LMFDB - Embedded newform 224.3.o.c.207.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(79,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.o (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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} + 2x^{10} - 12x^{9} + 12x^{8} - 12x^{7} + 148x^{6} - 48x^{5} + 192x^{4} - 768x^{3} + 512x^{2} + 4096 $ x^12 + 2x^10 - 12x^9 + 12x^8 - 12x^7 + 148x^6 - 48x^5 + 192x^4 - 768x^3 + 512*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			207.5
Root			$-0.685878 + 1.87872i$ of defining polynomial
Character	$\chi$	$=$	224.207
Dual form			224.3.o.c.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46995 - 2.54604i) q^{3} +(-7.59793 + 4.38667i) q^{5} +(3.55324 + 6.03112i) q^{7} +(0.178469 + 0.309118i) q^{9} +O(q^{10})$	\(q+(1.46995 - 2.54604i) q^{3} +(-7.59793 + 4.38667i) q^{5} +(3.55324 + 6.03112i) q^{7} +(0.178469 + 0.309118i) q^{9} +(-1.64842 + 2.85515i) q^{11} +4.10293i q^{13} +25.7928i q^{15} +(-11.6184 + 20.1236i) q^{17} +(2.76861 + 4.79537i) q^{19} +(20.5786 - 0.181210i) q^{21} +(12.8739 - 7.43273i) q^{23} +(25.9857 - 45.0085i) q^{25} +27.5085 q^{27} +43.1747i q^{29} +(-26.6958 - 15.4128i) q^{31} +(4.84621 + 8.39389i) q^{33} +(-53.4538 - 30.2371i) q^{35} +(11.3647 - 6.56141i) q^{37} +(10.4462 + 6.03112i) q^{39} -8.56863 q^{41} +11.3076 q^{43} +(-2.71199 - 1.56577i) q^{45} +(-31.9084 + 18.4223i) q^{47} +(-23.7489 + 42.8601i) q^{49} +(34.1570 + 59.1616i) q^{51} +(-53.2193 - 30.7262i) q^{53} -28.9243i q^{55} +16.2789 q^{57} +(-31.3354 + 54.2746i) q^{59} +(34.3623 - 19.8391i) q^{61} +(-1.23018 + 2.17474i) q^{63} +(-17.9982 - 31.1738i) q^{65} +(21.3147 - 36.9182i) q^{67} -43.7031i q^{69} -107.155i q^{71} +(-18.0085 + 31.1917i) q^{73} +(-76.3955 - 132.321i) q^{75} +(-23.0770 + 0.203211i) q^{77} +(36.3029 - 20.9595i) q^{79} +(38.8301 - 67.2557i) q^{81} +87.8010 q^{83} -203.864i q^{85} +(109.924 + 63.4648i) q^{87} +(-1.04794 - 1.81508i) q^{89} +(-24.7453 + 14.5787i) q^{91} +(-78.4831 + 45.3122i) q^{93} +(-42.0713 - 24.2899i) q^{95} -40.6387 q^{97} -1.17677 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 8 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 8 * q^9	$ 12 q - 6 q^{3} - 8 q^{9} + 14 q^{11} - 82 q^{17} + 94 q^{19} + 116 q^{25} + 60 q^{27} + 146 q^{33} - 270 q^{35} + 120 q^{41} - 40 q^{43} - 204 q^{49} + 106 q^{51} - 372 q^{57} - 62 q^{59} - 64 q^{65} + 178 q^{67} + 54 q^{73} - 140 q^{75} + 206 q^{81} + 392 q^{83} - 26 q^{89} + 88 q^{91} - 184 q^{97} - 872 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 8 * q^9 + 14 * q^11 - 82 * q^17 + 94 * q^19 + 116 * q^25 + 60 * q^27 + 146 * q^33 - 270 * q^35 + 120 * q^41 - 40 * q^43 - 204 * q^49 + 106 * q^51 - 372 * q^57 - 62 * q^59 - 64 * q^65 + 178 * q^67 + 54 * q^73 - 140 * q^75 + 206 * q^81 + 392 * q^83 - 26 * q^89 + 88 * q^91 - 184 * q^97 - 872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.46995	−	2.54604i	0.489985	−	0.848678i	−0.509949	−	0.860205i	$-0.670336\pi$
$3$	1.46995	−	2.54604i	0.489985	−	0.848678i	0.999934	+	0.0115263i	$0.00366901\pi$
$4$		0			0
$5$	−7.59793	+	4.38667i	−1.51959	+	0.877333i	−0.519852	+	0.854257i	$0.674013\pi$
$5$	−7.59793	+	4.38667i	−1.51959	+	0.877333i	−0.999734	+	0.0230765i	$0.992654\pi$
$6$		0			0
$7$	3.55324	+	6.03112i	0.507606	+	0.861589i
$7$	3.55324	+	6.03112i	0.507606	+	0.861589i
$8$		0			0
$9$	0.178469	+	0.309118i	0.0198299	+	0.0343464i
$10$		0			0
$11$	−1.64842	+	2.85515i	−0.149857	+	0.259559i	−0.931174	−	0.364574i	$-0.881215\pi$
$11$	−1.64842	+	2.85515i	−0.149857	+	0.259559i	0.781318	+	0.624134i	$0.214548\pi$
$12$		0			0
$13$			4.10293i			0.315610i	0.987470	+	0.157805i	$0.0504418\pi$
$13$			4.10293i			0.315610i	−0.987470	+	0.157805i	$0.949558\pi$
$14$		0			0
$15$			25.7928i			1.71952i
$16$		0			0
$17$	−11.6184	+	20.1236i	−0.683434	+	1.18374i	0.290492	+	0.956877i	$0.406181\pi$
$17$	−11.6184	+	20.1236i	−0.683434	+	1.18374i	−0.973926	+	0.226865i	$0.927152\pi$
$18$		0			0
$19$	2.76861	+	4.79537i	0.145716	+	0.252388i	0.929640	−	0.368469i	$-0.120118\pi$
$19$	2.76861	+	4.79537i	0.145716	+	0.252388i	−0.783924	+	0.620857i	$0.786785\pi$
$20$		0			0
$21$	20.5786	−	0.181210i	0.979931	−	0.00862905i
$22$		0			0
$23$	12.8739	−	7.43273i	0.559734	−	0.323162i	−0.193305	−	0.981139i	$-0.561921\pi$
$23$	12.8739	−	7.43273i	0.559734	−	0.323162i	0.753039	+	0.657976i	$0.228587\pi$
$24$		0			0
$25$	25.9857	−	45.0085i	1.03943	−	1.80034i
$26$		0			0
$27$	27.5085			1.01883
$28$		0			0
$29$			43.1747i			1.48878i	0.667744	+	0.744391i	$0.267260\pi$
$29$			43.1747i			1.48878i	−0.667744	+	0.744391i	$0.732740\pi$
$30$		0			0
$31$	−26.6958	−	15.4128i	−0.861153	−	0.497187i	0.00324492	−	0.999995i	$-0.498967\pi$
$31$	−26.6958	−	15.4128i	−0.861153	−	0.497187i	−0.864398	+	0.502808i	$0.832300\pi$
$32$		0			0
$33$	4.84621	+	8.39389i	0.146855	+	0.254360i
$34$		0			0
$35$	−53.4538	−	30.2371i	−1.52725	−	0.863918i
$36$		0			0
$37$	11.3647	−	6.56141i	0.307154	−	0.177335i	−0.338498	−	0.940967i	$-0.609919\pi$
$37$	11.3647	−	6.56141i	0.307154	−	0.177335i	0.645652	+	0.763632i	$0.276586\pi$
$38$		0			0
$39$	10.4462	+	6.03112i	0.267852	+	0.154644i
$40$		0			0
$41$	−8.56863			−0.208991			−0.104496	−	0.994525i	$-0.533323\pi$
$41$	−8.56863			−0.208991			−0.104496	+	0.994525i	$0.533323\pi$
$42$		0			0
$43$	11.3076			0.262967			0.131483	−	0.991318i	$-0.458026\pi$
$43$	11.3076			0.262967			0.131483	+	0.991318i	$0.458026\pi$
$44$		0			0
$45$	−2.71199	−	1.56577i	−0.0602665	−	0.0347949i
$46$		0			0
$47$	−31.9084	+	18.4223i	−0.678902	+	0.391964i	−0.799441	−	0.600744i	$-0.794871\pi$
$47$	−31.9084	+	18.4223i	−0.678902	+	0.391964i	0.120539	+	0.992709i	$0.461538\pi$
$48$		0			0
$49$	−23.7489	+	42.8601i	−0.484672	+	0.874696i
$50$		0			0
$51$	34.1570	+	59.1616i	0.669744	+	1.16003i
$52$		0			0
$53$	−53.2193	−	30.7262i	−1.00414	−	0.579739i	−0.0946675	−	0.995509i	$-0.530179\pi$
$53$	−53.2193	−	30.7262i	−1.00414	−	0.579739i	−0.909470	+	0.415770i	$0.863512\pi$
$54$		0			0
$55$		−	28.9243i		−	0.525897i
$56$		0			0
$57$	16.2789			0.285595
$58$		0			0
$59$	−31.3354	+	54.2746i	−0.531109	+	0.919908i	0.468232	+	0.883606i	$0.344891\pi$
$59$	−31.3354	+	54.2746i	−0.531109	+	0.919908i	−0.999341	+	0.0363022i	$0.988442\pi$
$60$		0			0
$61$	34.3623	−	19.8391i	0.563317	−	0.325231i	−0.191159	−	0.981559i	$-0.561225\pi$
$61$	34.3623	−	19.8391i	0.563317	−	0.325231i	0.754476	+	0.656328i	$0.227891\pi$
$62$		0			0
$63$	−1.23018	+	2.17474i	−0.0195267	+	0.0345197i
$64$		0			0
$65$	−17.9982	−	31.1738i	−0.276895	−	0.479597i
$66$		0			0
$67$	21.3147	−	36.9182i	0.318130	−	0.551018i	−0.661968	−	0.749533i	$-0.730278\pi$
$67$	21.3147	−	36.9182i	0.318130	−	0.551018i	0.980098	+	0.198514i	$0.0636117\pi$
$68$		0			0
$69$		−	43.7031i		−	0.633378i
$70$		0			0
$71$		−	107.155i		−	1.50922i	−0.656174	−	0.754610i	$-0.727826\pi$
$71$		−	107.155i		−	1.50922i	0.656174	−	0.754610i	$-0.272174\pi$
$72$		0			0
$73$	−18.0085	+	31.1917i	−0.246692	+	0.427284i	−0.962606	−	0.270905i	$-0.912677\pi$
$73$	−18.0085	+	31.1917i	−0.246692	+	0.427284i	0.715914	+	0.698189i	$0.246010\pi$
$74$		0			0
$75$	−76.3955	−	132.321i	−1.01861	−	1.76428i
$76$		0			0
$77$	−23.0770	+	0.203211i	−0.299702	+	0.00263910i
$78$		0			0
$79$	36.3029	−	20.9595i	0.459530	−	0.265310i	−0.252317	−	0.967645i	$-0.581192\pi$
$79$	36.3029	−	20.9595i	0.459530	−	0.265310i	0.711847	+	0.702335i	$0.247859\pi$
$80$		0			0
$81$	38.8301	−	67.2557i	0.479384	−	0.830317i
$82$		0			0
$83$	87.8010			1.05784			0.528922	−	0.848671i	$-0.322596\pi$
$83$	87.8010			1.05784			0.528922	+	0.848671i	$0.322596\pi$
$84$		0			0
$85$		−	203.864i		−	2.39840i
$86$		0			0
$87$	109.924	+	63.4648i	1.26350	+	0.729480i
$88$		0			0
$89$	−1.04794	−	1.81508i	−0.0117746	−	0.0203942i	0.860078	−	0.510162i	$-0.170415\pi$
$89$	−1.04794	−	1.81508i	−0.0117746	−	0.0203942i	−0.871853	+	0.489768i	$0.837081\pi$
$90$		0			0
$91$	−24.7453	+	14.5787i	−0.271926	+	0.160206i
$92$		0			0
$93$	−78.4831	+	45.3122i	−0.843904	+	0.487228i
$94$		0			0
$95$	−42.0713	−	24.2899i	−0.442856	−	0.255683i
$96$		0			0
$97$	−40.6387			−0.418956			−0.209478	−	0.977813i	$-0.567176\pi$
$97$	−40.6387			−0.418956			−0.209478	+	0.977813i	$0.567176\pi$
$98$		0			0
$99$	−1.17677			−0.0118866
$100$		0			0
$101$	24.4300	+	14.1047i	0.241882	+	0.139650i	0.616041	−	0.787714i	$-0.288735\pi$
$101$	24.4300	+	14.1047i	0.241882	+	0.139650i	−0.374160	+	0.927364i	$0.622069\pi$
$102$		0			0
$103$	74.6380	−	43.0923i	0.724641	−	0.418372i	−0.0918176	−	0.995776i	$-0.529268\pi$
$103$	74.6380	−	43.0923i	0.724641	−	0.418372i	0.816458	+	0.577404i	$0.195934\pi$
$104$		0			0
$105$	−155.559	+	91.6481i	−1.48152	+	0.872839i
$106$		0			0
$107$	32.1677	+	55.7161i	0.300633	+	0.520711i	0.976279	−	0.216515i	$-0.0694689\pi$
$107$	32.1677	+	55.7161i	0.300633	+	0.520711i	−0.675647	+	0.737225i	$0.736136\pi$
$108$		0			0
$109$	99.8826	+	57.6672i	0.916354	+	0.529057i	0.882470	−	0.470369i	$-0.155879\pi$
$109$	99.8826	+	57.6672i	0.916354	+	0.529057i	0.0338838	+	0.999426i	$0.489212\pi$
$110$		0			0
$111$		−	38.5799i		−	0.347566i
$112$		0			0
$113$	201.331			1.78169			0.890845	−	0.454308i	$-0.150113\pi$
$113$	201.331			1.78169			0.890845	+	0.454308i	$0.150113\pi$
$114$		0			0
$115$	−65.2098	+	112.947i	−0.567042	+	0.982146i
$116$		0			0
$117$	−1.26829	+	0.732248i	−0.0108401	+	0.00625853i
$118$		0			0
$119$	−162.651	+	1.43227i	−1.36681	+	0.0120359i
$120$		0			0
$121$	55.0654	+	95.3761i	0.455086	+	0.788232i
$122$		0			0
$123$	−12.5955	+	21.8160i	−0.102402	+	0.177366i
$124$		0			0
$125$			236.628i			1.89303i
$126$		0			0
$127$			105.675i			0.832088i	0.909344	+	0.416044i	$0.136584\pi$
$127$			105.675i			0.832088i	−0.909344	+	0.416044i	$0.863416\pi$
$128$		0			0
$129$	16.6216	−	28.7895i	0.128850	−	0.223174i
$130$		0			0
$131$	−81.8153	−	141.708i	−0.624544	−	1.08174i	−0.988629	−	0.150377i	$-0.951951\pi$
$131$	−81.8153	−	141.708i	−0.624544	−	1.08174i	0.364084	−	0.931366i	$-0.381382\pi$
$132$		0			0
$133$	−19.0839	+	33.7369i	−0.143488	+	0.253661i
$134$		0			0
$135$	−209.008	+	120.671i	−1.54821	+	0.893858i
$136$		0			0
$137$	16.0139	−	27.7368i	0.116889	−	0.202458i	−0.801644	−	0.597802i	$-0.796041\pi$
$137$	16.0139	−	27.7368i	0.116889	−	0.202458i	0.918533	+	0.395343i	$0.129374\pi$
$138$		0			0
$139$	27.2303			0.195901			0.0979507	−	0.995191i	$-0.468771\pi$
$139$	27.2303			0.195901			0.0979507	+	0.995191i	$0.468771\pi$
$140$		0			0
$141$			108.320i			0.768226i
$142$		0			0
$143$	−11.7145	−	6.76337i	−0.0819196	−	0.0472963i
$144$		0			0
$145$	−189.393	−	328.038i	−1.30616	−	2.26233i
$146$		0			0
$147$	74.2136	+	123.468i	0.504854	+	0.839918i
$148$		0			0
$149$	107.716	−	62.1901i	0.722930	−	0.417384i	−0.0929004	−	0.995675i	$-0.529614\pi$
$149$	107.716	−	62.1901i	0.722930	−	0.417384i	0.815830	+	0.578292i	$0.196280\pi$
$150$		0			0
$151$	92.9010	+	53.6364i	0.615238	+	0.355208i	0.775013	−	0.631945i	$-0.217743\pi$
$151$	92.9010	+	53.6364i	0.615238	+	0.355208i	−0.159774	+	0.987154i	$0.551077\pi$
$152$		0			0
$153$	−8.29410			−0.0542098
$154$		0			0
$155$	270.443			1.74480
$156$		0			0
$157$	92.7573	+	53.5534i	0.590811	+	0.341105i	0.765418	−	0.643533i	$-0.222532\pi$
$157$	92.7573	+	53.5534i	0.590811	+	0.341105i	−0.174607	+	0.984638i	$0.555866\pi$
$158$		0			0
$159$	−156.460	+	90.3321i	−0.984024	+	0.568126i
$160$		0			0
$161$	90.5718	+	51.2336i	0.562558	+	0.318221i
$162$		0			0
$163$	−100.378	−	173.859i	−0.615813	−	1.06662i	−0.990241	−	0.139364i	$-0.955494\pi$
$163$	−100.378	−	173.859i	−0.615813	−	1.06662i	0.374428	−	0.927256i	$-0.377839\pi$
$164$		0			0
$165$	−73.6424	−	42.5174i	−0.446317	−	0.257681i
$166$		0			0
$167$			207.929i			1.24508i	0.782587	+	0.622541i	$0.213900\pi$
$167$			207.929i			1.24508i	−0.782587	+	0.622541i	$0.786100\pi$
$168$		0			0
$169$	152.166			0.900390
$170$		0			0
$171$	−0.988223	+	1.71165i	−0.00577908	+	0.0100097i
$172$		0			0
$173$	−188.386	+	108.765i	−1.08894	+	0.628699i	−0.933294	−	0.359114i	$-0.883079\pi$
$173$	−188.386	+	108.765i	−1.08894	+	0.628699i	−0.155645	+	0.987813i	$0.549746\pi$
$174$		0			0
$175$	363.785	−	3.20341i	2.07877	−	0.0183052i
$176$		0			0
$177$	92.1233	+	159.562i	0.520471	+	0.901482i
$178$		0			0
$179$	−23.2072	+	40.1960i	−0.129649	+	0.224559i	−0.923541	−	0.383501i	$-0.874718\pi$
$179$	−23.2072	+	40.1960i	−0.129649	+	0.224559i	0.793892	+	0.608059i	$0.208052\pi$
$180$		0			0
$181$		−	247.523i		−	1.36753i	−0.729702	−	0.683765i	$-0.760341\pi$
$181$		−	247.523i		−	1.36753i	0.729702	−	0.683765i	$-0.239659\pi$
$182$		0			0
$183$		−	116.650i		−	0.637433i
$184$		0			0
$185$	−57.5654	+	99.7062i	−0.311164	+	0.538952i
$186$		0			0
$187$	−38.3040	−	66.3445i	−0.204834	−	0.354783i
$188$		0			0
$189$	97.7446	+	165.907i	0.517167	+	0.877817i
$190$		0			0
$191$	276.177	−	159.451i	1.44595	−	0.834822i	0.447717	−	0.894175i	$-0.352237\pi$
$191$	276.177	−	159.451i	1.44595	−	0.834822i	0.998237	+	0.0593533i	$0.0189039\pi$
$192$		0			0
$193$	−154.875	+	268.251i	−0.802461	+	1.38990i	0.115531	+	0.993304i	$0.463143\pi$
$193$	−154.875	+	268.251i	−0.802461	+	1.38990i	−0.917992	+	0.396599i	$0.870190\pi$
$194$		0			0
$195$	−105.826			−0.542698
$196$		0			0
$197$			157.969i			0.801872i	0.916106	+	0.400936i	$0.131315\pi$
$197$			157.969i			0.801872i	−0.916106	+	0.400936i	$0.868685\pi$
$198$		0			0
$199$	16.8606	+	9.73449i	0.0847268	+	0.0489171i	0.541765	−	0.840530i	$-0.317756\pi$
$199$	16.8606	+	9.73449i	0.0847268	+	0.0489171i	−0.457038	+	0.889447i	$0.651090\pi$
$200$		0			0
$201$	−62.6634	−	108.536i	−0.311758	−	0.539981i
$202$		0			0
$203$	−260.392	+	153.410i	−1.28272	+	0.755715i
$204$		0			0
$205$	65.1039	−	37.5877i	0.317580	−	0.183355i
$206$		0			0
$207$	4.59518	+	2.65303i	0.0221990	+	0.0128166i
$208$		0			0
$209$	−18.2553			−0.0873462
$210$		0			0
$211$	197.272			0.934937			0.467468	−	0.884010i	$-0.345166\pi$
$211$	197.272			0.934937			0.467468	+	0.884010i	$0.345166\pi$
$212$		0			0
$213$	−272.819	−	157.512i	−1.28084	−	0.739494i
$214$		0			0
$215$	−85.9141	+	49.6025i	−0.399600	+	0.230709i
$216$		0			0
$217$	−1.90003	−	215.771i	−0.00875589	−	0.994336i
$218$		0			0
$219$	52.9435	+	91.7008i	0.241751	+	0.418725i
$220$		0			0
$221$	−82.5659	−	47.6694i	−0.373601	−	0.215699i
$222$		0			0
$223$		−	263.559i		−	1.18188i	−0.806716	−	0.590940i	$-0.798757\pi$
$223$		−	263.559i		−	1.18188i	0.806716	−	0.590940i	$-0.201243\pi$
$224$		0			0
$225$	18.5506			0.0824470
$226$		0			0
$227$	48.5497	−	84.0905i	0.213875	−	0.370443i	−0.739049	−	0.673652i	$-0.764725\pi$
$227$	48.5497	−	84.0905i	0.213875	−	0.370443i	0.952924	+	0.303209i	$0.0980580\pi$
$228$		0			0
$229$	119.051	−	68.7339i	0.519872	−	0.300148i	−0.217011	−	0.976169i	$-0.569631\pi$
$229$	119.051	−	68.7339i	0.519872	−	0.300148i	0.736882	+	0.676021i	$0.236297\pi$
$230$		0			0
$231$	−33.4048	+	59.0537i	−0.144610	+	0.255644i
$232$		0			0
$233$	−68.6614	−	118.925i	−0.294684	−	0.510408i	0.680227	−	0.733001i	$-0.261881\pi$
$233$	−68.6614	−	118.925i	−0.294684	−	0.510408i	−0.974911	+	0.222593i	$0.928548\pi$
$234$		0			0
$235$	161.625	−	279.943i	0.687766	−	1.19125i
$236$		0			0
$237$		−	123.238i		−	0.519991i
$238$		0			0
$239$			325.305i			1.36111i	0.732697	+	0.680555i	$0.238261\pi$
$239$			325.305i			1.36111i	−0.732697	+	0.680555i	$0.761739\pi$
$240$		0			0
$241$	−126.919	+	219.830i	−0.526635	+	0.912159i	0.472883	+	0.881125i	$0.343213\pi$
$241$	−126.919	+	219.830i	−0.526635	+	0.912159i	−0.999518	+	0.0310335i	$0.990120\pi$
$242$		0			0
$243$	9.63158	+	16.6824i	0.0396361	+	0.0686518i
$244$		0			0
$245$	−7.57049	−	429.827i	−0.0309000	−	1.75439i
$246$		0			0
$247$	−19.6751	+	11.3594i	−0.0796562	+	0.0459895i
$248$		0			0
$249$	129.063	−	223.545i	0.518327	−	0.897769i
$250$		0			0
$251$	−192.899			−0.768521			−0.384261	−	0.923225i	$-0.625544\pi$
$251$	−192.899			−0.768521			−0.384261	+	0.923225i	$0.625544\pi$
$252$		0			0
$253$			49.0092i			0.193712i
$254$		0			0
$255$	−519.044	−	299.670i	−2.03547	−	1.17518i
$256$		0			0
$257$	−16.7985	−	29.0959i	−0.0653640	−	0.113214i	0.831491	−	0.555538i	$-0.187488\pi$
$257$	−16.7985	−	29.0959i	−0.0653640	−	0.113214i	−0.896855	+	0.442324i	$0.854154\pi$
$258$		0			0
$259$	79.9542	+	45.2276i	0.308703	+	0.174624i
$260$		0			0
$261$	−13.3461	+	7.70535i	−0.0511344	+	0.0295224i
$262$		0			0
$263$	−317.791	−	183.477i	−1.20833	−	0.697630i	−0.245936	−	0.969286i	$-0.579095\pi$
$263$	−317.791	−	183.477i	−1.20833	−	0.697630i	−0.962394	+	0.271656i	$0.912429\pi$
$264$		0			0
$265$	539.142			2.03450
$266$		0			0
$267$	−6.16168			−0.0230775
$268$		0			0
$269$	90.9729	+	52.5232i	0.338189	+	0.195254i	0.659471	−	0.751730i	$-0.270780\pi$
$269$	90.9729	+	52.5232i	0.338189	+	0.195254i	−0.321282	+	0.946984i	$0.604114\pi$
$270$		0			0
$271$	228.342	−	131.833i	0.842592	−	0.486470i	−0.0155528	−	0.999879i	$-0.504951\pi$
$271$	228.342	−	131.833i	0.842592	−	0.486470i	0.858144	+	0.513409i	$0.171617\pi$
$272$		0			0
$273$	0.743493	+	84.4325i	0.00272342	+	0.309276i
$274$		0			0
$275$	85.6708	+	148.386i	0.311530	+	0.539586i
$276$		0			0
$277$	240.983	+	139.132i	0.869974	+	0.502280i	0.867340	−	0.497717i	$-0.165828\pi$
$277$	240.983	+	139.132i	0.869974	+	0.502280i	0.00263452	+	0.999997i	$0.499161\pi$
$278$		0			0
$279$		−	11.0029i		−	0.0394367i
$280$		0			0
$281$	−400.248			−1.42437			−0.712184	−	0.701993i	$-0.752294\pi$
$281$	−400.248			−1.42437			−0.712184	+	0.701993i	$0.752294\pi$
$282$		0			0
$283$	−95.8351	+	165.991i	−0.338640	+	0.586541i	−0.984177	−	0.177187i	$-0.943300\pi$
$283$	−95.8351	+	165.991i	−0.338640	+	0.586541i	0.645537	+	0.763729i	$0.276633\pi$
$284$		0			0
$285$	−123.686	+	71.4101i	−0.433986	+	0.250562i
$286$		0			0
$287$	−30.4465	−	51.6785i	−0.106085	−	0.180064i
$288$		0			0
$289$	−125.473	−	217.326i	−0.434164	−	0.751994i
$290$		0			0
$291$	−59.7370	+	103.468i	−0.205282	+	0.355559i
$292$		0			0
$293$		−	33.7800i		−	0.115290i	−0.998337	−	0.0576451i	$-0.981641\pi$
$293$		−	33.7800i		−	0.115290i	0.998337	−	0.0576451i	$-0.0183592\pi$
$294$		0			0
$295$		−	549.832i		−	1.86384i
$296$		0			0
$297$	−45.3457	+	78.5411i	−0.152679	+	0.264448i
$298$		0			0
$299$	30.4960	+	52.8206i	0.101993	+	0.176658i
$300$		0			0
$301$	40.1786	+	68.1974i	0.133484	+	0.226569i
$302$		0			0
$303$	71.8221	−	41.4665i	0.237037	−	0.136853i
$304$		0			0
$305$	−174.055	+	301.472i	−0.570672	+	0.988433i
$306$		0			0
$307$	−493.884			−1.60874			−0.804371	−	0.594128i	$-0.797497\pi$
$307$	−493.884			−1.60874			−0.804371	+	0.594128i	$0.797497\pi$
$308$		0			0
$309$		−	253.375i		−	0.819983i
$310$		0			0
$311$	452.989	+	261.533i	1.45656	+	0.840943i	0.998840	−	0.0481545i	$-0.0153340\pi$
$311$	452.989	+	261.533i	1.45656	+	0.840943i	0.457717	+	0.889098i	$0.348667\pi$
$312$		0			0
$313$	75.6865	+	131.093i	0.241810	+	0.418827i	0.961230	−	0.275748i	$-0.0889256\pi$
$313$	75.6865	+	131.093i	0.241810	+	0.418827i	−0.719420	+	0.694575i	$0.755592\pi$
$314$		0			0
$315$	−0.193022	−	21.9199i	−0.000612768	−	0.0695871i
$316$		0			0
$317$	−0.375088	+	0.216557i	−0.00118324	+	0.000683145i	−0.500592	−	0.865684i	$-0.666884\pi$
$317$	−0.375088	+	0.216557i	−0.00118324	+	0.000683145i	0.499408	+	0.866367i	$0.333551\pi$
$318$		0			0
$319$	−123.270	−	71.1701i	−0.386427	−	0.223104i
$320$		0			0
$321$	189.140			0.589222
$322$		0			0
$323$	−128.667			−0.398349
$324$		0			0
$325$	184.667	+	106.617i	0.568206	+	0.328054i
$326$		0			0
$327$	293.646	−	169.536i	0.897999	−	0.518460i
$328$		0			0
$329$	−224.486	−	126.984i	−0.682327	−	0.385971i
$330$		0			0
$331$	−71.4511	−	123.757i	−0.215864	−	0.373888i	0.737675	−	0.675156i	$-0.235924\pi$
$331$	−71.4511	−	123.757i	−0.215864	−	0.373888i	−0.953540	+	0.301268i	$0.902590\pi$
$332$		0			0
$333$	4.05650	+	2.34202i	0.0121817	+	0.00703309i
$334$		0			0
$335$			374.003i			1.11643i
$336$		0			0
$337$	14.0248			0.0416167			0.0208084	−	0.999783i	$-0.493376\pi$
$337$	14.0248			0.0416167			0.0208084	+	0.999783i	$0.493376\pi$
$338$		0			0
$339$	295.947	−	512.596i	0.873001	−	1.51208i
$340$		0			0
$341$	88.0118	−	50.8137i	0.258099	−	0.149014i
$342$		0			0
$343$	−342.880	+	9.05985i	−0.999651	+	0.0264135i
$344$		0			0
$345$	191.711	+	332.053i	0.555684	+	0.962473i
$346$		0			0
$347$	187.840	−	325.348i	0.541325	−	0.937602i	−0.457504	−	0.889208i	$-0.651256\pi$
$347$	187.840	−	325.348i	0.541325	−	0.937602i	0.998828	−	0.0483939i	$-0.0154103\pi$
$348$		0			0
$349$		−	203.347i		−	0.582657i	−0.956623	−	0.291328i	$-0.905903\pi$
$349$		−	203.347i		−	0.582657i	0.956623	−	0.291328i	$-0.0940972\pi$
$350$		0			0
$351$			112.866i			0.321555i
$352$		0			0
$353$	259.114	−	448.799i	0.734035	−	1.27139i	−0.221110	−	0.975249i	$-0.570968\pi$
$353$	259.114	−	448.799i	0.734035	−	1.27139i	0.955145	−	0.296137i	$-0.0956986\pi$
$354$		0			0
$355$	470.051	+	814.152i	1.32409	+	2.29339i
$356$		0			0
$357$	−235.443	+	416.221i	−0.659504	+	1.16588i
$358$		0			0
$359$	−136.713	+	78.9312i	−0.380816	+	0.219864i	−0.678173	−	0.734902i	$-0.737228\pi$
$359$	−136.713	+	78.9312i	−0.380816	+	0.219864i	0.297357	+	0.954766i	$0.403895\pi$
$360$		0			0
$361$	165.170	−	286.082i	0.457534	−	0.792471i
$362$		0			0
$363$	323.774			0.891941
$364$		0			0
$365$		−	315.990i		−	0.865725i
$366$		0			0
$367$	269.087	+	155.358i	0.733208	+	0.423318i	0.819595	−	0.572944i	$-0.194199\pi$
$367$	269.087	+	155.358i	0.733208	+	0.423318i	−0.0863866	+	0.996262i	$0.527532\pi$
$368$		0			0
$369$	−1.52924	−	2.64872i	−0.00414428	−	0.00717810i
$370$		0			0
$371$	−3.78780	−	430.150i	−0.0102097	−	1.15943i
$372$		0			0
$373$	−348.944	+	201.463i	−0.935506	+	0.540115i	−0.888549	−	0.458782i	$-0.848286\pi$
$373$	−348.944	+	201.463i	−0.935506	+	0.540115i	−0.0469575	+	0.998897i	$0.514953\pi$
$374$		0			0
$375$	602.464	+	347.833i	1.60657	+	0.927554i
$376$		0			0
$377$	−177.143			−0.469875
$378$		0			0
$379$	−400.615			−1.05703			−0.528516	−	0.848923i	$-0.677251\pi$
$379$	−400.615			−1.05703			−0.528516	+	0.848923i	$0.677251\pi$
$380$		0			0
$381$	269.053	+	155.338i	0.706176	+	0.407711i
$382$		0			0
$383$	−375.665	+	216.890i	−0.980849	+	0.566293i	−0.902526	−	0.430635i	$-0.858290\pi$
$383$	−375.665	+	216.890i	−0.980849	+	0.566293i	−0.0783224	+	0.996928i	$0.524956\pi$
$384$		0			0
$385$	174.446	−	102.775i	0.453107	−	0.266949i
$386$		0			0
$387$	2.01806	+	3.49537i	0.00521461	+	0.00903197i
$388$		0			0
$389$	−280.337	−	161.853i	−0.720660	−	0.416073i	0.0943355	−	0.995540i	$-0.469927\pi$
$389$	−280.337	−	161.853i	−0.720660	−	0.416073i	−0.814996	+	0.579467i	$0.803261\pi$
$390$		0			0
$391$			345.425i			0.883441i
$392$		0			0
$393$	−481.059			−1.22407
$394$		0			0
$395$	−183.884	+	318.497i	−0.465530	+	0.806322i
$396$		0			0
$397$	71.0133	−	40.9996i	0.178875	−	0.103273i	−0.407889	−	0.913031i	$-0.633735\pi$
$397$	71.0133	−	40.9996i	0.178875	−	0.103273i	0.586764	+	0.809758i	$0.300402\pi$
$398$		0			0
$399$	57.8429	+	98.1801i	0.144970	+	0.246065i
$400$		0			0
$401$	−34.3758	−	59.5405i	−0.0857251	−	0.148480i	0.819975	−	0.572400i	$-0.193987\pi$
$401$	−34.3758	−	59.5405i	−0.0857251	−	0.148480i	−0.905700	+	0.423919i	$0.860654\pi$
$402$		0			0
$403$	63.2377	−	109.531i	0.156917	−	0.271789i
$404$		0			0
$405$			681.338i			1.68232i
$406$		0			0
$407$			43.2639i			0.106300i
$408$		0			0
$409$	−168.427	+	291.724i	−0.411802	+	0.713263i	−0.995087	−	0.0990053i	$-0.968434\pi$
$409$	−168.427	+	291.724i	−0.411802	+	0.713263i	0.583285	+	0.812268i	$0.301767\pi$
$410$		0			0
$411$	−47.0793	−	81.5437i	−0.114548	−	0.198403i
$412$		0			0
$413$	−438.679	+	3.86291i	−1.06218	+	0.00935328i
$414$		0			0
$415$	−667.106	+	385.154i	−1.60748	+	0.928081i
$416$		0			0
$417$	40.0273	−	69.3293i	0.0959887	−	0.166257i
$418$		0			0
$419$	619.580			1.47871			0.739356	−	0.673315i	$-0.235130\pi$
$419$	619.580			1.47871			0.739356	+	0.673315i	$0.235130\pi$
$420$		0			0
$421$			606.552i			1.44074i	0.693589	+	0.720371i	$0.256028\pi$
$421$			606.552i			1.44074i	−0.693589	+	0.720371i	$0.743972\pi$
$422$		0			0
$423$	−11.3893	−	6.57564i	−0.0269251	−	0.0155452i
$424$		0			0
$425$	603.823	+	1045.85i	1.42076	+	2.46083i
$426$		0			0
$427$	241.750	+	136.750i	0.566159	+	0.320258i
$428$		0			0
$429$	−34.4396	+	19.8837i	−0.0802787	+	0.0463489i
$430$		0			0
$431$	232.207	+	134.065i	0.538763	+	0.311055i	0.744577	−	0.667536i	$-0.232651\pi$
$431$	232.207	+	134.065i	0.538763	+	0.311055i	−0.205815	+	0.978591i	$0.565984\pi$
$432$		0			0
$433$	−397.578			−0.918194			−0.459097	−	0.888386i	$-0.651827\pi$
$433$	−397.578			−0.918194			−0.459097	+	0.888386i	$0.651827\pi$
$434$		0			0
$435$	−1113.59			−2.55999
$436$		0			0
$437$	71.2854	+	41.1566i	0.163124	+	0.0941799i
$438$		0			0
$439$	168.717	−	97.4090i	0.384322	−	0.221888i	−0.295375	−	0.955381i	$-0.595445\pi$
$439$	168.717	−	97.4090i	0.384322	−	0.221888i	0.679697	+	0.733493i	$0.262111\pi$
$440$		0			0
$441$	−17.4873	+	0.308002i	−0.0396537	+	0.000698417i
$442$		0			0
$443$	−47.3631	−	82.0352i	−0.106914	−	0.185181i	0.807604	−	0.589725i	$-0.200764\pi$
$443$	−47.3631	−	82.0352i	−0.106914	−	0.185181i	−0.914519	+	0.404544i	$0.867430\pi$
$444$		0			0
$445$	15.9243	+	9.19391i	0.0357850	+	0.0206605i
$446$		0			0
$447$		−	365.667i		−	0.818046i
$448$		0			0
$449$	212.378			0.473003			0.236502	−	0.971631i	$-0.423999\pi$
$449$	212.378			0.473003			0.236502	+	0.971631i	$0.423999\pi$
$450$		0			0
$451$	14.1247	−	24.4648i	0.0313187	−	0.0542456i
$452$		0			0
$453$	273.120	−	157.686i	0.602915	−	0.348093i
$454$		0			0
$455$	124.061	−	219.317i	0.272662	−	0.482016i
$456$		0			0
$457$	−109.467	−	189.602i	−0.239534	−	0.414884i	0.721047	−	0.692886i	$-0.243661\pi$
$457$	−109.467	−	189.602i	−0.239534	−	0.414884i	−0.960581	+	0.278002i	$0.910328\pi$
$458$		0			0
$459$	−319.605	+	553.571i	−0.696306	+	1.20604i
$460$		0			0
$461$			311.878i			0.676525i	0.941052	+	0.338263i	$0.109839\pi$
$461$			311.878i			0.676525i	−0.941052	+	0.338263i	$0.890161\pi$
$462$		0			0
$463$			219.733i			0.474586i	0.971438	+	0.237293i	$0.0762601\pi$
$463$			219.733i			0.474586i	−0.971438	+	0.237293i	$0.923740\pi$
$464$		0			0
$465$	397.539	−	688.558i	0.854923	−	1.48077i
$466$		0			0
$467$	43.0338	+	74.5368i	0.0921496	+	0.159608i	0.908415	−	0.418069i	$-0.137293\pi$
$467$	43.0338	+	74.5368i	0.0921496	+	0.159608i	−0.816266	+	0.577676i	$0.803960\pi$
$468$		0			0
$469$	298.395	−	2.62759i	0.636236	−	0.00560255i
$470$		0			0
$471$	272.698	−	157.442i	0.578976	−	0.334272i
$472$		0			0
$473$	−18.6397	+	32.2849i	−0.0394073	+	0.0682555i
$474$		0			0
$475$	287.776			0.605845
$476$		0			0
$477$		−	21.9347i		−	0.0459847i
$478$		0			0
$479$	−125.523	−	72.4708i	−0.262052	−	0.151296i	0.363218	−	0.931704i	$-0.381678\pi$
$479$	−125.523	−	72.4708i	−0.262052	−	0.151296i	−0.625270	+	0.780408i	$0.715011\pi$
$480$		0			0
$481$	26.9210	+	46.6286i	0.0559689	+	0.0969409i
$482$		0			0
$483$	263.579	−	155.288i	0.545712	−	0.321507i
$484$		0			0
$485$	308.770	−	178.268i	0.636639	−	0.367564i
$486$		0			0
$487$	−410.200	−	236.829i	−0.842300	−	0.486302i	0.0157454	−	0.999876i	$-0.494988\pi$
$487$	−410.200	−	236.829i	−0.842300	−	0.486302i	−0.858045	+	0.513574i	$0.828321\pi$
$488$		0			0
$489$	−590.202			−1.20696
$490$		0			0
$491$	895.083			1.82298			0.911490	−	0.411322i	$-0.134933\pi$
$491$	895.083			1.82298			0.911490	+	0.411322i	$0.134933\pi$
$492$		0			0
$493$	−868.831	−	501.620i	−1.76233	−	1.01748i
$494$		0			0
$495$	8.94103	−	5.16211i	0.0180627	−	0.0104285i
$496$		0			0
$497$	646.262	−	380.746i	1.30033	−	0.766089i
$498$		0			0
$499$	−379.515	−	657.339i	−0.760551	−	1.31731i	−0.942567	−	0.334017i	$-0.891596\pi$
$499$	−379.515	−	657.339i	−0.760551	−	1.31731i	0.182016	−	0.983296i	$-0.441738\pi$
$500$		0			0
$501$	529.394	+	305.646i	1.05667	+	0.610072i
$502$		0			0
$503$		−	802.733i		−	1.59589i	−0.602730	−	0.797945i	$-0.705920\pi$
$503$		−	802.733i		−	1.59589i	0.602730	−	0.797945i	$-0.294080\pi$
$504$		0			0
$505$	−247.490			−0.490080
$506$		0			0
$507$	223.677	−	387.420i	0.441177	−	0.764142i
$508$		0			0
$509$	617.270	−	356.381i	1.21271	−	0.700159i	0.249362	−	0.968410i	$-0.419779\pi$
$509$	617.270	−	356.381i	1.21271	−	0.700159i	0.963349	+	0.268251i	$0.0864458\pi$
$510$		0			0
$511$	−252.110	+	2.22002i	−0.493366	+	0.00434446i
$512$		0			0
$513$	76.1603	+	131.914i	0.148461	+	0.257141i
$514$		0			0
$515$	−378.063	+	654.824i	−0.734102	+	1.27150i
$516$		0			0
$517$		−	121.471i		−	0.234954i
$518$		0			0
$519$			639.518i			1.23221i
$520$		0			0
$521$	410.672	−	711.305i	0.788238	−	1.36527i	−0.138808	−	0.990319i	$-0.544327\pi$
$521$	410.672	−	711.305i	0.788238	−	1.36527i	0.927046	−	0.374949i	$-0.122340\pi$
$522$		0			0
$523$	−237.335	−	411.077i	−0.453796	−	0.785998i	0.544822	−	0.838552i	$-0.316597\pi$
$523$	−237.335	−	411.077i	−0.453796	−	0.785998i	−0.998618	+	0.0525541i	$0.983264\pi$
$524$		0			0
$525$	526.592	−	930.919i	1.00303	−	1.77318i
$526$		0			0
$527$	620.323	−	358.144i	1.17708	−	0.679589i
$528$		0			0
$529$	−154.009	+	266.751i	−0.291132	+	0.504256i
$530$		0			0
$531$	−22.3697			−0.0421274
$532$		0			0
$533$		−	35.1565i		−	0.0659597i
$534$		0			0
$535$	−488.816	−	282.218i	−0.913674	−	0.527510i
$536$		0			0
$537$	68.2270	+	118.173i	0.127052	+	0.220061i
$538$		0			0
$539$	−83.2239	−	138.458i	−0.154404	−	0.256880i
$540$		0			0
$541$	349.210	−	201.616i	0.645489	−	0.372673i	−0.141237	−	0.989976i	$-0.545108\pi$
$541$	349.210	−	201.616i	0.645489	−	0.372673i	0.786726	+	0.617303i	$0.211775\pi$
$542$		0			0
$543$	−630.202	−	363.847i	−1.16059	−	0.670069i
$544$		0			0
$545$	−1011.87			−1.85664
$546$		0			0
$547$	−623.273			−1.13944			−0.569719	−	0.821839i	$-0.692948\pi$
$547$	−623.273			−1.13944			−0.569719	+	0.821839i	$0.692948\pi$
$548$		0			0
$549$	12.2652	+	7.08134i	0.0223411	+	0.0128986i
$550$		0			0
$551$	−207.038	+	119.534i	−0.375750	+	0.216940i
$552$		0			0
$553$	255.402	+	144.473i	0.461848	+	0.261253i
$554$		0			0
$555$	169.237	+	293.127i	0.304932	+	0.528157i
$556$		0			0
$557$	19.3784	+	11.1881i	0.0347906	+	0.0200864i	0.517294	−	0.855808i	$-0.326939\pi$
$557$	19.3784	+	11.1881i	0.0347906	+	0.0200864i	−0.482504	+	0.875894i	$0.660273\pi$
$558$		0			0
$559$			46.3942i			0.0829950i
$560$		0			0
$561$	−225.221			−0.401463
$562$		0			0
$563$	−155.749	+	269.766i	−0.276642	+	0.479157i	−0.970548	−	0.240908i	$-0.922555\pi$
$563$	−155.749	+	269.766i	−0.276642	+	0.479157i	0.693906	+	0.720065i	$0.255888\pi$
$564$		0			0
$565$	−1529.70	+	883.171i	−2.70743	+	1.56314i
$566$		0			0
$567$	543.600	−	4.78681i	0.958730	−	0.00844235i
$568$		0			0
$569$	−245.668	−	425.509i	−0.431754	−	0.747820i	0.565271	−	0.824906i	$-0.308772\pi$
$569$	−245.668	−	425.509i	−0.431754	−	0.747820i	−0.997024	+	0.0770859i	$0.975438\pi$
$570$		0			0
$571$	−332.451	+	575.821i	−0.582225	+	1.00844i	0.412990	+	0.910736i	$0.364484\pi$
$571$	−332.451	+	575.821i	−0.582225	+	1.00844i	−0.995215	+	0.0977080i	$0.968849\pi$
$572$		0			0
$573$		−	937.543i		−	1.63620i
$574$		0			0
$575$		−	772.578i		−	1.34361i
$576$		0			0
$577$	−381.078	+	660.047i	−0.660448	+	1.14393i	0.320051	+	0.947400i	$0.396300\pi$
$577$	−381.078	+	660.047i	−0.660448	+	1.14393i	−0.980498	+	0.196528i	$0.937033\pi$
$578$		0			0
$579$	455.318	+	788.634i	0.786387	+	1.36206i
$580$		0			0
$581$	311.978	+	529.539i	0.536968	+	0.911427i
$582$		0			0
$583$	175.456	−	101.299i	0.300953	−	0.173756i
$584$		0			0
$585$	6.42425	−	11.1271i	0.0109816	−	0.0190207i
$586$		0			0
$587$	−551.907			−0.940216			−0.470108	−	0.882609i	$-0.655785\pi$
$587$	−551.907			−0.940216			−0.470108	+	0.882609i	$0.655785\pi$
$588$		0			0
$589$		−	170.688i		−	0.289793i
$590$		0			0
$591$	402.194	+	232.207i	0.680532	+	0.392905i
$592$		0			0
$593$	417.977	+	723.958i	0.704852	+	1.22084i	0.966745	+	0.255743i	$0.0823201\pi$
$593$	417.977	+	723.958i	0.704852	+	1.22084i	−0.261892	+	0.965097i	$0.584347\pi$
$594$		0			0
$595$	1229.53	−	724.378i	2.06643	−	1.21744i
$596$		0			0
$597$	49.5687	−	28.6185i	0.0830297	−	0.0479372i
$598$		0			0
$599$	226.579	+	130.816i	0.378263	+	0.218390i	0.677062	−	0.735926i	$-0.263253\pi$
$599$	226.579	+	130.816i	0.378263	+	0.218390i	−0.298799	+	0.954316i	$0.596586\pi$
$600$		0			0
$601$	731.253			1.21673			0.608364	−	0.793658i	$-0.291826\pi$
$601$	731.253			1.21673			0.608364	+	0.793658i	$0.291826\pi$
$602$		0			0
$603$	15.2161			0.0252340
$604$		0			0
$605$	−836.766	−	483.107i	−1.38308	−	0.798524i
$606$		0			0
$607$	10.5201	−	6.07378i	0.0173313	−	0.0100062i	−0.491309	−	0.870985i	$-0.663482\pi$
$607$	10.5201	−	6.07378i	0.0173313	−	0.0100062i	0.508641	+	0.860979i	$0.330148\pi$
$608$		0			0
$609$	7.82368	+	888.472i	0.0128468	+	1.45890i
$610$		0			0
$611$	−75.5855	−	130.918i	−0.123708	−	0.214268i
$612$		0			0
$613$	−1045.72	−	603.744i	−1.70590	−	0.984900i	−0.939510	−	0.342522i	$-0.888719\pi$
$613$	−1045.72	−	603.744i	−1.70590	−	0.984900i	−0.766388	−	0.642378i	$-0.777948\pi$
$614$		0			0
$615$		−	221.009i		−	0.359364i
$616$		0			0
$617$	48.0515			0.0778792			0.0389396	−	0.999242i	$-0.487602\pi$
$617$	48.0515			0.0778792			0.0389396	+	0.999242i	$0.487602\pi$
$618$		0			0
$619$	73.8783	−	127.961i	0.119351	−	0.206722i	−0.800160	−	0.599787i	$-0.795252\pi$
$619$	73.8783	−	127.961i	0.119351	−	0.206722i	0.919511	+	0.393065i	$0.128585\pi$
$620$		0			0
$621$	354.141	−	204.464i	0.570276	−	0.329249i
$622$		0			0
$623$	7.22340	−	12.7697i	0.0115945	−	0.0204971i
$624$		0			0
$625$	−388.368	−	672.673i	−0.621389	−	1.07628i
$626$		0			0
$627$	−26.8345	+	46.4788i	−0.0427983	+	0.0741288i
$628$		0			0
$629$			304.932i			0.484788i
$630$		0			0
$631$			912.286i			1.44578i	0.690964	+	0.722889i	$0.257186\pi$
$631$			912.286i			1.44578i	−0.690964	+	0.722889i	$0.742814\pi$
$632$		0			0
$633$	289.980	−	502.261i	0.458105	−	0.793461i
$634$		0			0
$635$	−463.562	−	802.913i	−0.730019	−	1.26443i
$636$		0			0
$637$	−175.852	−	97.4402i	−0.276063	−	0.152967i
$638$		0			0
$639$	33.1234	−	19.1238i	0.0518363	−	0.0299277i
$640$		0			0
$641$	−286.819	+	496.784i	−0.447455	+	0.775015i	−0.998220	−	0.0596460i	$-0.981003\pi$
$641$	−286.819	+	496.784i	−0.447455	+	0.775015i	0.550765	+	0.834661i	$0.314336\pi$
$642$		0			0
$643$	197.633			0.307360			0.153680	−	0.988121i	$-0.450887\pi$
$643$	197.633			0.307360			0.153680	+	0.988121i	$0.450887\pi$
$644$		0			0
$645$			291.654i			0.452176i
$646$		0			0
$647$	−869.817	−	502.189i	−1.34439	−	0.776181i	−0.356938	−	0.934128i	$-0.616179\pi$
$647$	−869.817	−	502.189i	−1.34439	−	0.776181i	−0.987448	+	0.157947i	$0.949513\pi$
$648$		0			0
$649$	−103.308	−	178.935i	−0.159180	−	0.275709i
$650$		0			0
$651$	−552.153	−	312.336i	−0.848162	−	0.479778i
$652$		0			0
$653$	−374.151	+	216.016i	−0.572973	+	0.330806i	−0.758336	−	0.651864i	$-0.773987\pi$
$653$	−374.151	+	216.016i	−0.572973	+	0.330806i	0.185363	+	0.982670i	$0.440654\pi$
$654$		0			0
$655$	1243.25	+	717.793i	1.89810	+	1.09587i
$656$		0			0
$657$	−12.8559			−0.0195676
$658$		0			0
$659$	−222.867			−0.338190			−0.169095	−	0.985600i	$-0.554084\pi$
$659$	−222.867			−0.338190			−0.169095	+	0.985600i	$0.554084\pi$
$660$		0			0
$661$	635.382	+	366.838i	0.961243	+	0.554974i	0.896555	−	0.442932i	$-0.146062\pi$
$661$	635.382	+	366.838i	0.961243	+	0.554974i	0.0646877	+	0.997906i	$0.479395\pi$
$662$		0			0
$663$	−242.736	+	140.144i	−0.366118	+	0.211378i
$664$		0			0
$665$	−2.99436	−	340.045i	−0.00450280	−	0.511347i
$666$		0			0
$667$	320.906	+	555.825i	0.481118	+	0.833321i
$668$		0			0
$669$	−671.031	−	387.420i	−1.00304	−	0.579103i
$670$		0			0
$671$			130.813i			0.194952i
$672$		0			0
$673$	331.486			0.492550			0.246275	−	0.969200i	$-0.420793\pi$
$673$	331.486			0.492550			0.246275	+	0.969200i	$0.420793\pi$
$674$		0			0
$675$	714.828	−	1238.12i	1.05900	−	1.83425i
$676$		0			0
$677$	893.931	−	516.111i	1.32043	−	0.762350i	0.336633	−	0.941636i	$-0.390712\pi$
$677$	893.931	−	516.111i	1.32043	−	0.762350i	0.983797	+	0.179286i	$0.0573786\pi$
$678$		0			0
$679$	−144.399	−	245.097i	−0.212665	−	0.360968i
$680$		0			0
$681$	−142.732	−	247.218i	−0.209591	−	0.363023i
$682$		0			0
$683$	82.4745	−	142.850i	0.120753	−	0.209151i	−0.799312	−	0.600917i	$-0.794802\pi$
$683$	82.4745	−	142.850i	0.120753	−	0.209151i	0.920065	+	0.391766i	$0.128136\pi$
$684$		0			0
$685$			280.990i			0.410204i
$686$		0			0
$687$		−	404.143i		−	0.588272i
$688$		0			0
$689$	126.067	−	218.355i	0.182972	−	0.316916i
$690$		0			0
$691$	302.018	+	523.111i	0.437074	+	0.757034i	0.997462	−	0.0711958i	$-0.0226815\pi$
$691$	302.018	+	523.111i	0.437074	+	0.757034i	−0.560389	+	0.828230i	$0.689348\pi$
$692$		0			0
$693$	−4.18136	−	7.09726i	−0.00603371	−	0.0102414i
$694$		0			0
$695$	−206.894	+	119.450i	−0.297689	+	0.171871i
$696$		0			0
$697$	99.5536	−	172.432i	0.142832	−	0.247392i
$698$		0			0
$699$	−403.716			−0.577563
$700$		0			0
$701$			307.326i			0.438410i	0.975679	+	0.219205i	$0.0703464\pi$
$701$			307.326i			0.438410i	−0.975679	+	0.219205i	$0.929654\pi$
$702$		0			0
$703$	62.9287	+	36.3319i	0.0895145	+	0.0516812i
$704$		0			0
$705$	−475.163	−	823.006i	−0.673990	−	1.16738i
$706$		0			0
$707$	1.73877	+	197.458i	0.00245936	+	0.279290i
$708$		0			0
$709$	−568.779	+	328.385i	−0.802228	+	0.463166i	−0.844250	−	0.535950i	$-0.819953\pi$
$709$	−568.779	+	328.385i	−0.802228	+	0.463166i	0.0420218	+	0.999117i	$0.486620\pi$
$710$		0			0
$711$	12.9579	+	7.48125i	0.0182249	+	0.0105222i
$712$		0			0
$713$	−458.237			−0.642689
$714$		0			0
$715$	118.675			0.165978
$716$		0			0
$717$	828.239	+	478.184i	1.15514	+	0.666923i
$718$		0			0
$719$	1047.32	−	604.668i	1.45663	−	0.840984i	0.457784	−	0.889063i	$-0.348643\pi$
$719$	1047.32	−	604.668i	1.45663	−	0.840984i	0.998844	+	0.0480788i	$0.0153099\pi$
$720$		0			0
$721$	525.102	+	297.034i	0.728297	+	0.411975i
$722$		0			0
$723$	373.130	+	646.281i	0.516086	+	0.893887i
$724$		0			0
$725$	1943.23	+	1121.92i	2.68031	+	1.54748i
$726$		0			0
$727$			1199.28i			1.64963i	0.565404	+	0.824814i	$0.308720\pi$
$727$			1199.28i			1.64963i	−0.565404	+	0.824814i	$0.691280\pi$
$728$		0			0
$729$	755.573			1.03645
$730$		0			0
$731$	−131.376	+	227.549i	−0.179720	+	0.311285i
$732$		0			0
$733$	495.767	−	286.231i	0.676354	−	0.390493i	−0.122126	−	0.992515i	$-0.538971\pi$
$733$	495.767	−	286.231i	0.676354	−	0.390493i	0.798480	+	0.602022i	$0.205638\pi$
$734$		0			0
$735$	−1105.48	−	612.551i	−1.50406	−	0.833402i
$736$		0			0
$737$	70.2714	+	121.714i	0.0953479	+	0.165147i
$738$		0			0
$739$	−437.226	+	757.297i	−0.591645	+	1.02476i	0.402366	+	0.915479i	$0.368188\pi$
$739$	−437.226	+	757.297i	−0.591645	+	1.02476i	−0.994011	+	0.109280i	$0.965145\pi$
$740$		0			0
$741$			66.7912i			0.0901366i
$742$		0			0
$743$		−	63.9768i		−	0.0861061i	−0.999073	−	0.0430530i	$-0.986292\pi$
$743$		−	63.9768i		−	0.0861061i	0.999073	−	0.0430530i	$-0.0137084\pi$
$744$		0			0
$745$	−545.615	+	945.032i	−0.732369	+	1.26850i
$746$		0			0
$747$	15.6698	+	27.1409i	0.0209770	+	0.0363332i
$748$		0			0
$749$	−221.731	+	391.980i	−0.296036	+	0.523338i
$750$		0			0
$751$	−498.130	+	287.595i	−0.663289	+	0.382950i	−0.793529	−	0.608533i	$-0.791758\pi$
$751$	−498.130	+	287.595i	−0.663289	+	0.382950i	0.130240	+	0.991482i	$0.458425\pi$
$752$		0			0
$753$	−283.552	+	491.127i	−0.376564	+	0.652227i
$754$		0			0
$755$	−941.140			−1.24654
$756$		0			0
$757$		−	130.657i		−	0.172598i	−0.996269	−	0.0862989i	$-0.972496\pi$
$757$		−	130.657i		−	0.172598i	0.996269	−	0.0862989i	$-0.0275040\pi$
$758$		0			0
$759$	124.779	+	72.0412i	0.164399	+	0.0949160i
$760$		0			0
$761$	−59.2992	−	102.709i	−0.0779228	−	0.134966i	0.824431	−	0.565963i	$-0.191495\pi$
$761$	−59.2992	−	102.709i	−0.0779228	−	0.134966i	−0.902354	+	0.430997i	$0.858162\pi$
$762$		0			0
$763$	7.10898	+	807.310i	0.00931715	+	1.05807i
$764$		0			0
$765$	63.0179	−	36.3834i	0.0823764	−	0.0475600i
$766$		0			0
$767$	−222.685	−	128.567i	−0.290332	−	0.167623i
$768$		0			0
$769$	1145.31			1.48935			0.744674	−	0.667429i	$-0.232605\pi$
$769$	1145.31			1.48935			0.744674	+	0.667429i	$0.232605\pi$
$770$		0			0
$771$	−98.7724			−0.128109
$772$		0			0
$773$	548.098	+	316.445i	0.709053	+	0.409372i	0.810710	−	0.585447i	$-0.199081\pi$
$773$	548.098	+	316.445i	0.709053	+	0.409372i	−0.101657	+	0.994819i	$0.532415\pi$
$774$		0			0
$775$	−1387.41	+	801.024i	−1.79021	+	1.03358i
$776$		0			0
$777$	232.680	−	137.084i	0.299459	−	0.176427i
$778$		0			0
$779$	−23.7232	−	41.0898i	−0.0304534	−	0.0527468i
$780$		0			0
$781$	305.943	+	176.636i	0.391732	+	0.226167i
$782$		0			0
$783$			1187.67i			1.51682i
$784$		0			0
$785$	−939.684			−1.19705
$786$		0			0
$787$	−46.8023	+	81.0639i	−0.0594692	+	0.103004i	−0.894227	−	0.447613i	$-0.852274\pi$
$787$	−46.8023	+	81.0639i	−0.0594692	+	0.103004i	0.834758	+	0.550617i	$0.185607\pi$
$788$		0			0
$789$	−934.276	+	539.405i	−1.18413	+	0.683656i
$790$		0			0
$791$	715.378	+	1214.25i	0.904397	+	1.53508i
$792$		0			0
$793$	81.3985	+	140.986i	0.102646	+	0.177789i
$794$		0			0
$795$	792.513	−	1372.67i	0.996872	−	1.72663i
$796$		0			0
$797$		−	214.365i		−	0.268965i	−0.990916	−	0.134483i	$-0.957063\pi$
$797$		−	214.365i		−	0.268965i	0.990916	−	0.134483i	$-0.0429372\pi$
$798$		0			0
$799$		−	856.150i		−	1.07153i
$800$		0			0
$801$	0.374050	−	0.647873i	0.000466978	−	0.000808830i
$802$		0			0
$803$	−59.3714	−	102.834i	−0.0739370	−	0.128063i
$804$		0			0
$805$	−912.902	+	8.03880i	−1.13404	+	0.00998609i
$806$		0			0
$807$	267.452	−	154.413i	0.331415	−	0.191343i
$808$		0			0
$809$	136.449	−	236.336i	0.168663	−	0.292133i	−0.769287	−	0.638904i	$-0.779388\pi$
$809$	136.449	−	236.336i	0.168663	−	0.292133i	0.937950	+	0.346770i	$0.112722\pi$
$810$		0			0
$811$	1339.86			1.65211			0.826054	−	0.563592i	$-0.190581\pi$
$811$	1339.86			1.65211			0.826054	+	0.563592i	$0.190581\pi$
$812$		0			0
$813$		−	775.157i		−	0.953452i
$814$		0			0
$815$	1525.32	+	880.646i	1.87156	+	1.08055i
$816$		0			0
$817$	31.3062	+	54.2240i	0.0383185	+	0.0663696i
$818$		0			0
$819$	−8.92282	−	5.04736i	−0.0108948	−	0.00616283i
$820$		0			0
$821$	−586.088	+	338.378i	−0.713871	+	0.412154i	−0.812493	−	0.582971i	$-0.801890\pi$
$821$	−586.088	+	338.378i	−0.713871	+	0.412154i	0.0986214	+	0.995125i	$0.468557\pi$
$822$		0			0
$823$	−984.303	−	568.288i	−1.19599	−	0.690507i	−0.236334	−	0.971672i	$-0.575946\pi$
$823$	−984.303	−	568.288i	−1.19599	−	0.690507i	−0.959660	+	0.281164i	$0.909279\pi$
$824$		0			0
$825$	503.728			0.610580
$826$		0			0
$827$	1140.05			1.37854			0.689269	−	0.724506i	$-0.257932\pi$
$827$	1140.05			1.37854			0.689269	+	0.724506i	$0.257932\pi$
$828$		0			0
$829$	898.011	+	518.467i	1.08325	+	0.625413i	0.931770	−	0.363048i	$-0.118264\pi$
$829$	898.011	+	518.467i	1.08325	+	0.625413i	0.151476	+	0.988461i	$0.451597\pi$
$830$		0			0
$831$	708.467	−	409.034i	0.852548	−	0.492219i
$832$		0			0
$833$	−586.577	−	975.879i	−0.704174	−	1.17152i
$834$		0			0
$835$	−912.114	−	1579.83i	−1.09235	−	1.89201i
$836$		0			0
$837$	−734.361	−	423.984i	−0.877373	−	0.506552i
$838$		0			0
$839$		−	1330.82i		−	1.58620i	−0.609091	−	0.793100i	$-0.708466\pi$
$839$		−	1330.82i		−	1.58620i	0.609091	−	0.793100i	$-0.291534\pi$
$840$		0			0
$841$	−1023.05			−1.21647
$842$		0			0
$843$	−588.346	+	1019.04i	−0.697919	+	1.20883i
$844$		0			0
$845$	−1156.15	+	667.501i	−1.36822	+	0.789942i
$846$		0			0
$847$	−379.564	+	671.001i	−0.448128	+	0.792209i
$848$		0			0
$849$	281.746	+	487.999i	0.331857	+	0.574793i
$850$		0			0
$851$	97.5384	−	168.941i	0.114616	−	0.198521i
$852$		0			0
$853$			1325.15i			1.55352i	0.629798	+	0.776759i	$0.283138\pi$
$853$			1325.15i			1.55352i	−0.629798	+	0.776759i	$0.716862\pi$
$854$		0			0
$855$		−	17.3400i		−	0.0202807i
$856$		0			0
$857$	−18.5345	+	32.1027i	−0.0216272	+	0.0374594i	−0.876636	−	0.481153i	$-0.840218\pi$
$857$	−18.5345	+	32.1027i	−0.0216272	+	0.0374594i	0.855009	+	0.518613i	$0.173551\pi$
$858$		0			0
$859$	−125.970	−	218.187i	−0.146648	−	0.254001i	0.783339	−	0.621595i	$-0.213515\pi$
$859$	−125.970	−	218.187i	−0.146648	−	0.254001i	−0.929986	+	0.367594i	$0.880182\pi$
$860$		0			0
$861$	−176.330	+	1.55272i	−0.204797	+	0.00180339i
$862$		0			0
$863$	−1443.94	+	833.661i	−1.67317	+	0.966004i	−0.707321	+	0.706893i	$0.750096\pi$
$863$	−1443.94	+	833.661i	−1.67317	+	0.966004i	−0.965848	+	0.259111i	$0.916570\pi$
$864$		0			0
$865$	954.231	−	1652.78i	1.10316	−	1.91072i
$866$		0			0
$867$	−737.761			−0.850935
$868$		0			0
$869$			138.200i			0.159034i
$870$		0			0
$871$	151.473	+	87.4530i	0.173907	+	0.100405i
$872$		0			0
$873$	−7.25276	−	12.5622i	−0.00830786	−	0.0143896i
$874$		0			0
$875$	−1427.14	+	840.798i	−1.63101	+	0.960913i
$876$		0			0
$877$	214.659	−	123.934i	0.244765	−	0.141315i	−0.372600	−	0.927992i	$-0.621533\pi$
$877$	214.659	−	123.934i	0.244765	−	0.141315i	0.617365	+	0.786677i	$0.288200\pi$
$878$		0			0
$879$	−86.0052	−	49.6551i	−0.0978443	−	0.0564905i
$880$		0			0
$881$	1130.22			1.28288			0.641440	−	0.767173i	$-0.278337\pi$
$881$	1130.22			1.28288			0.641440	+	0.767173i	$0.278337\pi$
$882$		0			0
$883$	−10.7432			−0.0121667			−0.00608335	−	0.999981i	$-0.501936\pi$
$883$	−10.7432			−0.0121667			−0.00608335	+	0.999981i	$0.501936\pi$
$884$		0			0
$885$	−1399.89	−	808.228i	−1.58180	−	0.913252i
$886$		0			0
$887$	776.894	−	448.540i	0.875866	−	0.505682i	0.00657316	−	0.999978i	$-0.497908\pi$
$887$	776.894	−	448.540i	0.875866	−	0.505682i	0.869293	+	0.494297i	$0.164574\pi$
$888$		0			0
$889$	−637.340	+	375.490i	−0.716918	+	0.422373i
$890$		0			0
$891$	128.017	+	221.732i	0.143678	+	0.248857i
$892$		0			0
$893$	−176.684	−	102.008i	−0.197854	−	0.114231i
$894$		0			0
$895$		−	407.209i		−	0.454982i
$896$		0			0
$897$	179.311			0.199901
$898$		0			0
$899$	665.443	−	1152.58i	0.740203	−	1.28207i
$900$		0			0
$901$	1236.64	−	713.976i	1.37252	−	0.792427i
$902$		0			0
$903$	232.694	−	2.04905i	0.257689	−	0.00226915i
$904$		0			0
$905$	1085.80	+	1880.66i	1.19978	+	2.07808i
$906$		0			0
$907$	837.264	−	1450.18i	0.923114	−	1.59888i	0.128547	−	0.991703i	$-0.458969\pi$
$907$	837.264	−	1450.18i	0.923114	−	1.59888i	0.794567	−	0.607176i	$-0.207698\pi$
$908$		0			0
$909$			10.0690i			0.0110770i
$910$		0			0
$911$		−	910.733i		−	0.999707i	−0.866110	−	0.499853i	$-0.833387\pi$
$911$		−	910.733i		−	0.999707i	0.866110	−	0.499853i	$-0.166613\pi$
$912$		0			0
$913$	−144.733	+	250.685i	−0.158525	+	0.274573i
$914$		0			0
$915$	511.706	+	886.300i	0.559241	+	0.968634i
$916$		0			0
$917$	563.950	−	996.962i	0.614995	−	1.08720i
$918$		0			0
$919$	1107.77	−	639.571i	1.20541	−	0.695943i	0.243655	−	0.969862i	$-0.421653\pi$
$919$	1107.77	−	639.571i	1.20541	−	0.695943i	0.961753	+	0.273919i	$0.0883201\pi$
$920$		0			0
$921$	−725.986	+	1257.45i	−0.788259	+	1.36530i
$922$		0			0
$923$	439.648			0.476325
$924$		0			0
$925$		−	682.010i		−	0.737308i
$926$		0			0
$927$	26.6412	+	15.3813i	0.0287392	+	0.0165926i
$928$		0			0
$929$	−14.0674	−	24.3654i	−0.0151425	−	0.0262276i	0.858355	−	0.513056i	$-0.171487\pi$
$929$	−14.0674	−	24.3654i	−0.0151425	−	0.0262276i	−0.873497	+	0.486829i	$0.838154\pi$
$930$		0			0
$931$	−271.281	+	4.77805i	−0.291387	+	0.00513217i
$932$		0			0
$933$	1331.75	−	768.884i	1.42738	−	0.824099i
$934$		0			0
$935$	582.062	+	336.054i	0.622526	+	0.359416i
$936$		0			0
$937$	−1165.92			−1.24431			−0.622154	−	0.782895i	$-0.713742\pi$
$937$	−1165.92			−1.24431			−0.622154	+	0.782895i	$0.713742\pi$
$938$		0			0
$939$	445.023			0.473933
$940$		0			0
$941$	−766.535	−	442.559i	−0.814596	−	0.470307i	0.0339534	−	0.999423i	$-0.489190\pi$
$941$	−766.535	−	442.559i	−0.814596	−	0.470307i	−0.848549	+	0.529116i	$0.822524\pi$
$942$		0			0
$943$	−110.312	+	63.6884i	−0.116979	+	0.0675381i
$944$		0			0
$945$	−1470.44	−	831.780i	−1.55602	−	0.880190i
$946$		0			0
$947$	748.589	+	1296.59i	0.790485	+	1.36916i	0.925667	+	0.378339i	$0.123505\pi$
$947$	748.589	+	1296.59i	0.790485	+	1.36916i	−0.135183	+	0.990821i	$0.543162\pi$
$948$		0			0
$949$	−127.978	−	73.8878i	−0.134855	−	0.0778586i
$950$		0			0
$951$			1.27332i			0.00133892i
$952$		0			0
$953$	3.14896			0.00330426			0.00165213	−	0.999999i	$-0.499474\pi$
$953$	3.14896			0.00330426			0.00165213	+	0.999999i	$0.499474\pi$
$954$		0			0
$955$	−1398.92	+	2422.99i	−1.46483	+	2.53717i
$956$		0			0
$957$	−362.403	+	209.234i	−0.378687	+	0.218635i
$958$		0			0
$959$	224.185	−	1.97412i	0.233770	−	0.00205852i
$960$		0			0
$961$	−5.39103	−	9.33753i	−0.00560981	−	0.00971647i
$962$		0			0
$963$	−11.4819	+	19.8872i	−0.0119230	+	0.0206513i
$964$		0			0
$965$		−	2717.54i		−	2.81610i
$966$		0			0
$967$			1451.63i			1.50117i	0.660775	+	0.750584i	$0.270228\pi$
$967$			1451.63i			1.50117i	−0.660775	+	0.750584i	$0.729772\pi$
$968$		0			0
$969$	−189.134	+	327.590i	−0.195185	+	0.338071i
$970$		0			0
$971$	−580.527	−	1005.50i	−0.597865	−	1.03553i	−0.993136	−	0.116968i	$-0.962683\pi$
$971$	−580.527	−	1005.50i	−0.597865	−	1.03553i	0.395271	−	0.918565i	$-0.370651\pi$
$972$		0			0
$973$	96.7559	+	164.229i	0.0994408	+	0.168786i
$974$		0			0
$975$	542.904	−	313.446i	0.556824	−	0.321483i
$976$		0			0
$977$	288.919	−	500.422i	0.295720	−	0.512202i	−0.679432	−	0.733738i	$-0.737774\pi$
$977$	288.919	−	500.422i	0.295720	−	0.512202i	0.975152	+	0.221536i	$0.0711071\pi$
$978$		0			0
$979$	6.90978			0.00705800
$980$		0			0
$981$			41.1673i			0.0419647i
$982$		0			0
$983$	−1086.94	−	627.545i	−1.10574	−	0.638398i	−0.168016	−	0.985784i	$-0.553736\pi$
$983$	−1086.94	−	627.545i	−1.10574	−	0.638398i	−0.937722	+	0.347386i	$0.887069\pi$
$984$		0			0
$985$	−692.956	−	1200.24i	−0.703509	−	1.21851i
$986$		0			0
$987$	−653.290	+	384.887i	−0.661895	+	0.389956i
$988$		0			0
$989$	145.572	−	84.0462i	0.147191	−	0.0849810i
$990$		0			0
$991$	−814.150	−	470.049i	−0.821543	−	0.474318i	0.0294050	−	0.999568i	$-0.490639\pi$
$991$	−814.150	−	470.049i	−0.821543	−	0.474318i	−0.850948	+	0.525249i	$0.823972\pi$
$992$		0			0
$993$	−420.120			−0.423081
$994$		0			0
$995$	−170.808			−0.171666
$996$		0			0
$997$	−195.863	−	113.082i	−0.196452	−	0.113422i	0.398547	−	0.917148i	$-0.369514\pi$
$997$	−195.863	−	113.082i	−0.196452	−	0.113422i	−0.595000	+	0.803726i	$0.702848\pi$
$998$		0			0
$999$	312.626	−	180.495i	0.312939	−	0.180675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.c.207.5		12
4.3	odd	2		56.3.k.c.11.3	yes	12
7.2	even	3	inner	224.3.o.c.79.6		12
7.3	odd	6		1568.3.g.i.687.6		6
7.4	even	3		1568.3.g.k.687.1		6
8.3	odd	2	inner	224.3.o.c.207.6		12
8.5	even	2		56.3.k.c.11.2	✓	12
28.3	even	6		392.3.g.l.99.6		6
28.11	odd	6		392.3.g.k.99.6		6
28.19	even	6		392.3.k.k.275.2		12
28.23	odd	6		56.3.k.c.51.2	yes	12
28.27	even	2		392.3.k.k.67.3		12
56.3	even	6		1568.3.g.i.687.5		6
56.5	odd	6		392.3.k.k.275.3		12
56.11	odd	6		1568.3.g.k.687.2		6
56.13	odd	2		392.3.k.k.67.2		12
56.37	even	6		56.3.k.c.51.3	yes	12
56.45	odd	6		392.3.g.l.99.5		6
56.51	odd	6	inner	224.3.o.c.79.5		12
56.53	even	6		392.3.g.k.99.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.c.11.2	✓	12	8.5	even	2
56.3.k.c.11.3	yes	12	4.3	odd	2
56.3.k.c.51.2	yes	12	28.23	odd	6
56.3.k.c.51.3	yes	12	56.37	even	6
224.3.o.c.79.5		12	56.51	odd	6	inner
224.3.o.c.79.6		12	7.2	even	3	inner
224.3.o.c.207.5		12	1.1	even	1	trivial
224.3.o.c.207.6		12	8.3	odd	2	inner
392.3.g.k.99.5		6	56.53	even	6
392.3.g.k.99.6		6	28.11	odd	6
392.3.g.l.99.5		6	56.45	odd	6
392.3.g.l.99.6		6	28.3	even	6
392.3.k.k.67.2		12	56.13	odd	2
392.3.k.k.67.3		12	28.27	even	2
392.3.k.k.275.2		12	28.19	even	6
392.3.k.k.275.3		12	56.5	odd	6
1568.3.g.i.687.5		6	56.3	even	6
1568.3.g.i.687.6		6	7.3	odd	6
1568.3.g.k.687.1		6	7.4	even	3
1568.3.g.k.687.2		6	56.11	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.46995 - 2.54604i) q^{3} +(-7.59793 + 4.38667i) q^{5} +(3.55324 + 6.03112i) q^{7} +(0.178469 + 0.309118i) q^{9} +O(q^{10})\)	\(q+(1.46995 - 2.54604i) q^{3} +(-7.59793 + 4.38667i) q^{5} +(3.55324 + 6.03112i) q^{7} +(0.178469 + 0.309118i) q^{9} +(-1.64842 + 2.85515i) q^{11} +4.10293i q^{13} +25.7928i q^{15} +(-11.6184 + 20.1236i) q^{17} +(2.76861 + 4.79537i) q^{19} +(20.5786 - 0.181210i) q^{21} +(12.8739 - 7.43273i) q^{23} +(25.9857 - 45.0085i) q^{25} +27.5085 q^{27} +43.1747i q^{29} +(-26.6958 - 15.4128i) q^{31} +(4.84621 + 8.39389i) q^{33} +(-53.4538 - 30.2371i) q^{35} +(11.3647 - 6.56141i) q^{37} +(10.4462 + 6.03112i) q^{39} -8.56863 q^{41} +11.3076 q^{43} +(-2.71199 - 1.56577i) q^{45} +(-31.9084 + 18.4223i) q^{47} +(-23.7489 + 42.8601i) q^{49} +(34.1570 + 59.1616i) q^{51} +(-53.2193 - 30.7262i) q^{53} -28.9243i q^{55} +16.2789 q^{57} +(-31.3354 + 54.2746i) q^{59} +(34.3623 - 19.8391i) q^{61} +(-1.23018 + 2.17474i) q^{63} +(-17.9982 - 31.1738i) q^{65} +(21.3147 - 36.9182i) q^{67} -43.7031i q^{69} -107.155i q^{71} +(-18.0085 + 31.1917i) q^{73} +(-76.3955 - 132.321i) q^{75} +(-23.0770 + 0.203211i) q^{77} +(36.3029 - 20.9595i) q^{79} +(38.8301 - 67.2557i) q^{81} +87.8010 q^{83} -203.864i q^{85} +(109.924 + 63.4648i) q^{87} +(-1.04794 - 1.81508i) q^{89} +(-24.7453 + 14.5787i) q^{91} +(-78.4831 + 45.3122i) q^{93} +(-42.0713 - 24.2899i) q^{95} -40.6387 q^{97} -1.17677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 8 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 8 * q^9	\( 12 q - 6 q^{3} - 8 q^{9} + 14 q^{11} - 82 q^{17} + 94 q^{19} + 116 q^{25} + 60 q^{27} + 146 q^{33} - 270 q^{35} + 120 q^{41} - 40 q^{43} - 204 q^{49} + 106 q^{51} - 372 q^{57} - 62 q^{59} - 64 q^{65} + 178 q^{67} + 54 q^{73} - 140 q^{75} + 206 q^{81} + 392 q^{83} - 26 q^{89} + 88 q^{91} - 184 q^{97} - 872 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 8 * q^9 + 14 * q^11 - 82 * q^17 + 94 * q^19 + 116 * q^25 + 60 * q^27 + 146 * q^33 - 270 * q^35 + 120 * q^41 - 40 * q^43 - 204 * q^49 + 106 * q^51 - 372 * q^57 - 62 * q^59 - 64 * q^65 + 178 * q^67 + 54 * q^73 - 140 * q^75 + 206 * q^81 + 392 * q^83 - 26 * q^89 + 88 * q^91 - 184 * q^97 - 872 * q^99

Introduction

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