LMFDB - Embedded newform 810.3.g.k.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(163,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("810.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.g (of order $4$, degree $2$, 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 54 x^{9} + 921 x^{8} - 1350 x^{7} + 1458 x^{6} - 18792 x^{5} + 231804 x^{4} - 552420 x^{3} + \cdots + 656100 $ x^12 - 54x^9 + 921x^8 - 1350x^7 + 1458x^6 - 18792x^5 + 231804x^4 - 552420x^3 + 583200x^2 + 874800*x + 656100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.2
Root			$2.21548 - 2.21548i$ of defining polynomial
Character	$\chi$	$=$	810.163
Dual form			810.3.g.k.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.07172 - 2.90192i) q^{5} +(7.16337 - 7.16337i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-6.97363 + 1.16980i) q^{10} +16.2243 q^{11} +(14.7899 + 14.7899i) q^{13} -14.3267i q^{14} -4.00000 q^{16} +(7.49936 - 7.49936i) q^{17} -1.15457i q^{19} +(-5.80383 + 8.14343i) q^{20} +(16.2243 - 16.2243i) q^{22} +(-14.0480 - 14.0480i) q^{23} +(8.15776 + 23.6316i) q^{25} +29.5797 q^{26} +(-14.3267 - 14.3267i) q^{28} -23.0747i q^{29} -5.01587 q^{31} +(-4.00000 + 4.00000i) q^{32} -14.9987i q^{34} +(-49.9547 + 8.37971i) q^{35} +(33.0094 - 33.0094i) q^{37} +(-1.15457 - 1.15457i) q^{38} +(2.33960 + 13.9473i) q^{40} -52.4953 q^{41} +(-24.4275 - 24.4275i) q^{43} -32.4486i q^{44} -28.0961 q^{46} +(-11.3980 + 11.3980i) q^{47} -53.6276i q^{49} +(31.7893 + 15.4738i) q^{50} +(29.5797 - 29.5797i) q^{52} +(-30.1924 - 30.1924i) q^{53} +(-66.0607 - 47.0815i) q^{55} -28.6535 q^{56} +(-23.0747 - 23.0747i) q^{58} +0.843880i q^{59} +31.7880 q^{61} +(-5.01587 + 5.01587i) q^{62} +8.00000i q^{64} +(-17.3012 - 103.139i) q^{65} +(-24.6543 + 24.6543i) q^{67} +(-14.9987 - 14.9987i) q^{68} +(-41.5750 + 58.3344i) q^{70} +1.68895 q^{71} +(100.701 + 100.701i) q^{73} -66.0188i q^{74} -2.30913 q^{76} +(116.220 - 116.220i) q^{77} -10.4071i q^{79} +(16.2869 + 11.6077i) q^{80} +(-52.4953 + 52.4953i) q^{82} +(16.4476 + 16.4476i) q^{83} +(-52.2978 + 8.77275i) q^{85} -48.8549 q^{86} +(-32.4486 - 32.4486i) q^{88} -102.749i q^{89} +211.891 q^{91} +(-28.0961 + 28.0961i) q^{92} +22.7959i q^{94} +(-3.35046 + 4.70107i) q^{95} +(16.0012 - 16.0012i) q^{97} +(-53.6276 - 53.6276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 6 q^{7} - 24 q^{8} - 6 q^{10} + 12 q^{11} - 48 q^{16} - 18 q^{17} - 12 q^{20} + 12 q^{22} + 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} - 48 q^{32} - 168 q^{35} + 66 q^{37} + 36 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 12 * q^2 + 6 * q^7 - 24 * q^8 - 6 * q^10 + 12 * q^11 - 48 * q^16 - 18 * q^17 - 12 * q^20 + 12 * q^22 + 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 - 48 * q^32 - 168 * q^35 + 66 * q^37 + 36 * q^38 - 12 * q^40 - 24 * q^41 - 108 * q^43 + 108 * q^46 - 48 * q^47 - 54 * q^50 + 192 * q^53 - 276 * q^55 - 24 * q^56 - 60 * q^58 + 456 * q^61 + 72 * q^62 - 264 * q^65 - 12 * q^67 + 36 * q^68 - 174 * q^70 - 84 * q^71 - 216 * q^73 + 72 * q^76 + 48 * q^77 - 24 * q^82 + 246 * q^83 - 324 * q^85 - 216 * q^86 - 24 * q^88 + 612 * q^91 + 108 * q^92 - 432 * q^95 + 102 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−4.07172	−	2.90192i	−0.814343	−	0.580383i
$5$	−4.07172	−	2.90192i	−0.814343	−	0.580383i
$6$		0			0
$7$	7.16337	−	7.16337i	1.02334	−	1.02334i	0.0236170	−	0.999721i	$-0.492482\pi$
$7$	7.16337	−	7.16337i	1.02334	−	1.02334i	0.999721	−	0.0236170i	$-0.00751823\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−6.97363	+	1.16980i	−0.697363	+	0.116980i
$11$	16.2243			1.47493			0.737467	−	0.675383i	$-0.236022\pi$
$11$	16.2243			1.47493			0.737467	+	0.675383i	$0.236022\pi$
$12$		0			0
$13$	14.7899	+	14.7899i	1.13768	+	1.13768i	0.988865	+	0.148818i	$0.0475468\pi$
$13$	14.7899	+	14.7899i	1.13768	+	1.13768i	0.148818	+	0.988865i	$0.452453\pi$
$14$		−	14.3267i		−	1.02334i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	7.49936	−	7.49936i	0.441139	−	0.441139i	−0.451256	−	0.892395i	$-0.649024\pi$
$17$	7.49936	−	7.49936i	0.441139	−	0.441139i	0.892395	+	0.451256i	$0.149024\pi$
$18$		0			0
$19$		−	1.15457i		−	0.0607666i	−0.999538	−	0.0303833i	$-0.990327\pi$
$19$		−	1.15457i		−	0.0607666i	0.999538	−	0.0303833i	$-0.00967280\pi$
$20$	−5.80383	+	8.14343i	−0.290192	+	0.407172i
$21$		0			0
$22$	16.2243	−	16.2243i	0.737467	−	0.737467i
$23$	−14.0480	−	14.0480i	−0.610785	−	0.610785i	0.332366	−	0.943151i	$-0.392153\pi$
$23$	−14.0480	−	14.0480i	−0.610785	−	0.610785i	−0.943151	+	0.332366i	$0.892153\pi$
$24$		0			0
$25$	8.15776	+	23.6316i	0.326310	+	0.945263i
$26$	29.5797			1.13768
$27$		0			0
$28$	−14.3267	−	14.3267i	−0.511669	−	0.511669i
$29$		−	23.0747i		−	0.795681i	−0.917455	−	0.397840i	$-0.869760\pi$
$29$		−	23.0747i		−	0.795681i	0.917455	−	0.397840i	$-0.130240\pi$
$30$		0			0
$31$	−5.01587			−0.161802			−0.0809011	−	0.996722i	$-0.525780\pi$
$31$	−5.01587			−0.161802			−0.0809011	+	0.996722i	$0.525780\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	14.9987i		−	0.441139i
$35$	−49.9547	+	8.37971i	−1.42728	+	0.239420i
$36$		0			0
$37$	33.0094	−	33.0094i	0.892146	−	0.892146i	−0.102579	−	0.994725i	$-0.532709\pi$
$37$	33.0094	−	33.0094i	0.892146	−	0.892146i	0.994725	+	0.102579i	$0.0327095\pi$
$38$	−1.15457	−	1.15457i	−0.0303833	−	0.0303833i
$39$		0			0
$40$	2.33960	+	13.9473i	0.0584900	+	0.348682i
$41$	−52.4953			−1.28037			−0.640186	−	0.768220i	$-0.721143\pi$
$41$	−52.4953			−1.28037			−0.640186	+	0.768220i	$0.721143\pi$
$42$		0			0
$43$	−24.4275	−	24.4275i	−0.568081	−	0.568081i	0.363510	−	0.931590i	$-0.381578\pi$
$43$	−24.4275	−	24.4275i	−0.568081	−	0.568081i	−0.931590	+	0.363510i	$0.881578\pi$
$44$		−	32.4486i		−	0.737467i
$45$		0			0
$46$	−28.0961			−0.610785
$47$	−11.3980	+	11.3980i	−0.242510	+	0.242510i	−0.817888	−	0.575378i	$-0.804855\pi$
$47$	−11.3980	+	11.3980i	−0.242510	+	0.242510i	0.575378	+	0.817888i	$0.304855\pi$
$48$		0			0
$49$		−	53.6276i		−	1.09444i
$50$	31.7893	+	15.4738i	0.635787	+	0.309476i
$51$		0			0
$52$	29.5797	−	29.5797i	0.568841	−	0.568841i
$53$	−30.1924	−	30.1924i	−0.569669	−	0.569669i	0.362367	−	0.932036i	$-0.381969\pi$
$53$	−30.1924	−	30.1924i	−0.569669	−	0.569669i	−0.932036	+	0.362367i	$0.881969\pi$
$54$		0			0
$55$	−66.0607	−	47.0815i	−1.20110	−	0.856027i
$56$	−28.6535			−0.511669
$57$		0			0
$58$	−23.0747	−	23.0747i	−0.397840	−	0.397840i
$59$			0.843880i			0.0143031i	0.999974	+	0.00715153i	$0.00227642\pi$
$59$			0.843880i			0.0143031i	−0.999974	+	0.00715153i	$0.997724\pi$
$60$		0			0
$61$	31.7880			0.521114			0.260557	−	0.965458i	$-0.416094\pi$
$61$	31.7880			0.521114			0.260557	+	0.965458i	$0.416094\pi$
$62$	−5.01587	+	5.01587i	−0.0809011	+	0.0809011i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	−17.3012	−	103.139i	−0.266172	−	1.58676i
$66$		0			0
$67$	−24.6543	+	24.6543i	−0.367975	+	0.367975i	−0.866738	−	0.498763i	$-0.833788\pi$
$67$	−24.6543	+	24.6543i	−0.367975	+	0.367975i	0.498763	+	0.866738i	$0.333788\pi$
$68$	−14.9987	−	14.9987i	−0.220569	−	0.220569i
$69$		0			0
$70$	−41.5750	+	58.3344i	−0.593928	+	0.833349i
$71$	1.68895			0.0237880			0.0118940	−	0.999929i	$-0.496214\pi$
$71$	1.68895			0.0237880			0.0118940	+	0.999929i	$0.496214\pi$
$72$		0			0
$73$	100.701	+	100.701i	1.37946	+	1.37946i	0.845520	+	0.533944i	$0.179291\pi$
$73$	100.701	+	100.701i	1.37946	+	1.37946i	0.533944	+	0.845520i	$0.320709\pi$
$74$		−	66.0188i		−	0.892146i
$75$		0			0
$76$	−2.30913			−0.0303833
$77$	116.220	−	116.220i	1.50936	−	1.50936i
$78$		0			0
$79$		−	10.4071i		−	0.131736i	−0.997828	−	0.0658679i	$-0.979018\pi$
$79$		−	10.4071i		−	0.131736i	0.997828	−	0.0658679i	$-0.0209816\pi$
$80$	16.2869	+	11.6077i	0.203586	+	0.145096i
$81$		0			0
$82$	−52.4953	+	52.4953i	−0.640186	+	0.640186i
$83$	16.4476	+	16.4476i	0.198164	+	0.198164i	0.799212	−	0.601049i	$-0.205250\pi$
$83$	16.4476	+	16.4476i	0.198164	+	0.198164i	−0.601049	+	0.799212i	$0.705250\pi$
$84$		0			0
$85$	−52.2978	+	8.77275i	−0.615268	+	0.103209i
$86$	−48.8549			−0.568081
$87$		0			0
$88$	−32.4486	−	32.4486i	−0.368734	−	0.368734i
$89$		−	102.749i		−	1.15449i	−0.816572	−	0.577243i	$-0.804129\pi$
$89$		−	102.749i		−	1.15449i	0.816572	−	0.577243i	$-0.195871\pi$
$90$		0			0
$91$	211.891			2.32847
$92$	−28.0961	+	28.0961i	−0.305392	+	0.305392i
$93$		0			0
$94$			22.7959i			0.242510i
$95$	−3.35046	+	4.70107i	−0.0352680	+	0.0494849i
$96$		0			0
$97$	16.0012	−	16.0012i	0.164961	−	0.164961i	−0.619799	−	0.784760i	$-0.712786\pi$
$97$	16.0012	−	16.0012i	0.164961	−	0.164961i	0.784760	+	0.619799i	$0.212786\pi$
$98$	−53.6276	−	53.6276i	−0.547221	−	0.547221i
$99$		0			0
$100$	47.2631	−	16.3155i	0.472631	−	0.163155i
$101$	−57.3605			−0.567926			−0.283963	−	0.958835i	$-0.591649\pi$
$101$	−57.3605			−0.567926			−0.283963	+	0.958835i	$0.591649\pi$
$102$		0			0
$103$	22.5019	+	22.5019i	0.218465	+	0.218465i	0.807851	−	0.589386i	$-0.200630\pi$
$103$	22.5019	+	22.5019i	0.218465	+	0.218465i	−0.589386	+	0.807851i	$0.700630\pi$
$104$		−	59.1595i		−	0.568841i
$105$		0			0
$106$	−60.3849			−0.569669
$107$	−16.8887	+	16.8887i	−0.157838	+	0.157838i	−0.781608	−	0.623770i	$-0.785600\pi$
$107$	−16.8887	+	16.8887i	−0.157838	+	0.157838i	0.623770	+	0.781608i	$0.285600\pi$
$108$		0			0
$109$		−	8.42672i		−	0.0773094i	−0.999253	−	0.0386547i	$-0.987693\pi$
$109$		−	8.42672i		−	0.0773094i	0.999253	−	0.0386547i	$-0.0123072\pi$
$110$	−113.142	+	18.9792i	−1.02857	+	0.172538i
$111$		0			0
$112$	−28.6535	+	28.6535i	−0.255835	+	0.255835i
$113$	35.3612	+	35.3612i	0.312931	+	0.312931i	0.846044	−	0.533113i	$-0.178978\pi$
$113$	35.3612	+	35.3612i	0.312931	+	0.312931i	−0.533113	+	0.846044i	$0.678978\pi$
$114$		0			0
$115$	16.4334	+	97.9659i	0.142899	+	0.851878i
$116$	−46.1495			−0.397840
$117$		0			0
$118$	0.843880	+	0.843880i	0.00715153	+	0.00715153i
$119$		−	107.441i		−	0.902869i
$120$		0			0
$121$	142.227			1.17543
$122$	31.7880	−	31.7880i	0.260557	−	0.260557i
$123$		0			0
$124$			10.0317i			0.0809011i
$125$	35.3608	−	119.894i	0.282886	−	0.959153i
$126$		0			0
$127$	−144.508	+	144.508i	−1.13786	+	1.13786i	−0.149025	+	0.988833i	$0.547614\pi$
$127$	−144.508	+	144.508i	−1.13786	+	1.13786i	−0.988833	+	0.149025i	$0.952386\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−120.440	−	85.8380i	−0.926464	−	0.660292i
$131$	−104.895			−0.800727			−0.400364	−	0.916356i	$-0.631116\pi$
$131$	−104.895			−0.800727			−0.400364	+	0.916356i	$0.631116\pi$
$132$		0			0
$133$	−8.27058	−	8.27058i	−0.0621848	−	0.0621848i
$134$			49.3087i			0.367975i
$135$		0			0
$136$	−29.9974			−0.220569
$137$	−40.7404	+	40.7404i	−0.297375	+	0.297375i	−0.839985	−	0.542610i	$-0.817436\pi$
$137$	−40.7404	+	40.7404i	−0.297375	+	0.297375i	0.542610	+	0.839985i	$0.317436\pi$
$138$		0			0
$139$			124.892i			0.898502i	0.893406	+	0.449251i	$0.148309\pi$
$139$			124.892i			0.898502i	−0.893406	+	0.449251i	$0.851691\pi$
$140$	16.7594	+	99.9094i	0.119710	+	0.713639i
$141$		0			0
$142$	1.68895	−	1.68895i	0.0118940	−	0.0118940i
$143$	239.955	+	239.955i	1.67801	+	1.67801i
$144$		0			0
$145$	−66.9610	+	93.9538i	−0.461800	+	0.647958i
$146$	201.402			1.37946
$147$		0			0
$148$	−66.0188	−	66.0188i	−0.446073	−	0.446073i
$149$			183.362i			1.23062i	0.788287	+	0.615308i	$0.210968\pi$
$149$			183.362i			1.23062i	−0.788287	+	0.615308i	$0.789032\pi$
$150$		0			0
$151$	91.2593			0.604367			0.302183	−	0.953250i	$-0.402285\pi$
$151$	91.2593			0.604367			0.302183	+	0.953250i	$0.402285\pi$
$152$	−2.30913	+	2.30913i	−0.0151917	+	0.0151917i
$153$		0			0
$154$		−	232.441i		−	1.50936i
$155$	20.4232	+	14.5556i	0.131763	+	0.0939073i
$156$		0			0
$157$	−25.3697	+	25.3697i	−0.161591	+	0.161591i	−0.783271	−	0.621680i	$-0.786450\pi$
$157$	−25.3697	+	25.3697i	−0.161591	+	0.161591i	0.621680	+	0.783271i	$0.286450\pi$
$158$	−10.4071	−	10.4071i	−0.0658679	−	0.0658679i
$159$		0			0
$160$	27.8945	−	4.67920i	0.174341	−	0.0292450i
$161$	−201.263			−1.25008
$162$		0			0
$163$	−158.678	−	158.678i	−0.973485	−	0.973485i	0.0261726	−	0.999657i	$-0.491668\pi$
$163$	−158.678	−	158.678i	−0.973485	−	0.973485i	−0.999657	+	0.0261726i	$0.991668\pi$
$164$			104.991i			0.640186i
$165$		0			0
$166$	32.8952			0.198164
$167$	141.399	−	141.399i	0.846698	−	0.846698i	−0.143022	−	0.989720i	$-0.545682\pi$
$167$	141.399	−	141.399i	0.846698	−	0.846698i	0.989720	+	0.143022i	$0.0456819\pi$
$168$		0			0
$169$			268.481i			1.58864i
$170$	−43.5250	+	61.0706i	−0.256030	+	0.359239i
$171$		0			0
$172$	−48.8549	+	48.8549i	−0.284040	+	0.284040i
$173$	172.639	+	172.639i	0.997915	+	0.997915i	0.999998	−	0.00208279i	$-0.000662974\pi$
$173$	172.639	+	172.639i	0.997915	+	0.997915i	−0.00208279	+	0.999998i	$0.500663\pi$
$174$		0			0
$175$	227.719	+	110.845i	1.30125	+	0.633398i
$176$	−64.8971			−0.368734
$177$		0			0
$178$	−102.749	−	102.749i	−0.577243	−	0.577243i
$179$		−	112.194i		−	0.626781i	−0.949624	−	0.313391i	$-0.898535\pi$
$179$		−	112.194i		−	0.626781i	0.949624	−	0.313391i	$-0.101465\pi$
$180$		0			0
$181$	−11.2065			−0.0619143			−0.0309572	−	0.999521i	$-0.509856\pi$
$181$	−11.2065			−0.0619143			−0.0309572	+	0.999521i	$0.509856\pi$
$182$	211.891	−	211.891i	1.16423	−	1.16423i
$183$		0			0
$184$			56.1922i			0.305392i
$185$	−230.195	+	38.6144i	−1.24430	+	0.208726i
$186$		0			0
$187$	121.672	−	121.672i	0.650651	−	0.650651i
$188$	22.7959	+	22.7959i	0.121255	+	0.121255i
$189$		0			0
$190$	1.35061	+	8.05152i	0.00710848	+	0.0423764i
$191$	−86.8819			−0.454879			−0.227439	−	0.973792i	$-0.573035\pi$
$191$	−86.8819			−0.454879			−0.227439	+	0.973792i	$0.573035\pi$
$192$		0			0
$193$	−58.4846	−	58.4846i	−0.303029	−	0.303029i	0.539169	−	0.842198i	$-0.318738\pi$
$193$	−58.4846	−	58.4846i	−0.303029	−	0.303029i	−0.842198	+	0.539169i	$0.818738\pi$
$194$		−	32.0024i		−	0.164961i
$195$		0			0
$196$	−107.255			−0.547221
$197$	91.8988	−	91.8988i	0.466492	−	0.466492i	−0.434284	−	0.900776i	$-0.642999\pi$
$197$	91.8988	−	91.8988i	0.466492	−	0.466492i	0.900776	+	0.434284i	$0.142999\pi$
$198$		0			0
$199$			67.5469i			0.339432i	0.985493	+	0.169716i	$0.0542850\pi$
$199$			67.5469i			0.339432i	−0.985493	+	0.169716i	$0.945715\pi$
$200$	30.9476	−	63.5787i	0.154738	−	0.317893i
$201$		0			0
$202$	−57.3605	+	57.3605i	−0.283963	+	0.283963i
$203$	−165.293	−	165.293i	−0.814251	−	0.814251i
$204$		0			0
$205$	213.746	+	152.337i	1.04266	+	0.743107i
$206$	45.0038			0.218465
$207$		0			0
$208$	−59.1595	−	59.1595i	−0.284421	−	0.284421i
$209$		−	18.7320i		−	0.0896268i
$210$		0			0
$211$	281.788			1.33549			0.667744	−	0.744391i	$-0.267260\pi$
$211$	281.788			1.33549			0.667744	+	0.744391i	$0.267260\pi$
$212$	−60.3849	+	60.3849i	−0.284834	+	0.284834i
$213$		0			0
$214$			33.7774i			0.157838i
$215$	28.5752	+	170.348i	0.132908	+	0.792317i
$216$		0			0
$217$	−35.9305	+	35.9305i	−0.165578	+	0.165578i
$218$	−8.42672	−	8.42672i	−0.0386547	−	0.0386547i
$219$		0			0
$220$	−94.1630	+	132.121i	−0.428014	+	0.600552i
$221$	221.829			1.00375
$222$		0			0
$223$	−248.247	−	248.247i	−1.11322	−	1.11322i	−0.992713	−	0.120502i	$-0.961550\pi$
$223$	−248.247	−	248.247i	−1.11322	−	1.11322i	−0.120502	−	0.992713i	$-0.538450\pi$
$224$			57.3069i			0.255835i
$225$		0			0
$226$	70.7223			0.312931
$227$	−236.952	+	236.952i	−1.04384	+	1.04384i	−0.0448460	+	0.998994i	$0.514280\pi$
$227$	−236.952	+	236.952i	−1.04384	+	1.04384i	−0.998994	+	0.0448460i	$0.985720\pi$
$228$		0			0
$229$		−	385.815i		−	1.68478i	−0.538868	−	0.842390i	$-0.681148\pi$
$229$		−	385.815i		−	1.68478i	0.538868	−	0.842390i	$-0.318852\pi$
$230$	114.399	+	81.5325i	0.497388	+	0.354489i
$231$		0			0
$232$	−46.1495	+	46.1495i	−0.198920	+	0.198920i
$233$	−30.9334	−	30.9334i	−0.132761	−	0.132761i	0.637603	−	0.770365i	$-0.279926\pi$
$233$	−30.9334	−	30.9334i	−0.132761	−	0.132761i	−0.770365	+	0.637603i	$0.779926\pi$
$234$		0			0
$235$	79.4852	−	13.3333i	0.338235	−	0.0567376i
$236$	1.68776			0.00715153
$237$		0			0
$238$	−107.441	−	107.441i	−0.451434	−	0.451434i
$239$		−	130.995i		−	0.548095i	−0.961716	−	0.274048i	$-0.911637\pi$
$239$		−	130.995i		−	0.548095i	0.961716	−	0.274048i	$-0.0883626\pi$
$240$		0			0
$241$	−65.3791			−0.271283			−0.135641	−	0.990758i	$-0.543309\pi$
$241$	−65.3791			−0.271283			−0.135641	+	0.990758i	$0.543309\pi$
$242$	142.227	−	142.227i	0.587716	−	0.587716i
$243$		0			0
$244$		−	63.5759i		−	0.260557i
$245$	−155.623	+	218.357i	−0.635196	+	0.891251i
$246$		0			0
$247$	17.0759	−	17.0759i	0.0691332	−	0.0691332i
$248$	10.0317	+	10.0317i	0.0404505	+	0.0404505i
$249$		0			0
$250$	−84.5334	−	155.255i	−0.338134	−	0.621020i
$251$	341.145			1.35914			0.679572	−	0.733609i	$-0.262166\pi$
$251$	341.145			1.35914			0.679572	+	0.733609i	$0.262166\pi$
$252$		0			0
$253$	−227.919	−	227.919i	−0.900867	−	0.900867i
$254$			289.016i			1.13786i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−231.884	+	231.884i	−0.902273	+	0.902273i	−0.995632	−	0.0933592i	$-0.970240\pi$
$257$	−231.884	+	231.884i	−0.902273	+	0.902273i	0.0933592	+	0.995632i	$0.470240\pi$
$258$		0			0
$259$		−	472.917i		−	1.82593i
$260$	−206.278	+	34.6024i	−0.793378	+	0.133086i
$261$		0			0
$262$	−104.895	+	104.895i	−0.400364	+	0.400364i
$263$	186.085	+	186.085i	0.707547	+	0.707547i	0.966019	−	0.258472i	$-0.0832190\pi$
$263$	186.085	+	186.085i	0.707547	+	0.707547i	−0.258472	+	0.966019i	$0.583219\pi$
$264$		0			0
$265$	35.3191	+	210.551i	0.133280	+	0.794532i
$266$	−16.5412			−0.0621848
$267$		0			0
$268$	49.3087	+	49.3087i	0.183988	+	0.183988i
$269$			424.447i			1.57787i	0.614476	+	0.788935i	$0.289367\pi$
$269$			424.447i			1.57787i	−0.614476	+	0.788935i	$0.710633\pi$
$270$		0			0
$271$	513.264			1.89396			0.946981	−	0.321290i	$-0.104116\pi$
$271$	513.264			1.89396			0.946981	+	0.321290i	$0.104116\pi$
$272$	−29.9974	+	29.9974i	−0.110285	+	0.110285i
$273$		0			0
$274$			81.4807i			0.297375i
$275$	132.354	+	383.405i	0.481286	+	1.39420i
$276$		0			0
$277$	−148.517	+	148.517i	−0.536163	+	0.536163i	−0.922400	−	0.386237i	$-0.873775\pi$
$277$	−148.517	+	148.517i	−0.536163	+	0.536163i	0.386237	+	0.922400i	$0.373775\pi$
$278$	124.892	+	124.892i	0.449251	+	0.449251i
$279$		0			0
$280$	116.669	+	83.1500i	0.416674	+	0.296964i
$281$	363.207			1.29255			0.646275	−	0.763104i	$-0.276326\pi$
$281$	363.207			1.29255			0.646275	+	0.763104i	$0.276326\pi$
$282$		0			0
$283$	−83.9729	−	83.9729i	−0.296724	−	0.296724i	0.543005	−	0.839729i	$-0.317286\pi$
$283$	−83.9729	−	83.9729i	−0.296724	−	0.296724i	−0.839729	+	0.543005i	$0.817286\pi$
$284$		−	3.37789i		−	0.0118940i
$285$		0			0
$286$	479.910			1.67801
$287$	−376.043	+	376.043i	−1.31025	+	1.31025i
$288$		0			0
$289$			176.519i			0.610793i
$290$	26.9928	+	160.915i	0.0930788	+	0.554879i
$291$		0			0
$292$	201.402	−	201.402i	0.689732	−	0.689732i
$293$	352.259	+	352.259i	1.20225	+	1.20225i	0.973481	+	0.228768i	$0.0734697\pi$
$293$	352.259	+	352.259i	1.20225	+	1.20225i	0.228768	+	0.973481i	$0.426530\pi$
$294$		0			0
$295$	2.44887	−	3.43604i	0.00830125	−	0.0116476i
$296$	−132.038			−0.446073
$297$		0			0
$298$	183.362	+	183.362i	0.615308	+	0.615308i
$299$		−	415.538i		−	1.38976i
$300$		0			0
$301$	−349.966			−1.16268
$302$	91.2593	−	91.2593i	0.302183	−	0.302183i
$303$		0			0
$304$			4.61827i			0.0151917i
$305$	−129.432	−	92.2460i	−0.424366	−	0.302446i
$306$		0			0
$307$	417.932	−	417.932i	1.36134	−	1.36134i	0.489135	−	0.872208i	$-0.337312\pi$
$307$	417.932	−	417.932i	1.36134	−	1.36134i	0.872208	−	0.489135i	$-0.162688\pi$
$308$	−232.441	−	232.441i	−0.754678	−	0.754678i
$309$		0			0
$310$	34.9788	−	5.86756i	0.112835	−	0.0189276i
$311$	365.940			1.17666			0.588328	−	0.808622i	$-0.299786\pi$
$311$	365.940			1.17666			0.588328	+	0.808622i	$0.299786\pi$
$312$		0			0
$313$	430.142	+	430.142i	1.37425	+	1.37425i	0.854030	+	0.520224i	$0.174152\pi$
$313$	430.142	+	430.142i	1.37425	+	1.37425i	0.520224	+	0.854030i	$0.325848\pi$
$314$			50.7395i			0.161591i
$315$		0			0
$316$	−20.8142			−0.0658679
$317$	−28.9879	+	28.9879i	−0.0914446	+	0.0914446i	−0.751349	−	0.659905i	$-0.770597\pi$
$317$	−28.9879	+	28.9879i	−0.0914446	+	0.0914446i	0.659905	+	0.751349i	$0.270597\pi$
$318$		0			0
$319$		−	374.371i		−	1.17358i
$320$	23.2153	−	32.5737i	0.0725479	−	0.101793i
$321$		0			0
$322$	−201.263	+	201.263i	−0.625039	+	0.625039i
$323$	−8.65851	−	8.65851i	−0.0268065	−	0.0268065i
$324$		0			0
$325$	−228.856	+	470.160i	−0.704171	+	1.44665i
$326$	−317.356			−0.973485
$327$		0			0
$328$	104.991	+	104.991i	0.320093	+	0.320093i
$329$			163.295i			0.496339i
$330$		0			0
$331$	145.615			0.439925			0.219962	−	0.975508i	$-0.429407\pi$
$331$	145.615			0.439925			0.219962	+	0.975508i	$0.429407\pi$
$332$	32.8952	−	32.8952i	0.0990818	−	0.0990818i
$333$		0			0
$334$		−	282.797i		−	0.846698i
$335$	171.930	−	28.8406i	0.513225	−	0.0860915i
$336$		0			0
$337$	−461.646	+	461.646i	−1.36987	+	1.36987i	−0.509251	+	0.860618i	$0.670078\pi$
$337$	−461.646	+	461.646i	−1.36987	+	1.36987i	−0.860618	+	0.509251i	$0.829922\pi$
$338$	268.481	+	268.481i	0.794322	+	0.794322i
$339$		0			0
$340$	17.5455	+	104.596i	0.0516044	+	0.307634i
$341$	−81.3788			−0.238648
$342$		0			0
$343$	−33.1495	−	33.1495i	−0.0966459	−	0.0966459i
$344$			97.7099i			0.284040i
$345$		0			0
$346$	345.279			0.997915
$347$	−250.585	+	250.585i	−0.722147	+	0.722147i	−0.969042	−	0.246895i	$-0.920590\pi$
$347$	−250.585	+	250.585i	−0.722147	+	0.722147i	0.246895	+	0.969042i	$0.420590\pi$
$348$		0			0
$349$		−	488.380i		−	1.39937i	−0.714452	−	0.699685i	$-0.753324\pi$
$349$		−	488.380i		−	1.39937i	0.714452	−	0.699685i	$-0.246676\pi$
$350$	338.563	−	116.874i	0.967323	−	0.333926i
$351$		0			0
$352$	−64.8971	+	64.8971i	−0.184367	+	0.184367i
$353$	−143.291	−	143.291i	−0.405923	−	0.405923i	0.474391	−	0.880314i	$-0.342668\pi$
$353$	−143.291	−	143.291i	−0.405923	−	0.405923i	−0.880314	+	0.474391i	$0.842668\pi$
$354$		0			0
$355$	−6.87691	−	4.90118i	−0.0193716	−	0.0138061i
$356$	−205.499			−0.577243
$357$		0			0
$358$	−112.194	−	112.194i	−0.313391	−	0.313391i
$359$		−	416.887i		−	1.16124i	−0.814173	−	0.580622i	$-0.802809\pi$
$359$		−	416.887i		−	1.16124i	0.814173	−	0.580622i	$-0.197191\pi$
$360$		0			0
$361$	359.667			0.996307
$362$	−11.2065	+	11.2065i	−0.0309572	+	0.0309572i
$363$		0			0
$364$		−	423.781i		−	1.16423i
$365$	−117.800	−	702.251i	−0.322739	−	1.92397i
$366$		0			0
$367$	−97.3771	+	97.3771i	−0.265333	+	0.265333i	−0.827216	−	0.561884i	$-0.810077\pi$
$367$	−97.3771	+	97.3771i	−0.265333	+	0.265333i	0.561884	+	0.827216i	$0.310077\pi$
$368$	56.1922	+	56.1922i	0.152696	+	0.152696i
$369$		0			0
$370$	−191.581	+	268.810i	−0.517787	+	0.726513i
$371$	−432.559			−1.16593
$372$		0			0
$373$	37.1504	+	37.1504i	0.0995989	+	0.0995989i	0.755150	−	0.655552i	$-0.227564\pi$
$373$	37.1504	+	37.1504i	0.0995989	+	0.0995989i	−0.655552	+	0.755150i	$0.727564\pi$
$374$		−	243.343i		−	0.650651i
$375$		0			0
$376$	45.5918			0.121255
$377$	341.273	−	341.273i	0.905232	−	0.905232i
$378$		0			0
$379$		−	430.016i		−	1.13461i	−0.823509	−	0.567303i	$-0.807987\pi$
$379$		−	430.016i		−	1.13461i	0.823509	−	0.567303i	$-0.192013\pi$
$380$	9.40213	+	6.70091i	0.0247425	+	0.0176340i
$381$		0			0
$382$	−86.8819	+	86.8819i	−0.227439	+	0.227439i
$383$	214.421	+	214.421i	0.559845	+	0.559845i	0.929263	−	0.369418i	$-0.120443\pi$
$383$	214.421	+	214.421i	0.559845	+	0.559845i	−0.369418	+	0.929263i	$0.620443\pi$
$384$		0			0
$385$	−810.479	+	135.955i	−2.10514	+	0.353129i
$386$	−116.969			−0.303029
$387$		0			0
$388$	−32.0024	−	32.0024i	−0.0824804	−	0.0824804i
$389$			41.4805i			0.106634i	0.998578	+	0.0533168i	$0.0169793\pi$
$389$			41.4805i			0.106634i	−0.998578	+	0.0533168i	$0.983021\pi$
$390$		0			0
$391$	−210.703			−0.538882
$392$	−107.255	+	107.255i	−0.273610	+	0.273610i
$393$		0			0
$394$		−	183.798i		−	0.466492i
$395$	−30.2006	+	42.3748i	−0.0764572	+	0.107278i
$396$		0			0
$397$	−26.1316	+	26.1316i	−0.0658226	+	0.0658226i	−0.739252	−	0.673429i	$-0.764821\pi$
$397$	−26.1316	+	26.1316i	−0.0658226	+	0.0658226i	0.673429	+	0.739252i	$0.264821\pi$
$398$	67.5469	+	67.5469i	0.169716	+	0.169716i
$399$		0			0
$400$	−32.6310	−	94.5263i	−0.0815776	−	0.236316i
$401$	380.291			0.948356			0.474178	−	0.880429i	$-0.342745\pi$
$401$	380.291			0.948356			0.474178	+	0.880429i	$0.342745\pi$
$402$		0			0
$403$	−74.1840	−	74.1840i	−0.184079	−	0.184079i
$404$			114.721i			0.283963i
$405$		0			0
$406$	−330.586			−0.814251
$407$	535.554	−	535.554i	1.31586	−	1.31586i
$408$		0			0
$409$			9.54256i			0.0233314i	0.999932	+	0.0116657i	$0.00371340\pi$
$409$			9.54256i			0.0233314i	−0.999932	+	0.0116657i	$0.996287\pi$
$410$	366.083	−	61.4090i	0.892885	−	0.149778i
$411$		0			0
$412$	45.0038	−	45.0038i	0.109233	−	0.109233i
$413$	6.04502	+	6.04502i	0.0146369	+	0.0146369i
$414$		0			0
$415$	−19.2404	−	114.699i	−0.0463624	−	0.276384i
$416$	−118.319			−0.284421
$417$		0			0
$418$	−18.7320	−	18.7320i	−0.0448134	−	0.0448134i
$419$		−	330.930i		−	0.789808i	−0.918722	−	0.394904i	$-0.870778\pi$
$419$		−	330.930i		−	0.789808i	0.918722	−	0.394904i	$-0.129222\pi$
$420$		0			0
$421$	178.379			0.423703			0.211852	−	0.977302i	$-0.432051\pi$
$421$	178.379			0.423703			0.211852	+	0.977302i	$0.432051\pi$
$422$	281.788	−	281.788i	0.667744	−	0.667744i
$423$		0			0
$424$			120.770i			0.284834i
$425$	238.400	+	116.044i	0.560940	+	0.273044i
$426$		0			0
$427$	227.709	−	227.709i	0.533276	−	0.533276i
$428$	33.7774	+	33.7774i	0.0789191	+	0.0789191i
$429$		0			0
$430$	198.923	+	141.773i	0.462613	+	0.329704i
$431$	249.781			0.579538			0.289769	−	0.957097i	$-0.406421\pi$
$431$	249.781			0.579538			0.289769	+	0.957097i	$0.406421\pi$
$432$		0			0
$433$	−24.9453	−	24.9453i	−0.0576103	−	0.0576103i	0.677715	−	0.735325i	$-0.262970\pi$
$433$	−24.9453	−	24.9453i	−0.0576103	−	0.0576103i	−0.735325	+	0.677715i	$0.762970\pi$
$434$			71.8610i			0.165578i
$435$		0			0
$436$	−16.8534			−0.0386547
$437$	−16.2194	+	16.2194i	−0.0371153	+	0.0371153i
$438$		0			0
$439$		−	109.350i		−	0.249089i	−0.992214	−	0.124544i	$-0.960253\pi$
$439$		−	109.350i		−	0.249089i	0.992214	−	0.124544i	$-0.0397469\pi$
$440$	37.9583	+	226.284i	0.0862689	+	0.514283i
$441$		0			0
$442$	221.829	−	221.829i	0.501876	−	0.501876i
$443$	261.468	+	261.468i	0.590222	+	0.590222i	0.937691	−	0.347470i	$-0.112959\pi$
$443$	261.468	+	261.468i	0.590222	+	0.590222i	−0.347470	+	0.937691i	$0.612959\pi$
$444$		0			0
$445$	−298.170	+	418.366i	−0.670044	+	0.940148i
$446$	−496.494			−1.11322
$447$		0			0
$448$	57.3069	+	57.3069i	0.127917	+	0.127917i
$449$			358.178i			0.797724i	0.917011	+	0.398862i	$0.130595\pi$
$449$			358.178i			0.797724i	−0.917011	+	0.398862i	$0.869405\pi$
$450$		0			0
$451$	−851.698			−1.88847
$452$	70.7223	−	70.7223i	0.156465	−	0.156465i
$453$		0			0
$454$			473.903i			1.04384i
$455$	−862.758	−	614.889i	−1.89617	−	1.35140i
$456$		0			0
$457$	−620.171	+	620.171i	−1.35705	+	1.35705i	−0.479514	+	0.877534i	$0.659187\pi$
$457$	−620.171	+	620.171i	−1.35705	+	1.35705i	−0.877534	+	0.479514i	$0.840813\pi$
$458$	−385.815	−	385.815i	−0.842390	−	0.842390i
$459$		0			0
$460$	195.932	−	32.8668i	0.425939	−	0.0714496i
$461$	214.672			0.465667			0.232833	−	0.972517i	$-0.425200\pi$
$461$	214.672			0.465667			0.232833	+	0.972517i	$0.425200\pi$
$462$		0			0
$463$	−237.738	−	237.738i	−0.513474	−	0.513474i	0.402115	−	0.915589i	$-0.368275\pi$
$463$	−237.738	−	237.738i	−0.513474	−	0.513474i	−0.915589	+	0.402115i	$0.868275\pi$
$464$			92.2990i			0.198920i
$465$		0			0
$466$	−61.8668			−0.132761
$467$	−551.200	+	551.200i	−1.18030	+	1.18030i	−0.200632	+	0.979667i	$0.564300\pi$
$467$	−551.200	+	551.200i	−1.18030	+	1.18030i	−0.979667	+	0.200632i	$0.935700\pi$
$468$		0			0
$469$			353.216i			0.753126i
$470$	66.1518	−	92.8185i	0.140749	−	0.197486i
$471$		0			0
$472$	1.68776	−	1.68776i	0.00357576	−	0.00357576i
$473$	−396.318	−	396.318i	−0.837882	−	0.837882i
$474$		0			0
$475$	27.2842	−	9.41867i	0.0574404	−	0.0198288i
$476$	−214.883			−0.451434
$477$		0			0
$478$	−130.995	−	130.995i	−0.274048	−	0.274048i
$479$			618.218i			1.29064i	0.763911	+	0.645321i	$0.223276\pi$
$479$			618.218i			1.29064i	−0.763911	+	0.645321i	$0.776724\pi$
$480$		0			0
$481$	976.410			2.02996
$482$	−65.3791	+	65.3791i	−0.135641	+	0.135641i
$483$		0			0
$484$		−	284.454i		−	0.587716i
$485$	−111.586	+	18.7182i	−0.230075	+	0.0385942i
$486$		0			0
$487$	−418.202	+	418.202i	−0.858732	+	0.858732i	−0.991189	−	0.132457i	$-0.957713\pi$
$487$	−418.202	+	418.202i	−0.858732	+	0.858732i	0.132457	+	0.991189i	$0.457713\pi$
$488$	−63.5759	−	63.5759i	−0.130279	−	0.130279i
$489$		0			0
$490$	62.7336	+	373.980i	0.128028	+	0.763224i
$491$	−326.463			−0.664894			−0.332447	−	0.943122i	$-0.607874\pi$
$491$	−326.463			−0.664894			−0.332447	+	0.943122i	$0.607874\pi$
$492$		0			0
$493$	−173.046	−	173.046i	−0.351006	−	0.351006i
$494$		−	34.1518i		−	0.0691332i
$495$		0			0
$496$	20.0635			0.0404505
$497$	12.0985	−	12.0985i	0.0243431	−	0.0243431i
$498$		0			0
$499$			227.119i			0.455147i	0.973761	+	0.227574i	$0.0730793\pi$
$499$			227.119i			0.455147i	−0.973761	+	0.227574i	$0.926921\pi$
$500$	−239.788	−	70.7215i	−0.479577	−	0.141443i
$501$		0			0
$502$	341.145	−	341.145i	0.679572	−	0.679572i
$503$	−521.931	−	521.931i	−1.03764	−	1.03764i	−0.999264	−	0.0383723i	$-0.987783\pi$
$503$	−521.931	−	521.931i	−1.03764	−	1.03764i	−0.0383723	−	0.999264i	$-0.512217\pi$
$504$		0			0
$505$	233.556	+	166.455i	0.462487	+	0.329615i
$506$	−455.839			−0.900867
$507$		0			0
$508$	289.016	+	289.016i	0.568929	+	0.568929i
$509$			243.797i			0.478973i	0.970900	+	0.239486i	$0.0769790\pi$
$509$			243.797i			0.478973i	−0.970900	+	0.239486i	$0.923021\pi$
$510$		0			0
$511$	1442.71			2.82332
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$			463.768i			0.902273i
$515$	−26.3227	−	156.920i	−0.0511121	−	0.304699i
$516$		0			0
$517$	−184.924	+	184.924i	−0.357686	+	0.357686i
$518$	−472.917	−	472.917i	−0.912967	−	0.912967i
$519$		0			0
$520$	−171.676	+	240.881i	−0.330146	+	0.463232i
$521$	411.938			0.790669			0.395334	−	0.918537i	$-0.370629\pi$
$521$	411.938			0.790669			0.395334	+	0.918537i	$0.370629\pi$
$522$		0			0
$523$	−109.244	−	109.244i	−0.208880	−	0.208880i	0.594911	−	0.803791i	$-0.297187\pi$
$523$	−109.244	−	109.244i	−0.208880	−	0.208880i	−0.803791	+	0.594911i	$0.797187\pi$
$524$			209.791i			0.400364i
$525$		0			0
$526$	372.170			0.707547
$527$	−37.6158	+	37.6158i	−0.0713772	+	0.0713772i
$528$		0			0
$529$		−	134.305i		−	0.253884i
$530$	245.870	+	175.232i	0.463906	+	0.330626i
$531$		0			0
$532$	−16.5412	+	16.5412i	−0.0310924	+	0.0310924i
$533$	−776.398	−	776.398i	−1.45666	−	1.45666i
$534$		0			0
$535$	117.776	−	19.7564i	0.220141	−	0.0369278i
$536$	98.6174			0.183988
$537$		0			0
$538$	424.447	+	424.447i	0.788935	+	0.788935i
$539$		−	870.070i		−	1.61423i
$540$		0			0
$541$	−944.075			−1.74506			−0.872528	−	0.488565i	$-0.837521\pi$
$541$	−944.075			−1.74506			−0.872528	+	0.488565i	$0.837521\pi$
$542$	513.264	−	513.264i	0.946981	−	0.946981i
$543$		0			0
$544$			59.9949i			0.110285i
$545$	−24.4536	+	34.3112i	−0.0448691	+	0.0629564i
$546$		0			0
$547$	−638.038	+	638.038i	−1.16643	+	1.16643i	−0.183391	+	0.983040i	$0.558707\pi$
$547$	−638.038	+	638.038i	−1.16643	+	1.16643i	−0.983040	+	0.183391i	$0.941293\pi$
$548$	81.4807	+	81.4807i	0.148687	+	0.148687i
$549$		0			0
$550$	515.759	+	251.051i	0.937743	+	0.456457i
$551$	−26.6413			−0.0483509
$552$		0			0
$553$	−74.5500	−	74.5500i	−0.134810	−	0.134810i
$554$			297.034i			0.536163i
$555$		0			0
$556$	249.784			0.449251
$557$	−195.150	+	195.150i	−0.350360	+	0.350360i	−0.860243	−	0.509884i	$-0.829688\pi$
$557$	−195.150	+	195.150i	−0.350360	+	0.350360i	0.509884	+	0.860243i	$0.329688\pi$
$558$		0			0
$559$		−	722.558i		−	1.29259i
$560$	199.819	−	33.5188i	0.356819	−	0.0598550i
$561$		0			0
$562$	363.207	−	363.207i	0.646275	−	0.646275i
$563$	44.3579	+	44.3579i	0.0787885	+	0.0787885i	0.745403	−	0.666614i	$-0.232257\pi$
$563$	44.3579	+	44.3579i	0.0787885	+	0.0787885i	−0.666614	+	0.745403i	$0.732257\pi$
$564$		0			0
$565$	−41.3655	−	246.596i	−0.0732132	−	0.436453i
$566$	−167.946			−0.296724
$567$		0			0
$568$	−3.37789	−	3.37789i	−0.00594699	−	0.00594699i
$569$		−	26.0928i		−	0.0458574i	−0.999737	−	0.0229287i	$-0.992701\pi$
$569$		−	26.0928i		−	0.0458574i	0.999737	−	0.0229287i	$-0.00729907\pi$
$570$		0			0
$571$	−936.052			−1.63932			−0.819660	−	0.572850i	$-0.805838\pi$
$571$	−936.052			−1.63932			−0.819660	+	0.572850i	$0.805838\pi$
$572$	479.910	−	479.910i	0.839004	−	0.839004i
$573$		0			0
$574$			752.086i			1.31025i
$575$	217.377	−	446.578i	0.378047	−	0.776657i
$576$		0			0
$577$	371.244	−	371.244i	0.643405	−	0.643405i	−0.307986	−	0.951391i	$-0.599655\pi$
$577$	371.244	−	371.244i	0.643405	−	0.643405i	0.951391	+	0.307986i	$0.0996551\pi$
$578$	176.519	+	176.519i	0.305396	+	0.305396i
$579$		0			0
$580$	187.908	+	133.922i	0.323979	+	0.230900i
$581$	235.640			0.405577
$582$		0			0
$583$	−489.851	−	489.851i	−0.840224	−	0.840224i
$584$		−	402.803i		−	0.689732i
$585$		0			0
$586$	704.518			1.20225
$587$	−439.287	+	439.287i	−0.748360	+	0.748360i	−0.974171	−	0.225811i	$-0.927497\pi$
$587$	−439.287	+	439.287i	−0.748360	+	0.748360i	0.225811	+	0.974171i	$0.427497\pi$
$588$		0			0
$589$			5.79115i			0.00983217i
$590$	−0.987171	−	5.88491i	−0.00167317	−	0.00997442i
$591$		0			0
$592$	−132.038	+	132.038i	−0.223036	+	0.223036i
$593$	300.303	+	300.303i	0.506413	+	0.506413i	0.913423	−	0.407011i	$-0.133429\pi$
$593$	300.303	+	300.303i	0.506413	+	0.506413i	−0.407011	+	0.913423i	$0.633429\pi$
$594$		0			0
$595$	−311.786	+	437.471i	−0.524010	+	0.735245i
$596$	366.724			0.615308
$597$		0			0
$598$	−415.538	−	415.538i	−0.694879	−	0.694879i
$599$		−	276.725i		−	0.461979i	−0.972956	−	0.230989i	$-0.925804\pi$
$599$		−	276.725i		−	0.461979i	0.972956	−	0.230989i	$-0.0741963\pi$
$600$		0			0
$601$	−642.155			−1.06848			−0.534238	−	0.845334i	$-0.679402\pi$
$601$	−642.155			−1.06848			−0.534238	+	0.845334i	$0.679402\pi$
$602$	−349.966	+	349.966i	−0.581338	+	0.581338i
$603$		0			0
$604$		−	182.519i		−	0.302183i
$605$	−579.109	−	412.732i	−0.957205	−	0.682201i
$606$		0			0
$607$	690.552	−	690.552i	1.13765	−	1.13765i	0.148777	−	0.988871i	$-0.452466\pi$
$607$	690.552	−	690.552i	1.13765	−	1.13765i	0.988871	−	0.148777i	$-0.0475336\pi$
$608$	4.61827	+	4.61827i	0.00759583	+	0.00759583i
$609$		0			0
$610$	−221.678	+	37.1856i	−0.363406	+	0.0609599i
$611$	−337.149			−0.551798
$612$		0			0
$613$	−409.139	−	409.139i	−0.667437	−	0.667437i	0.289685	−	0.957122i	$-0.406450\pi$
$613$	−409.139	−	409.139i	−0.667437	−	0.667437i	−0.957122	+	0.289685i	$0.906450\pi$
$614$		−	835.865i		−	1.36134i
$615$		0			0
$616$	−464.882			−0.754678
$617$	−507.604	+	507.604i	−0.822697	+	0.822697i	−0.986494	−	0.163797i	$-0.947626\pi$
$617$	−507.604	+	507.604i	−0.822697	+	0.822697i	0.163797	+	0.986494i	$0.447626\pi$
$618$		0			0
$619$		−	9.23290i		−	0.0149158i	−0.999972	−	0.00745791i	$-0.997626\pi$
$619$		−	9.23290i		−	0.0149158i	0.999972	−	0.00745791i	$-0.00237395\pi$
$620$	29.1113	−	40.8464i	0.0469536	−	0.0658813i
$621$		0			0
$622$	365.940	−	365.940i	0.588328	−	0.588328i
$623$	−736.031	−	736.031i	−1.18143	−	1.18143i
$624$		0			0
$625$	−491.902	+	385.561i	−0.787043	+	0.616898i
$626$	860.283			1.37425
$627$		0			0
$628$	50.7395	+	50.7395i	0.0807954	+	0.0807954i
$629$		−	495.099i		−	0.787121i
$630$		0			0
$631$	1103.76			1.74923			0.874614	−	0.484820i	$-0.161115\pi$
$631$	1103.76			1.74923			0.874614	+	0.484820i	$0.161115\pi$
$632$	−20.8142	+	20.8142i	−0.0329339	+	0.0329339i
$633$		0			0
$634$			57.9759i			0.0914446i
$635$	1007.75	−	169.046i	1.58700	−	0.266213i
$636$		0			0
$637$	793.146	−	793.146i	1.24513	−	1.24513i
$638$	−374.371	−	374.371i	−0.586789	−	0.586789i
$639$		0			0
$640$	−9.35840	−	55.7891i	−0.0146225	−	0.0871704i
$641$	523.986			0.817451			0.408726	−	0.912657i	$-0.365973\pi$
$641$	523.986			0.817451			0.408726	+	0.912657i	$0.365973\pi$
$642$		0			0
$643$	−289.145	−	289.145i	−0.449681	−	0.449681i	0.445568	−	0.895248i	$-0.353002\pi$
$643$	−289.145	−	289.145i	−0.449681	−	0.449681i	−0.895248	+	0.445568i	$0.853002\pi$
$644$			402.525i			0.625039i
$645$		0			0
$646$	−17.3170			−0.0268065
$647$	829.739	−	829.739i	1.28244	−	1.28244i	0.343166	−	0.939275i	$-0.388501\pi$
$647$	829.739	−	829.739i	1.28244	−	1.28244i	0.939275	−	0.343166i	$-0.111499\pi$
$648$		0			0
$649$			13.6913i			0.0210961i
$650$	241.304	+	699.016i	0.371238	+	1.07541i
$651$		0			0
$652$	−317.356	+	317.356i	−0.486742	+	0.486742i
$653$	−405.942	−	405.942i	−0.621656	−	0.621656i	0.324298	−	0.945955i	$-0.394872\pi$
$653$	−405.942	−	405.942i	−0.621656	−	0.621656i	−0.945955	+	0.324298i	$0.894872\pi$
$654$		0			0
$655$	427.104	+	304.397i	0.652067	+	0.464729i
$656$	209.981			0.320093
$657$		0			0
$658$	163.295	+	163.295i	0.248169	+	0.248169i
$659$		−	652.479i		−	0.990105i	−0.868863	−	0.495053i	$-0.835149\pi$
$659$		−	652.479i		−	0.990105i	0.868863	−	0.495053i	$-0.164851\pi$
$660$		0			0
$661$	883.297			1.33630			0.668152	−	0.744025i	$-0.267086\pi$
$661$	883.297			1.33630			0.668152	+	0.744025i	$0.267086\pi$
$662$	145.615	−	145.615i	0.219962	−	0.219962i
$663$		0			0
$664$		−	65.7903i		−	0.0990818i
$665$	9.67493	+	57.6760i	0.0145488	+	0.0867308i
$666$		0			0
$667$	−324.155	+	324.155i	−0.485990	+	0.485990i
$668$	−282.797	−	282.797i	−0.423349	−	0.423349i
$669$		0			0
$670$	143.090	−	200.771i	0.213567	−	0.299658i
$671$	515.737			0.768609
$672$		0			0
$673$	−416.448	−	416.448i	−0.618794	−	0.618794i	0.326428	−	0.945222i	$-0.394155\pi$
$673$	−416.448	−	416.448i	−0.618794	−	0.618794i	−0.945222	+	0.326428i	$0.894155\pi$
$674$			923.292i			1.36987i
$675$		0			0
$676$	536.961			0.794322
$677$	−820.922	+	820.922i	−1.21259	+	1.21259i	−0.242415	+	0.970173i	$0.577939\pi$
$677$	−820.922	+	820.922i	−1.21259	+	1.21259i	−0.970173	+	0.242415i	$0.922061\pi$
$678$		0			0
$679$		−	229.245i		−	0.337621i
$680$	122.141	+	87.0501i	0.179619	+	0.128015i
$681$		0			0
$682$	−81.3788	+	81.3788i	−0.119324	+	0.119324i
$683$	−31.6260	−	31.6260i	−0.0463045	−	0.0463045i	0.683575	−	0.729880i	$-0.260424\pi$
$683$	−31.6260	−	31.6260i	−0.0463045	−	0.0463045i	−0.729880	+	0.683575i	$0.760424\pi$
$684$		0			0
$685$	284.108	−	47.6581i	0.414757	−	0.0695738i
$686$	−66.2991			−0.0966459
$687$		0			0
$688$	97.7099	+	97.7099i	0.142020	+	0.142020i
$689$		−	893.085i		−	1.29620i
$690$		0			0
$691$	−594.049			−0.859694			−0.429847	−	0.902902i	$-0.641433\pi$
$691$	−594.049			−0.859694			−0.429847	+	0.902902i	$0.641433\pi$
$692$	345.279	−	345.279i	0.498958	−	0.498958i
$693$		0			0
$694$			501.170i			0.722147i
$695$	362.426	−	508.524i	0.521476	−	0.731689i
$696$		0			0
$697$	−393.681	+	393.681i	−0.564822	+	0.564822i
$698$	−488.380	−	488.380i	−0.699685	−	0.699685i
$699$		0			0
$700$	221.689	−	455.437i	0.316699	−	0.650625i
$701$	−539.121			−0.769075			−0.384537	−	0.923109i	$-0.625639\pi$
$701$	−539.121			−0.769075			−0.384537	+	0.923109i	$0.625639\pi$
$702$		0			0
$703$	−38.1115	−	38.1115i	−0.0542127	−	0.0542127i
$704$			129.794i			0.184367i
$705$		0			0
$706$	−286.582			−0.405923
$707$	−410.894	+	410.894i	−0.581180	+	0.581180i
$708$		0			0
$709$			696.873i			0.982896i	0.870907	+	0.491448i	$0.163532\pi$
$709$			696.873i			0.982896i	−0.870907	+	0.491448i	$0.836468\pi$
$710$	−11.7781	+	1.97573i	−0.0165889	+	0.00278272i
$711$		0			0
$712$	−205.499	+	205.499i	−0.288622	+	0.288622i
$713$	70.4631	+	70.4631i	0.0988263	+	0.0988263i
$714$		0			0
$715$	−280.699	−	1673.36i	−0.392587	−	2.34036i
$716$	−224.388			−0.313391
$717$		0			0
$718$	−416.887	−	416.887i	−0.580622	−	0.580622i
$719$			446.528i			0.621041i	0.950567	+	0.310520i	$0.100503\pi$
$719$			446.528i			0.621041i	−0.950567	+	0.310520i	$0.899497\pi$
$720$		0			0
$721$	322.379			0.447128
$722$	359.667	−	359.667i	0.498154	−	0.498154i
$723$		0			0
$724$			22.4130i			0.0309572i
$725$	545.292	−	188.238i	0.752128	−	0.259639i
$726$		0			0
$727$	330.471	−	330.471i	0.454569	−	0.454569i	−0.442299	−	0.896868i	$-0.645837\pi$
$727$	330.471	−	330.471i	0.454569	−	0.454569i	0.896868	+	0.442299i	$0.145837\pi$
$728$	−423.781	−	423.781i	−0.582117	−	0.582117i
$729$		0			0
$730$	−820.051	−	584.451i	−1.12336	−	0.800618i
$731$	−366.381			−0.501205
$732$		0			0
$733$	−561.400	−	561.400i	−0.765894	−	0.765894i	0.211487	−	0.977381i	$-0.432169\pi$
$733$	−561.400	−	561.400i	−0.765894	−	0.765894i	−0.977381	+	0.211487i	$0.932169\pi$
$734$			194.754i			0.265333i
$735$		0			0
$736$	112.384			0.152696
$737$	−399.999	+	399.999i	−0.542739	+	0.542739i
$738$		0			0
$739$			5.34957i			0.00723893i	0.999993	+	0.00361947i	$0.00115211\pi$
$739$			5.34957i			0.00723893i	−0.999993	+	0.00361947i	$0.998848\pi$
$740$	77.2288	+	460.391i	0.104363	+	0.622150i
$741$		0			0
$742$	−432.559	+	432.559i	−0.582964	+	0.582964i
$743$	1016.29	+	1016.29i	1.36782	+	1.36782i	0.863540	+	0.504280i	$0.168242\pi$
$743$	1016.29	+	1016.29i	1.36782	+	1.36782i	0.504280	+	0.863540i	$0.331758\pi$
$744$		0			0
$745$	532.101	−	746.597i	0.714229	−	1.00214i
$746$	74.3008			0.0995989
$747$		0			0
$748$	−243.343	−	243.343i	−0.325326	−	0.325326i
$749$			241.960i			0.323044i
$750$		0			0
$751$	209.367			0.278785			0.139392	−	0.990237i	$-0.455485\pi$
$751$	209.367			0.278785			0.139392	+	0.990237i	$0.455485\pi$
$752$	45.5918	−	45.5918i	0.0606274	−	0.0606274i
$753$		0			0
$754$		−	682.545i		−	0.905232i
$755$	−371.582	−	264.827i	−0.492162	−	0.350764i
$756$		0			0
$757$	−854.924	+	854.924i	−1.12936	+	1.12936i	−0.139076	+	0.990282i	$0.544413\pi$
$757$	−854.924	+	854.924i	−1.12936	+	1.12936i	−0.990282	+	0.139076i	$0.955587\pi$
$758$	−430.016	−	430.016i	−0.567303	−	0.567303i
$759$		0			0
$760$	16.1030	−	2.70122i	0.0211882	−	0.00355424i
$761$	−428.892			−0.563591			−0.281795	−	0.959475i	$-0.590930\pi$
$761$	−428.892			−0.563591			−0.281795	+	0.959475i	$0.590930\pi$
$762$		0			0
$763$	−60.3637	−	60.3637i	−0.0791136	−	0.0791136i
$764$			173.764i			0.227439i
$765$		0			0
$766$	428.842			0.559845
$767$	−12.4809	+	12.4809i	−0.0162723	+	0.0162723i
$768$		0			0
$769$			481.976i			0.626757i	0.949628	+	0.313379i	$0.101461\pi$
$769$			481.976i			0.626757i	−0.949628	+	0.313379i	$0.898539\pi$
$770$	−674.524	+	946.434i	−0.876005	+	1.22913i
$771$		0			0
$772$	−116.969	+	116.969i	−0.151514	+	0.151514i
$773$	398.239	+	398.239i	0.515187	+	0.515187i	0.916111	−	0.400924i	$-0.131311\pi$
$773$	398.239	+	398.239i	0.515187	+	0.515187i	−0.400924	+	0.916111i	$0.631311\pi$
$774$		0			0
$775$	−40.9182	−	118.533i	−0.0527977	−	0.152946i
$776$	−64.0048			−0.0824804
$777$		0			0
$778$	41.4805	+	41.4805i	0.0533168	+	0.0533168i
$779$			60.6093i			0.0778039i
$780$		0			0
$781$	27.4019			0.0350857
$782$	−210.703	+	210.703i	−0.269441	+	0.269441i
$783$		0			0
$784$			214.511i			0.273610i
$785$	176.919	−	29.6775i	0.225375	−	0.0378058i
$786$		0			0
$787$	−503.039	+	503.039i	−0.639185	+	0.639185i	−0.950354	−	0.311169i	$-0.899279\pi$
$787$	−503.039	+	503.039i	−0.639185	+	0.639185i	0.311169	+	0.950354i	$0.399279\pi$
$788$	−183.798	−	183.798i	−0.233246	−	0.233246i
$789$		0			0
$790$	12.1743	+	72.5754i	0.0154104	+	0.0918677i
$791$	506.610			0.640468
$792$		0			0
$793$	470.140	+	470.140i	0.592863	+	0.592863i
$794$			52.2631i			0.0658226i
$795$		0			0
$796$	135.094			0.169716
$797$	485.469	−	485.469i	0.609120	−	0.609120i	−0.333596	−	0.942716i	$-0.608262\pi$
$797$	485.469	−	485.469i	0.609120	−	0.609120i	0.942716	+	0.333596i	$0.108262\pi$
$798$		0			0
$799$			170.955i			0.213961i
$800$	−127.157	−	61.8952i	−0.158947	−	0.0773691i
$801$		0			0
$802$	380.291	−	380.291i	0.474178	−	0.474178i
$803$	1633.80	+	1633.80i	2.03462	+	2.03462i
$804$		0			0
$805$	819.484	+	584.047i	1.01799	+	0.725525i
$806$	−148.368			−0.184079
$807$		0			0
$808$	114.721	+	114.721i	0.141981	+	0.141981i
$809$			1351.77i			1.67092i	0.549552	+	0.835459i	$0.314798\pi$
$809$			1351.77i			1.67092i	−0.549552	+	0.835459i	$0.685202\pi$
$810$		0			0
$811$	226.208			0.278925			0.139463	−	0.990227i	$-0.455463\pi$
$811$	226.208			0.278925			0.139463	+	0.990227i	$0.455463\pi$
$812$	−330.586	+	330.586i	−0.407125	+	0.407125i
$813$		0			0
$814$		−	1071.11i		−	1.31586i
$815$	185.622	+	1106.56i	0.227757	+	1.35775i
$816$		0			0
$817$	−28.2031	+	28.2031i	−0.0345204	+	0.0345204i
$818$	9.54256	+	9.54256i	0.0116657	+	0.0116657i
$819$		0			0
$820$	304.674	−	427.492i	0.371553	−	0.521331i
$821$	622.696			0.758460			0.379230	−	0.925302i	$-0.376189\pi$
$821$	622.696			0.758460			0.379230	+	0.925302i	$0.376189\pi$
$822$		0			0
$823$	835.573	+	835.573i	1.01528	+	1.01528i	0.999881	+	0.0153956i	$0.00490075\pi$
$823$	835.573	+	835.573i	1.01528	+	1.01528i	0.0153956	+	0.999881i	$0.495099\pi$
$824$		−	90.0077i		−	0.109233i
$825$		0			0
$826$	12.0900			0.0146369
$827$	−269.820	+	269.820i	−0.326264	+	0.326264i	−0.851164	−	0.524900i	$-0.824103\pi$
$827$	−269.820	+	269.820i	−0.326264	+	0.326264i	0.524900	+	0.851164i	$0.324103\pi$
$828$		0			0
$829$			228.498i			0.275630i	0.990458	+	0.137815i	$0.0440080\pi$
$829$			228.498i			0.275630i	−0.990458	+	0.137815i	$0.955992\pi$
$830$	−133.940	−	95.4590i	−0.161373	−	0.115011i
$831$		0			0
$832$	−118.319	+	118.319i	−0.142210	+	0.142210i
$833$	−402.173	−	402.173i	−0.482801	−	0.482801i
$834$		0			0
$835$	−986.062	+	165.408i	−1.18091	+	0.198093i
$836$	−37.4640			−0.0448134
$837$		0			0
$838$	−330.930	−	330.930i	−0.394904	−	0.394904i
$839$			1361.25i			1.62247i	0.584721	+	0.811234i	$0.301204\pi$
$839$			1361.25i			1.62247i	−0.584721	+	0.811234i	$0.698796\pi$
$840$		0			0
$841$	308.556			0.366892
$842$	178.379	−	178.379i	0.211852	−	0.211852i
$843$		0			0
$844$		−	563.576i		−	0.667744i
$845$	779.109	−	1093.18i	0.922022	−	1.29370i
$846$		0			0
$847$	1018.83	−	1018.83i	1.20286	−	1.20286i
$848$	120.770	+	120.770i	0.142417	+	0.142417i
$849$		0			0
$850$	354.443	−	122.356i	0.416992	−	0.143948i
$851$	−927.435			−1.08982
$852$		0			0
$853$	580.249	+	580.249i	0.680245	+	0.680245i	0.960055	−	0.279810i	$-0.0902715\pi$
$853$	580.249	+	580.249i	0.680245	+	0.680245i	−0.279810	+	0.960055i	$0.590271\pi$
$854$		−	455.418i		−	0.533276i
$855$		0			0
$856$	67.5548			0.0789191
$857$	−82.0233	+	82.0233i	−0.0957098	+	0.0957098i	−0.753340	−	0.657631i	$-0.771559\pi$
$857$	−82.0233	+	82.0233i	−0.0957098	+	0.0957098i	0.657631	+	0.753340i	$0.271559\pi$
$858$		0			0
$859$		−	1112.52i		−	1.29513i	−0.762010	−	0.647565i	$-0.775787\pi$
$859$		−	1112.52i		−	1.29513i	0.762010	−	0.647565i	$-0.224213\pi$
$860$	340.696	−	57.1505i	0.396159	−	0.0664541i
$861$		0			0
$862$	249.781	−	249.781i	0.289769	−	0.289769i
$863$	354.960	+	354.960i	0.411309	+	0.411309i	0.882194	−	0.470885i	$-0.156065\pi$
$863$	354.960	+	354.960i	0.411309	+	0.411309i	−0.470885	+	0.882194i	$0.656065\pi$
$864$		0			0
$865$	−201.953	−	1203.92i	−0.233472	−	1.39182i
$866$	−49.8905			−0.0576103
$867$		0			0
$868$	71.8610	+	71.8610i	0.0827892	+	0.0827892i
$869$		−	168.848i		−	0.194302i
$870$		0			0
$871$	−729.269			−0.837278
$872$	−16.8534	+	16.8534i	−0.0193273	+	0.0193273i
$873$		0			0
$874$			32.4388i			0.0371153i
$875$	−605.544	−	1112.15i	−0.692050	−	1.27103i
$876$		0			0
$877$	263.905	−	263.905i	0.300918	−	0.300918i	−0.540455	−	0.841373i	$-0.681748\pi$
$877$	263.905	−	263.905i	0.300918	−	0.300918i	0.841373	+	0.540455i	$0.181748\pi$
$878$	−109.350	−	109.350i	−0.124544	−	0.124544i
$879$		0			0
$880$	264.243	+	188.326i	0.300276	+	0.214007i
$881$	1377.92			1.56404			0.782022	−	0.623251i	$-0.214188\pi$
$881$	1377.92			1.56404			0.782022	+	0.623251i	$0.214188\pi$
$882$		0			0
$883$	−25.5579	−	25.5579i	−0.0289444	−	0.0289444i	0.692486	−	0.721431i	$-0.256515\pi$
$883$	−25.5579	−	25.5579i	−0.0289444	−	0.0289444i	−0.721431	+	0.692486i	$0.756515\pi$
$884$		−	443.658i		−	0.501876i
$885$		0			0
$886$	522.936			0.590222
$887$	−108.041	+	108.041i	−0.121805	+	0.121805i	−0.765382	−	0.643576i	$-0.777450\pi$
$887$	−108.041	+	108.041i	−0.121805	+	0.121805i	0.643576	+	0.765382i	$0.277450\pi$
$888$		0			0
$889$			2070.33i			2.32883i
$890$	120.196	+	716.536i	0.135052	+	0.805096i
$891$		0			0
$892$	−496.494	+	496.494i	−0.556608	+	0.556608i
$893$	13.1597	+	13.1597i	0.0147365	+	0.0147365i
$894$		0			0
$895$	−325.577	+	456.822i	−0.363773	+	0.510415i
$896$	114.614			0.127917
$897$		0			0
$898$	358.178	+	358.178i	0.398862	+	0.398862i
$899$			115.740i			0.128743i
$900$		0			0
$901$	−452.848			−0.502606
$902$	−851.698	+	851.698i	−0.944233	+	0.944233i
$903$		0			0
$904$		−	141.445i		−	0.156465i
$905$	45.6297	+	32.5203i	0.0504195	+	0.0359341i
$906$		0			0
$907$	1172.84	−	1172.84i	1.29310	−	1.29310i	0.360237	−	0.932861i	$-0.382696\pi$
$907$	1172.84	−	1172.84i	1.29310	−	1.29310i	0.932861	−	0.360237i	$-0.117304\pi$
$908$	473.903	+	473.903i	0.521920	+	0.521920i
$909$		0			0
$910$	−1477.65	+	247.870i	−1.62379	+	0.272384i
$911$	−158.322			−0.173789			−0.0868947	−	0.996217i	$-0.527694\pi$
$911$	−158.322			−0.173789			−0.0868947	+	0.996217i	$0.527694\pi$
$912$		0			0
$913$	266.850	+	266.850i	0.292278	+	0.292278i
$914$			1240.34i			1.35705i
$915$		0			0
$916$	−771.629			−0.842390
$917$	−751.403	+	751.403i	−0.819415	+	0.819415i
$918$		0			0
$919$		−	449.294i		−	0.488894i	−0.969663	−	0.244447i	$-0.921394\pi$
$919$		−	449.294i		−	0.488894i	0.969663	−	0.244447i	$-0.0786065\pi$
$920$	163.065	−	228.799i	0.177245	−	0.248694i
$921$		0			0
$922$	214.672	−	214.672i	0.232833	−	0.232833i
$923$	24.9793	+	24.9793i	0.0270632	+	0.0270632i
$924$		0			0
$925$	1049.35	+	510.781i	1.13443	+	0.552196i
$926$	−475.477			−0.513474
$927$		0			0
$928$	92.2990	+	92.2990i	0.0994601	+	0.0994601i
$929$		−	983.056i		−	1.05819i	−0.848563	−	0.529094i	$-0.822532\pi$
$929$		−	983.056i		−	1.05819i	0.848563	−	0.529094i	$-0.177468\pi$
$930$		0			0
$931$	−61.9167			−0.0665056
$932$	−61.8668	+	61.8668i	−0.0663807	+	0.0663807i
$933$		0			0
$934$			1102.40i			1.18030i
$935$	−848.494	+	142.332i	−0.907480	+	0.152226i
$936$		0			0
$937$	−890.763	+	890.763i	−0.950654	+	0.950654i	−0.998838	−	0.0481843i	$-0.984657\pi$
$937$	−890.763	+	890.763i	−0.950654	+	0.950654i	0.0481843	+	0.998838i	$0.484657\pi$
$938$	353.216	+	353.216i	0.376563	+	0.376563i
$939$		0			0
$940$	−26.6667	−	158.970i	−0.0283688	−	0.169117i
$941$	−282.903			−0.300641			−0.150320	−	0.988637i	$-0.548031\pi$
$941$	−282.903			−0.300641			−0.150320	+	0.988637i	$0.548031\pi$
$942$		0			0
$943$	737.456	+	737.456i	0.782032	+	0.782032i
$944$		−	3.37552i		−	0.00357576i
$945$		0			0
$946$	−792.636			−0.837882
$947$	307.334	−	307.334i	0.324534	−	0.324534i	−0.525970	−	0.850503i	$-0.676297\pi$
$947$	307.334	−	307.334i	0.324534	−	0.324534i	0.850503	+	0.525970i	$0.176297\pi$
$948$		0			0
$949$			2978.71i			3.13878i
$950$	17.8655	−	36.7029i	0.0188058	−	0.0386346i
$951$		0			0
$952$	−214.883	+	214.883i	−0.225717	+	0.225717i
$953$	−521.907	−	521.907i	−0.547647	−	0.547647i	0.378113	−	0.925760i	$-0.376573\pi$
$953$	−521.907	−	521.907i	−0.547647	−	0.547647i	−0.925760	+	0.378113i	$0.876573\pi$
$954$		0			0
$955$	353.758	+	252.124i	0.370428	+	0.264004i
$956$	−261.990			−0.274048
$957$		0			0
$958$	618.218	+	618.218i	0.645321	+	0.645321i
$959$			583.676i			0.608630i
$960$		0			0
$961$	−935.841			−0.973820
$962$	976.410	−	976.410i	1.01498	−	1.01498i
$963$		0			0
$964$			130.758i			0.135641i
$965$	68.4153	+	407.850i	0.0708966	+	0.422642i
$966$		0			0
$967$	995.944	−	995.944i	1.02993	−	1.02993i	0.0303941	−	0.999538i	$-0.490324\pi$
$967$	995.944	−	995.944i	1.02993	−	1.02993i	0.999538	−	0.0303941i	$-0.00967623\pi$
$968$	−284.454	−	284.454i	−0.293858	−	0.293858i
$969$		0			0
$970$	−92.8683	+	130.305i	−0.0957405	+	0.134335i
$971$	−684.172			−0.704605			−0.352303	−	0.935886i	$-0.614601\pi$
$971$	−684.172			−0.704605			−0.352303	+	0.935886i	$0.614601\pi$
$972$		0			0
$973$	894.646	+	894.646i	0.919472	+	0.919472i
$974$			836.405i			0.858732i
$975$		0			0
$976$	−127.152			−0.130279
$977$	−770.809	+	770.809i	−0.788955	+	0.788955i	−0.981323	−	0.192368i	$-0.938383\pi$
$977$	−770.809	+	770.809i	−0.788955	+	0.788955i	0.192368	+	0.981323i	$0.438383\pi$
$978$		0			0
$979$		−	1667.03i		−	1.70279i
$980$	436.713	+	311.246i	0.445626	+	0.317598i
$981$		0			0
$982$	−326.463	+	326.463i	−0.332447	+	0.332447i
$983$	985.249	+	985.249i	1.00229	+	1.00229i	0.999997	+	0.00229052i	$0.000729096\pi$
$983$	985.249	+	985.249i	1.00229	+	1.00229i	0.00229052	+	0.999997i	$0.499271\pi$
$984$		0			0
$985$	−640.869	+	107.503i	−0.650628	+	0.109140i
$986$	−346.092			−0.351006
$987$		0			0
$988$	−34.1518	−	34.1518i	−0.0345666	−	0.0345666i
$989$			686.316i			0.693950i
$990$		0			0
$991$	−454.036			−0.458160			−0.229080	−	0.973408i	$-0.573572\pi$
$991$	−454.036			−0.458160			−0.229080	+	0.973408i	$0.573572\pi$
$992$	20.0635	−	20.0635i	0.0202253	−	0.0202253i
$993$		0			0
$994$		−	24.1971i		−	0.0243431i
$995$	196.016	−	275.032i	0.197001	−	0.276414i
$996$		0			0
$997$	466.031	−	466.031i	0.467433	−	0.467433i	−0.433649	−	0.901082i	$-0.642774\pi$
$997$	466.031	−	466.031i	0.467433	−	0.467433i	0.901082	+	0.433649i	$0.142774\pi$
$998$	227.119	+	227.119i	0.227574	+	0.227574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.g.k.163.2		12
3.2	odd	2		810.3.g.i.163.5		12
5.2	odd	4	inner	810.3.g.k.487.2		12
9.2	odd	6		270.3.l.b.253.1		24
9.4	even	3		90.3.k.a.43.2	yes	24
9.5	odd	6		270.3.l.b.73.3		24
9.7	even	3		90.3.k.a.13.2	yes	24
15.2	even	4		810.3.g.i.487.5		12
45.2	even	12		270.3.l.b.37.3		24
45.7	odd	12		90.3.k.a.67.2	yes	24
45.22	odd	12		90.3.k.a.7.2	✓	24
45.32	even	12		270.3.l.b.127.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.2	✓	24	45.22	odd	12
90.3.k.a.13.2	yes	24	9.7	even	3
90.3.k.a.43.2	yes	24	9.4	even	3
90.3.k.a.67.2	yes	24	45.7	odd	12
270.3.l.b.37.3		24	45.2	even	12
270.3.l.b.73.3		24	9.5	odd	6
270.3.l.b.127.1		24	45.32	even	12
270.3.l.b.253.1		24	9.2	odd	6
810.3.g.i.163.5		12	3.2	odd	2
810.3.g.i.487.5		12	15.2	even	4
810.3.g.k.163.2		12	1.1	even	1	trivial
810.3.g.k.487.2		12	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.07172 - 2.90192i) q^{5} +(7.16337 - 7.16337i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-6.97363 + 1.16980i) q^{10} +16.2243 q^{11} +(14.7899 + 14.7899i) q^{13} -14.3267i q^{14} -4.00000 q^{16} +(7.49936 - 7.49936i) q^{17} -1.15457i q^{19} +(-5.80383 + 8.14343i) q^{20} +(16.2243 - 16.2243i) q^{22} +(-14.0480 - 14.0480i) q^{23} +(8.15776 + 23.6316i) q^{25} +29.5797 q^{26} +(-14.3267 - 14.3267i) q^{28} -23.0747i q^{29} -5.01587 q^{31} +(-4.00000 + 4.00000i) q^{32} -14.9987i q^{34} +(-49.9547 + 8.37971i) q^{35} +(33.0094 - 33.0094i) q^{37} +(-1.15457 - 1.15457i) q^{38} +(2.33960 + 13.9473i) q^{40} -52.4953 q^{41} +(-24.4275 - 24.4275i) q^{43} -32.4486i q^{44} -28.0961 q^{46} +(-11.3980 + 11.3980i) q^{47} -53.6276i q^{49} +(31.7893 + 15.4738i) q^{50} +(29.5797 - 29.5797i) q^{52} +(-30.1924 - 30.1924i) q^{53} +(-66.0607 - 47.0815i) q^{55} -28.6535 q^{56} +(-23.0747 - 23.0747i) q^{58} +0.843880i q^{59} +31.7880 q^{61} +(-5.01587 + 5.01587i) q^{62} +8.00000i q^{64} +(-17.3012 - 103.139i) q^{65} +(-24.6543 + 24.6543i) q^{67} +(-14.9987 - 14.9987i) q^{68} +(-41.5750 + 58.3344i) q^{70} +1.68895 q^{71} +(100.701 + 100.701i) q^{73} -66.0188i q^{74} -2.30913 q^{76} +(116.220 - 116.220i) q^{77} -10.4071i q^{79} +(16.2869 + 11.6077i) q^{80} +(-52.4953 + 52.4953i) q^{82} +(16.4476 + 16.4476i) q^{83} +(-52.2978 + 8.77275i) q^{85} -48.8549 q^{86} +(-32.4486 - 32.4486i) q^{88} -102.749i q^{89} +211.891 q^{91} +(-28.0961 + 28.0961i) q^{92} +22.7959i q^{94} +(-3.35046 + 4.70107i) q^{95} +(16.0012 - 16.0012i) q^{97} +(-53.6276 - 53.6276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 6 q^{7} - 24 q^{8} - 6 q^{10} + 12 q^{11} - 48 q^{16} - 18 q^{17} - 12 q^{20} + 12 q^{22} + 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} - 48 q^{32} - 168 q^{35} + 66 q^{37} + 36 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 12 * q^2 + 6 * q^7 - 24 * q^8 - 6 * q^10 + 12 * q^11 - 48 * q^16 - 18 * q^17 - 12 * q^20 + 12 * q^22 + 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 - 48 * q^32 - 168 * q^35 + 66 * q^37 + 36 * q^38 - 12 * q^40 - 24 * q^41 - 108 * q^43 + 108 * q^46 - 48 * q^47 - 54 * q^50 + 192 * q^53 - 276 * q^55 - 24 * q^56 - 60 * q^58 + 456 * q^61 + 72 * q^62 - 264 * q^65 - 12 * q^67 + 36 * q^68 - 174 * q^70 - 84 * q^71 - 216 * q^73 + 72 * q^76 + 48 * q^77 - 24 * q^82 + 246 * q^83 - 324 * q^85 - 216 * q^86 - 24 * q^88 + 612 * q^91 + 108 * q^92 - 432 * q^95 + 102 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more