
$645$		0			0
$646$	7957.85	−	13783.4i	0.0190691	−	0.0330287i
$647$		−	278596.i		−	0.665529i	−0.943010	−	0.332764i	$-0.892019\pi$
$647$		−	278596.i		−	0.665529i	0.943010	−	0.332764i	$-0.107981\pi$
$648$		0			0
$649$	87304.7			0.207276
$650$	−13109.0	−	7568.47i	−0.0310272	−	0.0179135i
$651$		0			0
$652$	201813.	+	349551.i	0.474738	+	0.822271i
$653$	67988.8	−	39253.4i	0.159445	−	0.0920557i	−0.418154	−	0.908376i	$-0.637323\pi$
$653$	67988.8	−	39253.4i	0.159445	−	0.0920557i	0.577600	+	0.816320i	$0.303990\pi$
$654$		0			0
$655$	52448.0	−	90842.6i	0.122249	−	0.211742i
$656$		−	647111.i		−	1.50373i
$657$		0			0
$658$	−8994.34			−0.0207739
$659$	742420.	+	428637.i	1.70954	+	0.987003i	0.935121	+	0.354328i	$0.115290\pi$
$659$	742420.	+	428637.i	1.70954	+	0.987003i	0.774418	+	0.632675i	$0.218043\pi$
$660$		0			0
$661$	−11172.0	−	19350.4i	−0.0255698	−	0.0442882i	0.852957	−	0.521981i	$-0.174807\pi$
$661$	−11172.0	−	19350.4i	−0.0255698	−	0.0442882i	−0.878527	+	0.477692i	$0.841473\pi$
$662$	31017.4	−	17907.9i	0.0707765	−	0.0408628i
$663$		0			0
$664$	52396.4	−	90753.2i	0.118841	−	0.205838i
$665$		−	125526.i		−	0.283850i
$666$		0			0
$667$	430584.			0.967846
$668$	−481876.	−	278211.i	−1.07990	−	0.623479i
$669$		0			0
$670$	27802.0	+	48154.6i	0.0619337	+	0.107272i
$671$	−95122.1	+	54918.8i	−0.211269	+	0.121976i
$672$		0			0
$673$	331739.	−	574588.i	0.732430	−	1.26861i	−0.223412	−	0.974724i	$-0.571719\pi$
$673$	331739.	−	574588.i	0.732430	−	1.26861i	0.955842	−	0.293882i	$-0.0949472\pi$
$674$			14241.1i			0.0313489i
$675$		0			0
$676$	−368095.			−0.805501
$677$	197558.	+	114060.i	0.431040	+	0.248861i	0.699790	−	0.714349i	$-0.253277\pi$
$677$	197558.	+	114060.i	0.431040	+	0.248861i	−0.268749	+	0.963210i	$0.586610\pi$
$678$		0			0
$679$	104093.	+	180294.i	0.225777	+	0.391058i
$680$	−131786.	+	76086.6i	−0.285004	+	0.164547i
$681$		0			0
$682$	5585.01	−	9673.52i	0.0120076	−	0.0207977i
$683$		−	53606.6i		−	0.114915i	−0.998348	−	0.0574575i	$-0.981701\pi$
$683$		−	53606.6i		−	0.114915i	0.998348	−	0.0574575i	$-0.0182994\pi$
$684$		0			0
$685$	352474.			0.751182
$686$	−36749.6	−	21217.4i	−0.0780916	−	0.0450862i
$687$		0			0
$688$	−249974.	−	432967.i	−0.528102	−	0.914699i
$689$	140980.	−	81394.6i	0.296974	−	0.171458i
$690$		0			0
$691$	−378663.	+	655863.i	−0.793043	+	1.37359i	0.131031	+	0.991378i	$0.458171\pi$
$691$	−378663.	+	655863.i	−0.793043	+	1.37359i	−0.924074	+	0.382213i	$0.875162\pi$
$692$			233353.i			0.487305i
$693$		0			0
$694$	−80400.9			−0.166933
$695$	1.05661e6	+	610036.i	2.18749	+	1.26295i
$696$		0			0
$697$	−500923.	−	867624.i	−1.03111	−	1.78594i
$698$	24484.5	−	14136.2i	0.0502552	−	0.0290149i
$699$		0			0
$700$	−144033.	+	249472.i	−0.293944	+	0.509126i
$701$		−	506359.i		−	1.03044i	−0.857058	−	0.515220i	$-0.827710\pi$
$701$		−	506359.i		−	1.03044i	0.857058	−	0.515220i	$-0.172290\pi$
$702$		0			0
$703$	104076.			0.210591
$704$	−195162.	−	112677.i	−0.393777	−	0.227347i
$705$		0			0
$706$	−24848.7	−	43039.2i	−0.0498534	−	0.0863485i
$707$	247321.	−	142791.i	0.494791	−	0.285668i
$708$		0			0
$709$	325622.	−	563993.i	0.647770	−	1.12197i	−0.335885	−	0.941903i	$-0.609035\pi$
$709$	325622.	−	563993.i	0.647770	−	1.12197i	0.983654	−	0.180067i	$-0.0576314\pi$
$710$			49268.4i			0.0977354i
$711$		0			0
$712$	−101098.			−0.199427
$713$	−258668.	−	149342.i	−0.508819	−	0.293767i
$714$		0			0
$715$	−73487.2	−	127284.i	−0.143747	−	0.248978i
$716$	509367.	−	294083.i	0.993584	−	0.573646i
$717$		0			0
$718$	−37581.8	+	65093.5i	−0.0729001	+	0.126267i
$719$			69724.6i			0.134874i	0.997724	+	0.0674370i	$0.0214822\pi$
$719$			69724.6i			0.134874i	−0.997724	+	0.0674370i	$0.978518\pi$
$720$		0			0
$721$	−477913.			−0.919345
$722$	35962.8	+	20763.1i	0.0689888	+	0.0398307i
$723$		0			0
$724$	314816.	+	545277.i	0.600591	+	1.04025i
$725$	395425.	−	228299.i	0.752294	−	0.434337i
$726$		0			0
$727$	373864.	−	647552.i	0.707367	−	1.22520i	−0.258463	−	0.966021i	$-0.583216\pi$
$727$	373864.	−	647552.i	0.707367	−	1.22520i	0.965830	−	0.259175i	$-0.0834506\pi$
$728$			25898.6i			0.0488667i
$729$		0			0
$730$	42398.6			0.0795620
$731$	−670313.	−	387006.i	−1.25442	−	0.724240i
$732$		0			0
$733$	−32869.3	−	56931.2i	−0.0611761	−	0.105960i	0.833815	−	0.552044i	$-0.186152\pi$
$733$	−32869.3	−	56931.2i	−0.0611761	−	0.105960i	−0.894991	+	0.446083i	$0.852818\pi$
$734$	−9841.29	+	5681.87i	−0.0182667	+	0.0105463i
$735$		0			0
$736$	74000.7	−	128173.i	0.136609	−	0.236614i
$737$			260201.i			0.479042i
$738$		0			0
$739$	977921.			1.79067			0.895334	−	0.445395i	$-0.146937\pi$
$739$	977921.			1.79067			0.895334	+	0.445395i	$0.146937\pi$
$740$	−429181.	−	247788.i	−0.783750	−	0.452498i
$741$		0			0
$742$	12310.7	+	21322.7i	0.0223601	+	0.0387288i
$743$	−437233.	+	252437.i	−0.792019	+	0.457272i	−0.840673	−	0.541543i	$-0.817840\pi$
$743$	−437233.	+	252437.i	−0.792019	+	0.457272i	0.0486539	+	0.998816i	$0.484507\pi$
$744$		0			0
$745$	−649209.	+	1.12446e6i	−1.16969	+	2.02597i
$746$		−	43740.5i		−	0.0785971i
$747$		0			0
$748$	−354640.			−0.633847
$749$	−164860.	−	95181.9i	−0.293867	−	0.169664i
$750$		0			0
$751$	266395.	+	461411.i	0.472332	+	0.818102i	0.999499	−	0.0316593i	$-0.0100792\pi$
$751$	266395.	+	461411.i	0.472332	+	0.818102i	−0.527167	+	0.849762i	$0.676746\pi$
$752$	−175634.	+	101402.i	−0.310579	+	0.179313i
$753$		0			0
$754$	10222.0	−	17705.0i	0.0179801	−	0.0311425i
$755$			1.15559e6i			2.02727i
$756$		0			0
$757$	−293571.			−0.512297			−0.256148	−	0.966637i	$-0.582454\pi$
$757$	−293571.			−0.512297			−0.256148	+	0.966637i	$0.582454\pi$
$758$	35843.0	+	20694.0i	0.0623830	+	0.0360168i
$759$		0			0
$760$	22766.1	+	39432.1i	0.0394150	+	0.0682688i
$761$	22249.2	−	12845.6i	0.0384190	−	0.0221812i	−0.480667	−	0.876903i	$-0.659606\pi$
$761$	22249.2	−	12845.6i	0.0384190	−	0.0221812i	0.519086	+	0.854722i	$0.326272\pi$
$762$		0			0
$763$	236727.	−	410022.i	0.406629	−	0.704301i
$764$			914920.i			1.56746i
$765$		0			0
$766$	64328.9			0.109635
$767$	−95991.7	−	55420.9i	−0.163171	−	0.0942069i
$768$		0			0
$769$	323572.	+	560443.i	0.547165	+	0.947717i	0.998467	+	0.0553463i	$0.0176263\pi$
$769$	323572.	+	560443.i	0.547165	+	0.947717i	−0.451302	+	0.892371i	$0.649040\pi$
$770$	19251.2	−	11114.7i	0.0324696	−	0.0187463i
$771$		0			0
$772$	−33173.4	+	57458.0i	−0.0556615	+	0.0964086i
$773$		−	610238.i		−	1.02127i	−0.859798	−	0.510634i	$-0.829411\pi$
$773$		−	610238.i		−	1.02127i	0.859798	−	0.510634i	$-0.170589\pi$
$774$		0			0
$775$	−316728.			−0.527331
$776$	−65398.4	−	37757.8i	−0.108604	−	0.0627023i
$777$		0			0
$778$	−9026.64	−	15634.6i	−0.0149131	−	0.0258302i
$779$	−259605.	+	149883.i	−0.427797	+	0.246989i
$780$		0			0
$781$	−115276.	+	199665.i	−0.188990	+	0.327340i
$782$		−	75366.6i		−	0.123244i
$783$		0			0
$784$	−356664.			−0.580266
$785$	−243059.	−	140330.i	−0.394432	−	0.227726i
$786$		0			0
$787$	290160.	+	502572.i	0.468477	+	0.811427i	0.999351	−	0.0360244i	$-0.0114694\pi$
$787$	290160.	+	502572.i	0.468477	+	0.811427i	−0.530874	+	0.847451i	$0.678136\pi$
$788$	305069.	−	176132.i	0.491299	−	0.283652i
$789$		0			0
$790$	7419.33	−	12850.7i	0.0118880	−	0.0205907i
$791$		−	42854.5i		−	0.0684926i
$792$		0			0
$793$	139449.			0.221753
$794$	−70351.5	−	40617.4i	−0.111592	−	0.0644276i
$795$		0			0
$796$	−401678.	−	695726.i	−0.633945	−	1.09802i
$797$	915508.	−	528569.i	1.44127	−	0.832118i	0.443336	−	0.896355i	$-0.353795\pi$
$797$	915508.	−	528569.i	1.44127	−	0.832118i	0.997935	+	0.0642373i	$0.0204615\pi$
$798$		0			0
$799$	−156989.	+	271913.i	−0.245910	+	0.425928i
$800$		−	156943.i		−	0.245223i
$801$		0			0
$802$	67105.5			0.104330
$803$	171824.	+	99202.7i	0.266473	+	0.153848i
$804$		0			0
$805$	−297205.	−	514774.i	−0.458631	−	0.794373i
$806$	−12281.5	+	7090.71i	−0.0189051	+	0.0109149i
$807$		0			0
$808$	−51794.8	+	89711.2i	−0.0793348	+	0.137412i
$809$			355969.i			0.543895i	0.962312	+	0.271947i	$0.0876677\pi$
$809$			355969.i			0.543895i	−0.962312	+	0.271947i	$0.912332\pi$
$810$		0			0
$811$	−136417.			−0.207409			−0.103704	−	0.994608i	$-0.533070\pi$
$811$	−136417.			−0.207409			−0.103704	+	0.994608i	$0.533070\pi$
$812$	−336937.	−	194531.i	−0.511019	−	0.295037i
$813$		0			0
$814$	9215.43	+	15961.6i	0.0139081	+	0.0240895i
$815$	−764857.	+	441590.i	−1.15150	+	0.664820i
$816$		0			0
$817$	−115797.	+	200567.i	−0.173482	+	0.300479i
$818$			98538.4i			0.147265i
$819$		0			0
$820$	1.42739e6			2.12282
$821$	394889.	+	227989.i	0.585854	+	0.338243i	0.763456	−	0.645860i	$-0.223501\pi$
$821$	394889.	+	227989.i	0.585854	+	0.338243i	−0.177603	+	0.984102i	$0.556834\pi$
$822$		0			0
$823$	−251795.	−	436122.i	−0.371747	−	0.643885i	0.618087	−	0.786109i	$-0.287908\pi$
$823$	−251795.	−	436122.i	−0.371747	−	0.643885i	−0.989834	+	0.142225i	$0.954574\pi$
$824$	150129.	−	86677.3i	0.221112	−	0.127659i
$825$		0			0
$826$	8382.22	−	14518.4i	0.0122857	−	0.0212794i
$827$		−	551861.i		−	0.806898i	−0.915002	−	0.403449i	$-0.867811\pi$
$827$		−	551861.i		−	0.806898i	0.915002	−	0.403449i	$-0.132189\pi$
$828$		0			0
$829$	−182308.			−0.265275			−0.132638	−	0.991165i	$-0.542345\pi$
$829$	−182308.			−0.265275			−0.132638	+	0.991165i	$0.542345\pi$
$830$	98896.3	+	57097.8i	0.143557	+	0.0828826i
$831$		0			0
$832$	143054.	+	247777.i	0.206659	+	0.357944i
$833$	−478203.	+	276091.i	−0.689164	+	0.397889i
$834$		0			0
$835$	608759.	−	1.05440e6i	0.873117	−	1.51228i
$836$			106113.i			0.151829i
$837$		0			0
$838$	−36379.0			−0.0518039
$839$	359993.	+	207842.i	0.511410	+	0.295263i	0.733413	−	0.679783i	$-0.237926\pi$
$839$	359993.	+	207842.i	0.511410	+	0.295263i	−0.222003	+	0.975046i	$0.571259\pi$
$840$		0			0
$841$	−45299.7	−	78461.4i	−0.0640477	−	0.110934i
$842$	14499.0	−	8371.03i	0.0204510	−	0.0118074i
$843$		0			0
$844$	70781.8	−	122598.i	0.0993658	−	0.172107i
$845$		−	805434.i		−	1.12802i
$846$		0			0
$847$	−352935.			−0.491958
$848$	480784.	+	277581.i	0.668587	+	0.386009i
$849$		0			0
$850$	−39959.9	−	69212.6i	−0.0553078	−	0.0957959i
$851$	426809.	−	246419.i	0.589352	−	0.340263i
$852$		0			0
$853$	−75135.3	+	130138.i	−0.103263	+	0.178857i	−0.913027	−	0.407898i	$-0.866262\pi$
$853$	−75135.3	+	130138.i	−0.103263	+	0.178857i	0.809764	+	0.586756i	$0.199595\pi$
$854$			21091.3i			0.0289192i
$855$		0			0
$856$	69051.1			0.0942374
$857$	−125373.	−	72383.9i	−0.170703	−	0.0985554i	0.412214	−	0.911087i	$-0.364755\pi$
$857$	−125373.	−	72383.9i	−0.170703	−	0.0985554i	−0.582917	+	0.812532i	$0.698089\pi$
$858$		0			0
$859$	−166948.	−	289163.i	−0.226254	−	0.391883i	0.730441	−	0.682976i	$-0.239315\pi$
$859$	−166948.	−	289163.i	−0.226254	−	0.391883i	−0.956695	+	0.291093i	$0.905981\pi$
$860$	955033.	−	551389.i	1.29128	−	0.745523i
$861$		0			0
$862$	−8090.47	+	14013.1i	−0.0108883	+	0.0188591i
$863$		−	1.13280e6i		−	1.52101i	−0.649330	−	0.760507i	$-0.724951\pi$
$863$		−	1.13280e6i		−	1.52101i	0.649330	−	0.760507i	$-0.275049\pi$
$864$		0			0
$865$	−510603.			−0.682418
$866$	−64473.1	−	37223.6i	−0.0859692	−	0.0496343i
$867$		0			0
$868$	134940.	+	233724.i	0.179103	+	0.310215i
$869$	60135.0	−	34718.9i	0.0796320	−	0.0459755i
$870$		0			0
$871$	165175.	−	286092.i	0.217725	−	0.377111i
$872$			171737.i			0.225855i
$873$		0			0
$874$	−22550.7			−0.0295214
$875$	40898.3	+	23612.6i	0.0534181	+	0.0308410i
$876$		0			0
$877$	−248271.	−	430017.i	−0.322795	−	0.559097i	0.658269	−	0.752783i	$-0.271289\pi$
$877$	−248271.	−	430017.i	−0.322795	−	0.559097i	−0.981064	+	0.193686i	$0.937956\pi$
$878$	−56501.5	+	32621.2i	−0.0732945	+	0.0423166i
$879$		0			0
$880$	250614.	−	434076.i	0.323623	−	0.560532i
$881$			1.21533e6i			1.56583i	0.622131	+	0.782913i	$0.286267\pi$
$881$			1.21533e6i			1.56583i	−0.622131	+	0.782913i	$0.713733\pi$
$882$		0			0
$883$	−999070.			−1.28137			−0.640685	−	0.767804i	$-0.721349\pi$
$883$	−999070.			−1.28137			−0.640685	+	0.767804i	$0.721349\pi$
$884$	389928.	+	225125.i	0.498976	+	0.288084i
$885$		0			0
$886$	−20590.8	−	35664.2i	−0.0262304	−	0.0454324i
$887$	−938048.	+	541582.i	−1.19228	+	0.688362i	−0.958823	−	0.284005i	$-0.908337\pi$
$887$	−938048.	+	541582.i	−1.19228	+	0.688362i	−0.233456	+	0.972367i	$0.575003\pi$
$888$		0			0
$889$	−298882.	+	517678.i	−0.378178	+	0.655023i
$890$		−	110169.i		−	0.139085i
$891$		0			0
$892$	−134888.			−0.169529
$893$	81360.0	+	46973.2i	0.102025	+	0.0589044i
$894$		0			0
$895$	643488.	+	1.11455e6i	0.803330	+	1.39141i
$896$	−154209.	+	89032.4i	−0.192085	+	0.110900i
$897$		0			0
$898$	−58417.8	+	101183.i	−0.0724423	+	0.125474i
$899$		−	427774.i		−	0.529292i
$900$		0			0
$901$	859491.			1.05875
$902$	−45973.5	−	26542.8i	−0.0565060	−	0.0326238i
$903$		0			0
$904$	7772.36	+	13462.1i	0.00951078	+	0.0164731i
$905$	−1.19313e6	+	688853.i	−1.45677	+	0.841065i
$906$		0			0
$907$	−638426.	+	1.10579e6i	−0.776061	+	1.34418i	0.158135	+	0.987417i	$0.449452\pi$
$907$	−638426.	+	1.10579e6i	−0.776061	+	1.34418i	−0.934196	+	0.356760i	$0.883882\pi$
$908$			303235.i			0.367796i
$909$		0			0
$910$	−28222.4			−0.0340809
$911$	−236846.	−	136743.i	−0.285383	−	0.164766i	0.350475	−	0.936572i	$-0.386020\pi$
$911$	−236846.	−	136743.i	−0.285383	−	0.164766i	−0.635858	+	0.771806i	$0.719354\pi$
$912$		0			0
$913$	267191.	+	462788.i	0.320538	+	0.555188i
$914$	−65438.2	+	37780.8i	−0.0783320	+	0.0452250i
$915$		0			0
$916$	85107.7	−	147411.i	0.101433	−	0.175687i
$917$		−	94256.7i		−	0.112092i
$918$		0			0
$919$	1.15882e6			1.37210			0.686051	−	0.727553i	$-0.259343\pi$
$919$	1.15882e6			1.37210			0.686051	+	0.727553i	$0.259343\pi$
$920$	186725.	+	107806.i	0.220611	+	0.127370i
$921$		0			0
$922$	−8604.07	−	14902.7i	−0.0101214	−	0.0175308i
$923$	253493.	−	146355.i	0.297552	−	0.171792i
$924$		0			0
$925$	261306.	−	452595.i	0.305397	−	0.528964i
$926$			60062.6i			0.0700459i
$927$		0			0
$928$	211967.			0.246135
$929$	−738465.	−	426353.i	−0.855655	−	0.494012i	0.00690018	−	0.999976i	$-0.497804\pi$
$929$	−738465.	−	426353.i	−0.855655	−	0.494012i	−0.862555	+	0.505964i	$0.831137\pi$
$930$		0			0
$931$	82610.0	+	143085.i	0.0953089	+	0.165080i
$932$	−1.40495e6	+	811151.i	−1.61745	+	0.933834i
$933$		0			0
$934$	9704.86	−	16809.3i	0.0111249	−	0.0192689i
$935$		−	775993.i		−	0.887636i
$936$		0			0
$937$	629989.			0.717552			0.358776	−	0.933424i	$-0.383194\pi$
$937$	629989.			0.717552			0.358776	+	0.933424i	$0.383194\pi$
$938$	43270.4	+	24982.2i	0.0491796	+	0.0283939i
$939$		0			0
$940$	−223671.	−	387410.i	−0.253136	−	0.438445i
$941$	366547.	−	211626.i	0.413953	−	0.238996i	−0.278534	−	0.960426i	$-0.589848\pi$
$941$	366547.	−	211626.i	0.413953	−	0.238996i	0.692487	+	0.721431i	$0.256515\pi$
$942$		0			0
$943$	−709749.	+	1.22932e6i	−0.798145	+	1.38243i
$944$		−	378004.i		−	0.424182i
$945$		0			0
$946$	−41013.1			−0.0458290
$947$	1.20762e6	+	697219.i	1.34657	+	0.777444i	0.987762	−	0.155967i	$-0.0498493\pi$
$947$	1.20762e6	+	697219.i	1.34657	+	0.777444i	0.358810	+	0.933411i	$0.383183\pi$
$948$		0			0
$949$	−125947.	−	218147.i	−0.139848	−	0.242224i
$950$	−20709.3	+	11956.5i	−0.0229466	+	0.0132482i
$951$		0			0
$952$	−68369.4	+	118419.i	−0.0754376	+	0.130662i
$953$		−	24001.0i		−	0.0264267i	−0.999913	−	0.0132134i	$-0.995794\pi$
$953$		−	24001.0i		−	0.0264267i	0.999913	−	0.0132134i	$-0.00420607\pi$
$954$		0			0
$955$	−2.00195e6			−2.19506
$956$	213358.	+	123183.i	0.233450	+	0.134782i
$957$		0			0
$958$	−24610.5	−	42626.6i	−0.0268157	−	0.0464461i
$959$	274290.	−	158362.i	0.298245	−	0.172192i
$960$		0			0
$961$	313393.	−	542813.i	0.339346	−	0.587765i
$962$		−	23399.8i		−	0.0252849i
$963$		0			0
$964$	−1.14225e6			−1.22915
$965$	−125725.	−	72587.2i	−0.135010	−	0.0779481i
$966$		0			0
$967$	−522031.	−	904183.i	−0.558268	−	0.966949i	−0.997641	−	0.0686443i	$-0.978133\pi$
$967$	−522031.	−	904183.i	−0.558268	−	0.966949i	0.439373	−	0.898305i	$-0.355201\pi$
$968$	110869.	−	64010.5i	0.118321	−	0.0683126i
$969$		0			0
$970$	41145.7	−	71266.5i	0.0437302	−	0.0757429i
$971$			605213.i			0.641904i	0.947096	+	0.320952i	$0.104003\pi$
$971$			605213.i			0.641904i	−0.947096	+	0.320952i	$0.895997\pi$
$972$		0			0
$973$	1.09632e6			1.15801
$974$	−7217.58	−	4167.07i	−0.00760806	−	0.00439251i
$975$		0			0
$976$	237783.	+	411851.i	0.249621	+	0.432355i
$977$	−41660.2	+	24052.5i	−0.0436448	+	0.0251983i	−0.521664	−	0.853151i	$-0.674688\pi$
$977$	−41660.2	+	24052.5i	−0.0436448	+	0.0251983i	0.478019	+	0.878350i	$0.341355\pi$
$978$		0			0
$979$	257770.	−	446471.i	0.268947	−	0.465831i
$980$		−	786724.i		−	0.819163i
$981$		0			0
$982$	26399.9			0.0273766
$983$	107286.	+	61941.5i	0.111029	+	0.0641024i	0.554486	−	0.832193i	$-0.312915\pi$
$983$	107286.	+	61941.5i	0.111029	+	0.0641024i	−0.443457	+	0.896295i	$0.646248\pi$
$984$		0			0
$985$	385397.	+	667527.i	0.397224	+	0.688012i
$986$	93478.7	−	53969.9i	0.0961521	−	0.0555134i
$987$		0			0
$988$	67360.3	−	116672.i	0.0690066	−	0.119523i
$989$			1.09668e6i			1.12121i
$990$		0			0
$991$	851418.			0.866953			0.433477	−	0.901165i	$-0.357287\pi$
$991$	851418.			0.866953			0.433477	+	0.901165i	$0.357287\pi$
$992$	−127336.	−	73517.8i	−0.129399	−	0.0747083i
$993$		0			0
$994$	22135.6	+	38340.0i	0.0224037	+	0.0388043i
$995$	1.52233e6	−	878917.i	1.53767	−	0.887773i
$996$		0			0
$997$	801524.	−	1.38828e6i	0.806355	−	1.39665i	−0.109018	−	0.994040i	$-0.534771\pi$
$997$	801524.	−	1.38828e6i	0.806355	−	1.39665i	0.915373	−	0.402607i	$-0.131896\pi$
$998$		−	6738.62i		−	0.00676566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.d.a.8.2		6
3.2	odd	2		9.5.d.a.2.2	✓	6
4.3	odd	2		432.5.q.a.305.3		6
9.2	odd	6		81.5.b.a.80.3		6
9.4	even	3		9.5.d.a.5.2	yes	6
9.5	odd	6	inner	27.5.d.a.17.2		6
9.7	even	3		81.5.b.a.80.4		6
12.11	even	2		144.5.q.a.65.1		6
36.7	odd	6		1296.5.e.c.161.6		6
36.11	even	6		1296.5.e.c.161.1		6
36.23	even	6		432.5.q.a.17.3		6
36.31	odd	6		144.5.q.a.113.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.2	✓	6	3.2	odd	2
9.5.d.a.5.2	yes	6	9.4	even	3
27.5.d.a.8.2		6	1.1	even	1	trivial
27.5.d.a.17.2		6	9.5	odd	6	inner
81.5.b.a.80.3		6	9.2	odd	6
81.5.b.a.80.4		6	9.7	even	3
144.5.q.a.65.1		6	12.11	even	2
144.5.q.a.113.1		6	36.31	odd	6
432.5.q.a.17.3		6	36.23	even	6
432.5.q.a.305.3		6	4.3	odd	2
1296.5.e.c.161.1		6	36.11	even	6
1296.5.e.c.161.6		6	36.7	odd	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.307601 - 0.177594i) q^{2} +(-7.93692 - 13.7472i) q^{4} +(30.0804 - 17.3669i) q^{5} +(15.6054 - 27.0294i) q^{7} +11.3212i q^{8} -12.3370 q^{10} +(-49.9968 - 28.8657i) q^{11} +(36.6478 + 63.4758i) q^{13} +(-9.60051 + 5.54285i) q^{14} +(-124.980 + 216.472i) q^{16} +386.985i q^{17} +115.791 q^{19} +(-477.491 - 275.679i) q^{20} +(10.2527 + 17.7583i) q^{22} +(474.852 - 274.156i) q^{23} +(290.719 - 503.539i) q^{25} -26.0337i q^{26} -495.436 q^{28} +(680.082 + 392.645i) q^{29} +(-272.367 - 471.753i) q^{31} +(233.759 - 134.961i) q^{32} +(68.7261 - 119.037i) q^{34} -1084.07i q^{35} +898.827 q^{37} +(-35.6175 - 20.5637i) q^{38} +(196.614 + 340.546i) q^{40} +(-2242.01 + 1294.43i) q^{41} +(-1000.05 + 1732.14i) q^{43} +916.419i q^{44} -194.753 q^{46} +(702.646 + 405.673i) q^{47} +(713.441 + 1235.72i) q^{49} +(-178.851 + 103.260i) q^{50} +(581.741 - 1007.61i) q^{52} -2221.00i q^{53} -2005.23 q^{55} +(306.005 + 176.672i) q^{56} +(-139.463 - 241.557i) q^{58} +(-1309.65 + 756.128i) q^{59} +(951.281 - 1647.67i) q^{61} +193.483i q^{62} +3903.49 q^{64} +(2204.76 + 1272.92i) q^{65} +(-2253.55 - 3903.26i) q^{67} +(5319.94 - 3071.47i) q^{68} +(-192.524 + 333.462i) q^{70} -3993.54i q^{71} -3436.70 q^{73} +(-276.480 - 159.626i) q^{74} +(-919.023 - 1591.80i) q^{76} +(-1560.44 + 900.923i) q^{77} +(-601.388 + 1041.63i) q^{79} +8682.07i q^{80} +919.529 q^{82} +(-8016.22 - 4628.17i) q^{83} +(6720.72 + 11640.6i) q^{85} +(615.236 - 355.207i) q^{86} +(326.794 - 566.024i) q^{88} +8929.99i q^{89} +2287.62 q^{91} +(-7537.72 - 4351.91i) q^{92} +(-144.090 - 249.571i) q^{94} +(3483.03 - 2010.93i) q^{95} +(-3335.14 + 5776.64i) q^{97} -506.811i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29}+ \cdots - 28959 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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