LMFDB - Embedded newform 342.2.s.a.179.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(107,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("342.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.s (of order $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	342.179
Dual form			342.2.s.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} -3.44949 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} -3.44949 q^{7} +1.00000 q^{8} +(-1.22474 + 0.707107i) q^{10} +6.29253i q^{11} +(-2.17423 + 1.25529i) q^{13} +(1.72474 - 2.98735i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.22474 + 2.43916i) q^{17} +(4.00000 + 1.73205i) q^{19} -1.41421i q^{20} +(-5.44949 - 3.14626i) q^{22} +(-4.89898 + 2.82843i) q^{23} +(-1.50000 - 2.59808i) q^{25} -2.51059i q^{26} +(1.72474 + 2.98735i) q^{28} +(-1.22474 - 2.12132i) q^{29} +9.43879i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.22474 + 2.43916i) q^{34} +(-4.22474 - 2.43916i) q^{35} -5.97469i q^{37} +(-3.50000 + 2.59808i) q^{38} +(1.22474 + 0.707107i) q^{40} +(2.94949 - 5.10867i) q^{43} +(5.44949 - 3.14626i) q^{44} -5.65685i q^{46} +(-4.22474 + 2.43916i) q^{47} +4.89898 q^{49} +3.00000 q^{50} +(2.17423 + 1.25529i) q^{52} +(2.44949 + 4.24264i) q^{53} +(-4.44949 + 7.70674i) q^{55} -3.44949 q^{56} +2.44949 q^{58} +(4.77526 - 8.27098i) q^{59} +(-0.724745 - 1.25529i) q^{61} +(-8.17423 - 4.71940i) q^{62} +1.00000 q^{64} -3.55051 q^{65} +(5.84847 - 3.37662i) q^{67} -4.87832i q^{68} +(4.22474 - 2.43916i) q^{70} +(3.00000 - 5.19615i) q^{71} +(5.94949 - 10.3048i) q^{73} +(5.17423 + 2.98735i) q^{74} +(-0.500000 - 4.33013i) q^{76} -21.7060i q^{77} +(8.17423 + 4.71940i) q^{79} +(-1.22474 + 0.707107i) q^{80} +8.97809i q^{83} +(3.44949 + 5.97469i) q^{85} +(2.94949 + 5.10867i) q^{86} +6.29253i q^{88} +(6.12372 + 10.6066i) q^{89} +(7.50000 - 4.33013i) q^{91} +(4.89898 + 2.82843i) q^{92} -4.87832i q^{94} +(3.67423 + 4.94975i) q^{95} +(-1.65153 - 0.953512i) q^{97} +(-2.44949 + 4.24264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 12 q^{17} + 16 q^{19} - 12 q^{22} - 6 q^{25} + 2 q^{28} - 2 q^{32} - 12 q^{34} - 12 q^{35} - 14 q^{38} + 2 q^{43} + 12 q^{44} - 12 q^{47} + 12 q^{50} - 6 q^{52} - 8 q^{55} - 4 q^{56} + 24 q^{59} + 2 q^{61} - 18 q^{62} + 4 q^{64} - 24 q^{65} - 6 q^{67} + 12 q^{70} + 12 q^{71} + 14 q^{73} + 6 q^{74} - 2 q^{76} + 18 q^{79} + 4 q^{85} + 2 q^{86} + 30 q^{91} - 36 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 12 * q^17 + 16 * q^19 - 12 * q^22 - 6 * q^25 + 2 * q^28 - 2 * q^32 - 12 * q^34 - 12 * q^35 - 14 * q^38 + 2 * q^43 + 12 * q^44 - 12 * q^47 + 12 * q^50 - 6 * q^52 - 8 * q^55 - 4 * q^56 + 24 * q^59 + 2 * q^61 - 18 * q^62 + 4 * q^64 - 24 * q^65 - 6 * q^67 + 12 * q^70 + 12 * q^71 + 14 * q^73 + 6 * q^74 - 2 * q^76 + 18 * q^79 + 4 * q^85 + 2 * q^86 + 30 * q^91 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	0.748203	−	0.663470i	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$		0			0
$7$	−3.44949			−1.30378			−0.651892	−	0.758312i	$-0.726025\pi$
$7$	−3.44949			−1.30378			−0.651892	+	0.758312i	$0.726025\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.22474	+	0.707107i	−0.387298	+	0.223607i
$11$			6.29253i			1.89727i	0.316374	+	0.948634i	$0.397534\pi$
$11$			6.29253i			1.89727i	−0.316374	+	0.948634i	$0.602466\pi$
$12$		0			0
$13$	−2.17423	+	1.25529i	−0.603024	+	0.348156i	−0.770230	−	0.637766i	$-0.779859\pi$
$13$	−2.17423	+	1.25529i	−0.603024	+	0.348156i	0.167206	+	0.985922i	$0.446525\pi$
$14$	1.72474	−	2.98735i	0.460957	−	0.798402i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.22474	+	2.43916i	1.02465	+	0.591583i	0.915448	−	0.402437i	$-0.131837\pi$
$17$	4.22474	+	2.43916i	1.02465	+	0.591583i	0.109203	+	0.994019i	$0.465170\pi$
$18$		0			0
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$		−	1.41421i		−	0.316228i
$21$		0			0
$22$	−5.44949	−	3.14626i	−1.16184	−	0.670786i
$23$	−4.89898	+	2.82843i	−1.02151	+	0.589768i	−0.914540	−	0.404495i	$-0.867447\pi$
$23$	−4.89898	+	2.82843i	−1.02151	+	0.589768i	−0.106967	+	0.994263i	$0.534114\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		−	2.51059i		−	0.492367i
$27$		0			0
$28$	1.72474	+	2.98735i	0.325946	+	0.564555i
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$		0			0
$31$			9.43879i			1.69526i	0.530590	+	0.847629i	$0.321970\pi$
$31$			9.43879i			1.69526i	−0.530590	+	0.847629i	$0.678030\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−4.22474	+	2.43916i	−0.724538	+	0.418312i
$35$	−4.22474	−	2.43916i	−0.714112	−	0.412293i
$36$		0			0
$37$		−	5.97469i		−	0.982233i	−0.871094	−	0.491117i	$-0.836589\pi$
$37$		−	5.97469i		−	0.982233i	0.871094	−	0.491117i	$-0.163411\pi$
$38$	−3.50000	+	2.59808i	−0.567775	+	0.421464i
$39$		0			0
$40$	1.22474	+	0.707107i	0.193649	+	0.111803i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	2.94949	−	5.10867i	0.449793	−	0.779064i	−0.548579	−	0.836099i	$-0.684831\pi$
$43$	2.94949	−	5.10867i	0.449793	−	0.779064i	0.998372	+	0.0570343i	$0.0181644\pi$
$44$	5.44949	−	3.14626i	0.821541	−	0.474317i
$45$		0			0
$46$		−	5.65685i		−	0.834058i
$47$	−4.22474	+	2.43916i	−0.616242	+	0.355788i	−0.775405	−	0.631465i	$-0.782454\pi$
$47$	−4.22474	+	2.43916i	−0.616242	+	0.355788i	0.159162	+	0.987252i	$0.449121\pi$
$48$		0			0
$49$	4.89898			0.699854
$50$	3.00000			0.424264
$51$		0			0
$52$	2.17423	+	1.25529i	0.301512	+	0.174078i
$53$	2.44949	+	4.24264i	0.336463	+	0.582772i	0.983765	−	0.179463i	$-0.0574359\pi$
$53$	2.44949	+	4.24264i	0.336463	+	0.582772i	−0.647302	+	0.762234i	$0.724103\pi$
$54$		0			0
$55$	−4.44949	+	7.70674i	−0.599969	+	1.03918i
$56$	−3.44949			−0.460957
$57$		0			0
$58$	2.44949			0.321634
$59$	4.77526	−	8.27098i	0.621685	−	1.07679i	−0.367487	−	0.930029i	$-0.619782\pi$
$59$	4.77526	−	8.27098i	0.621685	−	1.07679i	0.989172	−	0.146762i	$-0.0468850\pi$
$60$		0			0
$61$	−0.724745	−	1.25529i	−0.0927941	−	0.160724i	0.815892	−	0.578205i	$-0.196246\pi$
$61$	−0.724745	−	1.25529i	−0.0927941	−	0.160724i	−0.908686	+	0.417481i	$0.862913\pi$
$62$	−8.17423	−	4.71940i	−1.03813	−	0.599364i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.55051			−0.440387
$66$		0			0
$67$	5.84847	−	3.37662i	0.714504	−	0.412519i	−0.0982223	−	0.995164i	$-0.531316\pi$
$67$	5.84847	−	3.37662i	0.714504	−	0.412519i	0.812727	+	0.582645i	$0.197982\pi$
$68$		−	4.87832i		−	0.591583i
$69$		0			0
$70$	4.22474	−	2.43916i	0.504954	−	0.291535i
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	5.94949	−	10.3048i	0.696335	−	1.20609i	−0.273393	−	0.961902i	$-0.588146\pi$
$73$	5.94949	−	10.3048i	0.696335	−	1.20609i	0.969729	−	0.244185i	$-0.0785206\pi$
$74$	5.17423	+	2.98735i	0.601493	+	0.347272i
$75$		0			0
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$		−	21.7060i		−	2.47363i
$78$		0			0
$79$	8.17423	+	4.71940i	0.919673	+	0.530974i	0.883531	−	0.468373i	$-0.155160\pi$
$79$	8.17423	+	4.71940i	0.919673	+	0.530974i	0.0361424	+	0.999347i	$0.488493\pi$
$80$	−1.22474	+	0.707107i	−0.136931	+	0.0790569i
$81$		0			0
$82$		0			0
$83$			8.97809i			0.985474i	0.870178	+	0.492737i	$0.164003\pi$
$83$			8.97809i			0.985474i	−0.870178	+	0.492737i	$0.835997\pi$
$84$		0			0
$85$	3.44949	+	5.97469i	0.374150	+	0.648046i
$86$	2.94949	+	5.10867i	0.318052	+	0.550882i
$87$		0			0
$88$			6.29253i			0.670786i
$89$	6.12372	+	10.6066i	0.649113	+	1.12430i	0.983335	+	0.181803i	$0.0581933\pi$
$89$	6.12372	+	10.6066i	0.649113	+	1.12430i	−0.334221	+	0.942495i	$0.608473\pi$
$90$		0			0
$91$	7.50000	−	4.33013i	0.786214	−	0.453921i
$92$	4.89898	+	2.82843i	0.510754	+	0.294884i
$93$		0			0
$94$		−	4.87832i		−	0.503160i
$95$	3.67423	+	4.94975i	0.376969	+	0.507833i
$96$		0			0
$97$	−1.65153	−	0.953512i	−0.167688	−	0.0968144i	0.413807	−	0.910364i	$-0.364199\pi$
$97$	−1.65153	−	0.953512i	−0.167688	−	0.0968144i	−0.581495	+	0.813550i	$0.697532\pi$
$98$	−2.44949	+	4.24264i	−0.247436	+	0.428571i
$99$		0			0
$100$	−1.50000	+	2.59808i	−0.150000	+	0.259808i
$101$	−6.55051	+	3.78194i	−0.651800	+	0.376317i	−0.789146	−	0.614206i	$-0.789476\pi$
$101$	−6.55051	+	3.78194i	−0.651800	+	0.376317i	0.137345	+	0.990523i	$0.456143\pi$
$102$		0			0
$103$		−	10.9959i		−	1.08346i	−0.840554	−	0.541728i	$-0.817770\pi$
$103$		−	10.9959i		−	1.08346i	0.840554	−	0.541728i	$-0.182230\pi$
$104$	−2.17423	+	1.25529i	−0.213201	+	0.123092i
$105$		0			0
$106$	−4.89898			−0.475831
$107$	−3.79796			−0.367163			−0.183581	−	0.983005i	$-0.558769\pi$
$107$	−3.79796			−0.367163			−0.183581	+	0.983005i	$0.558769\pi$
$108$		0			0
$109$	14.6969	+	8.48528i	1.40771	+	0.812743i	0.995167	−	0.0981950i	$-0.0313069\pi$
$109$	14.6969	+	8.48528i	1.40771	+	0.812743i	0.412544	+	0.910938i	$0.364640\pi$
$110$	−4.44949	−	7.70674i	−0.424242	−	0.734809i
$111$		0			0
$112$	1.72474	−	2.98735i	0.162973	−	0.282278i
$113$	17.1464			1.61300			0.806500	−	0.591234i	$-0.201359\pi$
$113$	17.1464			1.61300			0.806500	+	0.591234i	$0.201359\pi$
$114$		0			0
$115$	−8.00000			−0.746004
$116$	−1.22474	+	2.12132i	−0.113715	+	0.196960i
$117$		0			0
$118$	4.77526	+	8.27098i	0.439598	+	0.761406i
$119$	−14.5732	−	8.41385i	−1.33592	−	0.771296i
$120$		0			0
$121$	−28.5959			−2.59963
$122$	1.44949			0.131231
$123$		0			0
$124$	8.17423	−	4.71940i	0.734068	−	0.423814i
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	−7.34847	+	4.24264i	−0.652071	+	0.376473i	−0.789249	−	0.614073i	$-0.789530\pi$
$127$	−7.34847	+	4.24264i	−0.652071	+	0.376473i	0.137178	+	0.990546i	$0.456197\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	1.77526	−	3.07483i	0.155700	−	0.269681i
$131$	−6.79796	−	3.92480i	−0.593940	−	0.342912i	0.172714	−	0.984972i	$-0.444746\pi$
$131$	−6.79796	−	3.92480i	−0.593940	−	0.342912i	−0.766654	+	0.642060i	$0.778080\pi$
$132$		0			0
$133$	−13.7980	−	5.97469i	−1.19643	−	0.518071i
$134$			6.75323i			0.583390i
$135$		0			0
$136$	4.22474	+	2.43916i	0.362269	+	0.209156i
$137$	−0.550510	+	0.317837i	−0.0470333	+	0.0271547i	−0.523332	−	0.852129i	$-0.675311\pi$
$137$	−0.550510	+	0.317837i	−0.0470333	+	0.0271547i	0.476299	+	0.879283i	$0.341978\pi$
$138$		0			0
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	−0.678551	+	0.734553i	$0.737392\pi$
$140$			4.87832i			0.412293i
$141$		0			0
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	−7.89898	−	13.6814i	−0.660546	−	1.14410i
$144$		0			0
$145$		−	3.46410i		−	0.287678i
$146$	5.94949	+	10.3048i	0.492383	+	0.852833i
$147$		0			0
$148$	−5.17423	+	2.98735i	−0.425319	+	0.245558i
$149$	12.5505	+	7.24604i	1.02818	+	0.593619i	0.916462	−	0.400121i	$-0.131032\pi$
$149$	12.5505	+	7.24604i	1.02818	+	0.593619i	0.111716	+	0.993740i	$0.464365\pi$
$150$		0			0
$151$		−	15.4135i		−	1.25433i	−0.778886	−	0.627166i	$-0.784215\pi$
$151$		−	15.4135i		−	1.25433i	0.778886	−	0.627166i	$-0.215785\pi$
$152$	4.00000	+	1.73205i	0.324443	+	0.140488i
$153$		0			0
$154$	18.7980	+	10.8530i	1.51478	+	0.874560i
$155$	−6.67423	+	11.5601i	−0.536087	+	0.928531i
$156$		0			0
$157$	1.17423	−	2.03383i	0.0937141	−	0.162318i	−0.815357	−	0.578958i	$-0.803459\pi$
$157$	1.17423	−	2.03383i	0.0937141	−	0.162318i	0.909071	+	0.416641i	$0.136793\pi$
$158$	−8.17423	+	4.71940i	−0.650307	+	0.375455i
$159$		0			0
$160$		−	1.41421i		−	0.111803i
$161$	16.8990	−	9.75663i	1.33183	−	0.768930i
$162$		0			0
$163$	−21.6969			−1.69944			−0.849718	−	0.527238i	$-0.823228\pi$
$163$	−21.6969			−1.69944			−0.849718	+	0.527238i	$0.823228\pi$
$164$		0			0
$165$		0			0
$166$	−7.77526	−	4.48905i	−0.603477	−	0.348418i
$167$	1.77526	+	3.07483i	0.137373	+	0.237938i	0.926502	−	0.376291i	$-0.122801\pi$
$167$	1.77526	+	3.07483i	0.137373	+	0.237938i	−0.789128	+	0.614228i	$0.789467\pi$
$168$		0			0
$169$	−3.34847	+	5.79972i	−0.257575	+	0.446132i
$170$	−6.89898			−0.529128
$171$		0			0
$172$	−5.89898			−0.449793
$173$	6.12372	−	10.6066i	0.465578	−	0.806405i	−0.533649	−	0.845706i	$-0.679180\pi$
$173$	6.12372	−	10.6066i	0.465578	−	0.806405i	0.999227	+	0.0393009i	$0.0125131\pi$
$174$		0			0
$175$	5.17423	+	8.96204i	0.391135	+	0.677466i
$176$	−5.44949	−	3.14626i	−0.410771	−	0.237159i
$177$		0			0
$178$	−12.2474			−0.917985
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−19.3485	+	11.1708i	−1.43816	+	0.830322i	−0.997722	−	0.0674605i	$-0.978510\pi$
$181$	−19.3485	+	11.1708i	−1.43816	+	0.830322i	−0.440438	+	0.897783i	$0.645177\pi$
$182$			8.66025i			0.641941i
$183$		0			0
$184$	−4.89898	+	2.82843i	−0.361158	+	0.208514i
$185$	4.22474	−	7.31747i	0.310609	−	0.537991i
$186$		0			0
$187$	−15.3485	+	26.5843i	−1.12239	+	1.94404i
$188$	4.22474	+	2.43916i	0.308121	+	0.177894i
$189$		0			0
$190$	−6.12372	+	0.707107i	−0.444262	+	0.0512989i
$191$			12.4422i			0.900285i	0.892957	+	0.450143i	$0.148627\pi$
$191$			12.4422i			0.900285i	−0.892957	+	0.450143i	$0.851373\pi$
$192$		0			0
$193$	0.151531	+	0.0874863i	0.0109074	+	0.00629740i	0.505444	−	0.862860i	$-0.331329\pi$
$193$	0.151531	+	0.0874863i	0.0109074	+	0.00629740i	−0.494536	+	0.869157i	$0.664662\pi$
$194$	1.65153	−	0.953512i	0.118573	−	0.0684582i
$195$		0			0
$196$	−2.44949	−	4.24264i	−0.174964	−	0.303046i
$197$			0.492810i			0.0351113i	0.999846	+	0.0175556i	$0.00558842\pi$
$197$			0.492810i			0.0351113i	−0.999846	+	0.0175556i	$0.994412\pi$
$198$		0			0
$199$	3.62372	+	6.27647i	0.256879	+	0.444927i	0.965404	−	0.260758i	$-0.0839725\pi$
$199$	3.62372	+	6.27647i	0.256879	+	0.444927i	−0.708525	+	0.705686i	$0.750639\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$		0			0
$202$		−	7.56388i		−	0.532193i
$203$	4.22474	+	7.31747i	0.296519	+	0.513586i
$204$		0			0
$205$		0			0
$206$	9.52270	+	5.49794i	0.663478	+	0.383059i
$207$		0			0
$208$		−	2.51059i		−	0.174078i
$209$	−10.8990	+	25.1701i	−0.753898	+	1.74105i
$210$		0			0
$211$	17.8485	+	10.3048i	1.22874	+	0.709413i	0.966766	−	0.255662i	$-0.0822935\pi$
$211$	17.8485	+	10.3048i	1.22874	+	0.709413i	0.261973	+	0.965075i	$0.415627\pi$
$212$	2.44949	−	4.24264i	0.168232	−	0.291386i
$213$		0			0
$214$	1.89898	−	3.28913i	0.129812	−	0.224840i
$215$	7.22474	−	4.17121i	0.492724	−	0.284474i
$216$		0			0
$217$		−	32.5590i		−	2.21025i
$218$	−14.6969	+	8.48528i	−0.995402	+	0.574696i
$219$		0			0
$220$	8.89898			0.599969
$221$	−12.2474			−0.823853
$222$		0			0
$223$	5.17423	+	2.98735i	0.346492	+	0.200047i	0.663139	−	0.748496i	$-0.269224\pi$
$223$	5.17423	+	2.98735i	0.346492	+	0.200047i	−0.316647	+	0.948543i	$0.602557\pi$
$224$	1.72474	+	2.98735i	0.115239	+	0.199600i
$225$		0			0
$226$	−8.57321	+	14.8492i	−0.570282	+	0.987757i
$227$	11.1464			0.739814			0.369907	−	0.929069i	$-0.379389\pi$
$227$	11.1464			0.739814			0.369907	+	0.929069i	$0.379389\pi$
$228$		0			0
$229$	5.24745			0.346761			0.173381	−	0.984855i	$-0.444531\pi$
$229$	5.24745			0.346761			0.173381	+	0.984855i	$0.444531\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$		0			0
$232$	−1.22474	−	2.12132i	−0.0804084	−	0.139272i
$233$	9.24745	+	5.33902i	0.605821	+	0.349771i	0.771328	−	0.636438i	$-0.219593\pi$
$233$	9.24745	+	5.33902i	0.605821	+	0.349771i	−0.165507	+	0.986209i	$0.552926\pi$
$234$		0			0
$235$	−6.89898			−0.450040
$236$	−9.55051			−0.621685
$237$		0			0
$238$	14.5732	−	8.41385i	0.944641	−	0.545389i
$239$			8.62815i			0.558108i	0.960275	+	0.279054i	$0.0900209\pi$
$239$			8.62815i			0.558108i	−0.960275	+	0.279054i	$0.909979\pi$
$240$		0			0
$241$	26.8485	−	15.5010i	1.72946	−	0.998505i	0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.8485	−	15.5010i	1.72946	−	0.998505i	0.892058	−	0.451920i	$-0.149261\pi$
$242$	14.2980	−	24.7648i	0.919108	−	1.59194i
$243$		0			0
$244$	−0.724745	+	1.25529i	−0.0463970	+	0.0803620i
$245$	6.00000	+	3.46410i	0.383326	+	0.221313i
$246$		0			0
$247$	−10.8712	+	1.25529i	−0.691716	+	0.0798725i
$248$			9.43879i			0.599364i
$249$		0			0
$250$	9.79796	+	5.65685i	0.619677	+	0.357771i
$251$	−1.22474	+	0.707107i	−0.0773052	+	0.0446322i	−0.538154	−	0.842846i	$-0.680878\pi$
$251$	−1.22474	+	0.707107i	−0.0773052	+	0.0446322i	0.460849	+	0.887478i	$0.347545\pi$
$252$		0			0
$253$	−17.7980	−	30.8270i	−1.11895	−	1.93807i
$254$		−	8.48528i		−	0.532414i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$		0			0
$259$			20.6096i			1.28062i
$260$	1.77526	+	3.07483i	0.110097	+	0.190693i
$261$		0			0
$262$	6.79796	−	3.92480i	0.419979	−	0.242475i
$263$	−18.7980	−	10.8530i	−1.15913	−	0.669225i	−0.208036	−	0.978121i	$-0.566707\pi$
$263$	−18.7980	−	10.8530i	−1.15913	−	0.669225i	−0.951096	+	0.308896i	$0.900040\pi$
$264$		0			0
$265$			6.92820i			0.425596i
$266$	12.0732	−	8.96204i	0.740256	−	0.549498i
$267$		0			0
$268$	−5.84847	−	3.37662i	−0.357252	−	0.206260i
$269$	7.77526	−	13.4671i	0.474066	−	0.821106i	−0.525493	−	0.850798i	$-0.676119\pi$
$269$	7.77526	−	13.4671i	0.474066	−	0.821106i	0.999559	+	0.0296918i	$0.00945259\pi$
$270$		0			0
$271$	13.6969	−	23.7238i	0.832030	−	1.44112i	−0.0643963	−	0.997924i	$-0.520512\pi$
$271$	13.6969	−	23.7238i	0.832030	−	1.44112i	0.896426	−	0.443193i	$-0.146155\pi$
$272$	−4.22474	+	2.43916i	−0.256163	+	0.147896i
$273$		0			0
$274$		−	0.635674i		−	0.0384025i
$275$	16.3485	−	9.43879i	0.985850	−	0.569181i
$276$		0			0
$277$	18.8990			1.13553			0.567765	−	0.823191i	$-0.307808\pi$
$277$	18.8990			1.13553			0.567765	+	0.823191i	$0.307808\pi$
$278$	−7.00000			−0.419832
$279$		0			0
$280$	−4.22474	−	2.43916i	−0.252477	−	0.145768i
$281$	5.57321	+	9.65309i	0.332470	+	0.575855i	0.982996	−	0.183629i	$-0.0587846\pi$
$281$	5.57321	+	9.65309i	0.332470	+	0.575855i	−0.650525	+	0.759484i	$0.725451\pi$
$282$		0			0
$283$	2.55051	−	4.41761i	0.151612	−	0.262600i	−0.780208	−	0.625520i	$-0.784887\pi$
$283$	2.55051	−	4.41761i	0.151612	−	0.262600i	0.931820	+	0.362920i	$0.118220\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	15.7980			0.934153
$287$		0			0
$288$		0			0
$289$	3.39898	+	5.88721i	0.199940	+	0.346306i
$290$	3.00000	+	1.73205i	0.176166	+	0.101710i
$291$		0			0
$292$	−11.8990			−0.696335
$293$	−25.3485			−1.48087			−0.740437	−	0.672126i	$-0.765381\pi$
$293$	−25.3485			−1.48087			−0.740437	+	0.672126i	$0.765381\pi$
$294$		0			0
$295$	11.6969	−	6.75323i	0.681022	−	0.393188i
$296$		−	5.97469i		−	0.347272i
$297$		0			0
$298$	−12.5505	+	7.24604i	−0.727032	+	0.419752i
$299$	7.10102	−	12.2993i	0.410663	−	0.711289i
$300$		0			0
$301$	−10.1742	+	17.6223i	−0.586433	+	1.01573i
$302$	13.3485	+	7.70674i	0.768118	+	0.443473i
$303$		0			0
$304$	−3.50000	+	2.59808i	−0.200739	+	0.149010i
$305$		−	2.04989i		−	0.117376i
$306$		0			0
$307$	1.34847	+	0.778539i	0.0769612	+	0.0444336i	0.537987	−	0.842953i	$-0.319185\pi$
$307$	1.34847	+	0.778539i	0.0769612	+	0.0444336i	−0.461026	+	0.887387i	$0.652518\pi$
$308$	−18.7980	+	10.8530i	−1.07111	+	0.618407i
$309$		0			0
$310$	−6.67423	−	11.5601i	−0.379071	−	0.656570i
$311$			25.9487i			1.47141i	0.677300	+	0.735707i	$0.263150\pi$
$311$			25.9487i			1.47141i	−0.677300	+	0.735707i	$0.736850\pi$
$312$		0			0
$313$	3.34847	+	5.79972i	0.189267	+	0.327819i	0.945006	−	0.327053i	$-0.106056\pi$
$313$	3.34847	+	5.79972i	0.189267	+	0.327819i	−0.755739	+	0.654873i	$0.772722\pi$
$314$	1.17423	+	2.03383i	0.0662659	+	0.114776i
$315$		0			0
$316$		−	9.43879i		−	0.530974i
$317$	−3.67423	−	6.36396i	−0.206366	−	0.357436i	0.744201	−	0.667955i	$-0.232830\pi$
$317$	−3.67423	−	6.36396i	−0.206366	−	0.357436i	−0.950567	+	0.310520i	$0.899497\pi$
$318$		0			0
$319$	13.3485	−	7.70674i	0.747371	−	0.431495i
$320$	1.22474	+	0.707107i	0.0684653	+	0.0395285i
$321$		0			0
$322$			19.5133i			1.08743i
$323$	12.6742	+	17.0741i	0.705213	+	0.950029i
$324$		0			0
$325$	6.52270	+	3.76588i	0.361815	+	0.208894i
$326$	10.8485	−	18.7901i	0.600841	−	1.04069i
$327$		0			0
$328$		0			0
$329$	14.5732	−	8.41385i	0.803447	−	0.463871i
$330$		0			0
$331$		−	15.2385i		−	0.837584i	−0.908082	−	0.418792i	$-0.862454\pi$
$331$		−	15.2385i		−	0.837584i	0.908082	−	0.418792i	$-0.137546\pi$
$332$	7.77526	−	4.48905i	0.426723	−	0.246368i
$333$		0			0
$334$	−3.55051			−0.194275
$335$	9.55051			0.521800
$336$		0			0
$337$	31.1969	+	18.0116i	1.69941	+	0.981152i	0.946321	+	0.323229i	$0.104768\pi$
$337$	31.1969	+	18.0116i	1.69941	+	0.981152i	0.753085	+	0.657924i	$0.228565\pi$
$338$	−3.34847	−	5.79972i	−0.182133	−	0.315463i
$339$		0			0
$340$	3.44949	−	5.97469i	0.187075	−	0.324023i
$341$	−59.3939			−3.21636
$342$		0			0
$343$	7.24745			0.391325
$344$	2.94949	−	5.10867i	0.159026	−	0.275441i
$345$		0			0
$346$	6.12372	+	10.6066i	0.329213	+	0.570214i
$347$	−25.7753	−	14.8814i	−1.38369	−	0.798873i	−0.391094	−	0.920351i	$-0.627903\pi$
$347$	−25.7753	−	14.8814i	−1.38369	−	0.798873i	−0.992594	+	0.121478i	$0.961237\pi$
$348$		0			0
$349$	−1.24745			−0.0667744			−0.0333872	−	0.999442i	$-0.510629\pi$
$349$	−1.24745			−0.0667744			−0.0333872	+	0.999442i	$0.510629\pi$
$350$	−10.3485			−0.553149
$351$		0			0
$352$	5.44949	−	3.14626i	0.290459	−	0.167696i
$353$			17.4634i			0.929482i	0.885447	+	0.464741i	$0.153852\pi$
$353$			17.4634i			0.929482i	−0.885447	+	0.464741i	$0.846148\pi$
$354$		0			0
$355$	7.34847	−	4.24264i	0.390016	−	0.225176i
$356$	6.12372	−	10.6066i	0.324557	−	0.562149i
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	−9.79796	−	5.65685i	−0.517116	−	0.298557i	0.218638	−	0.975806i	$-0.429839\pi$
$359$	−9.79796	−	5.65685i	−0.517116	−	0.298557i	−0.735754	+	0.677249i	$0.763172\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		−	22.3417i		−	1.17425i
$363$		0			0
$364$	−7.50000	−	4.33013i	−0.393107	−	0.226960i
$365$	14.5732	−	8.41385i	0.762797	−	0.440401i
$366$		0			0
$367$	−0.174235	−	0.301783i	−0.00909497	−	0.0157530i	0.861442	−	0.507856i	$-0.169562\pi$
$367$	−0.174235	−	0.301783i	−0.00909497	−	0.0157530i	−0.870537	+	0.492103i	$0.836228\pi$
$368$		−	5.65685i		−	0.294884i
$369$		0			0
$370$	4.22474	+	7.31747i	0.219634	+	0.380417i
$371$	−8.44949	−	14.6349i	−0.438676	−	0.759809i
$372$		0			0
$373$			29.2699i			1.51554i	0.652523	+	0.757769i	$0.273710\pi$
$373$			29.2699i			1.51554i	−0.652523	+	0.757769i	$0.726290\pi$
$374$	−15.3485	−	26.5843i	−0.793650	−	1.37464i
$375$		0			0
$376$	−4.22474	+	2.43916i	−0.217875	+	0.125790i
$377$	5.32577	+	3.07483i	0.274291	+	0.158362i
$378$		0			0
$379$		−	19.0526i		−	0.978664i	−0.872098	−	0.489332i	$-0.837241\pi$
$379$		−	19.0526i		−	0.978664i	0.872098	−	0.489332i	$-0.162759\pi$
$380$	2.44949	−	5.65685i	0.125656	−	0.290191i
$381$		0			0
$382$	−10.7753	−	6.22110i	−0.551310	−	0.318299i
$383$	−0.550510	+	0.953512i	−0.0281298	+	0.0487222i	−0.879748	−	0.475441i	$-0.842288\pi$
$383$	−0.550510	+	0.953512i	−0.0281298	+	0.0487222i	0.851618	+	0.524163i	$0.175622\pi$
$384$		0			0
$385$	15.3485	−	26.5843i	0.782230	−	1.35486i
$386$	−0.151531	+	0.0874863i	−0.00771271	+	0.00445294i
$387$		0			0
$388$			1.90702i			0.0968144i
$389$	13.1010	−	7.56388i	0.664248	−	0.383504i	−0.129646	−	0.991560i	$-0.541384\pi$
$389$	13.1010	−	7.56388i	0.664248	−	0.383504i	0.793894	+	0.608057i	$0.208051\pi$
$390$		0			0
$391$	−27.5959			−1.39559
$392$	4.89898			0.247436
$393$		0			0
$394$	−0.426786	−	0.246405i	−0.0215012	−	0.0124137i
$395$	6.67423	+	11.5601i	0.335817	+	0.581652i
$396$		0			0
$397$	−18.1742	+	31.4787i	−0.912139	+	1.57987i	−0.101101	+	0.994876i	$0.532237\pi$
$397$	−18.1742	+	31.4787i	−0.912139	+	1.57987i	−0.811037	+	0.584994i	$0.801097\pi$
$398$	−7.24745			−0.363282
$399$		0			0
$400$	3.00000			0.150000
$401$	−12.1237	+	20.9989i	−0.605430	+	1.04864i	0.386553	+	0.922267i	$0.373665\pi$
$401$	−12.1237	+	20.9989i	−0.605430	+	1.04864i	−0.991983	+	0.126368i	$0.959668\pi$
$402$		0			0
$403$	−11.8485	−	20.5222i	−0.590214	−	1.02228i
$404$	6.55051	+	3.78194i	0.325900	+	0.188158i
$405$		0			0
$406$	−8.44949			−0.419341
$407$	37.5959			1.86356
$408$		0			0
$409$	19.0454	−	10.9959i	0.941735	−	0.543711i	0.0512311	−	0.998687i	$-0.483685\pi$
$409$	19.0454	−	10.9959i	0.941735	−	0.543711i	0.890504	+	0.454976i	$0.150352\pi$
$410$		0			0
$411$		0			0
$412$	−9.52270	+	5.49794i	−0.469150	+	0.270864i
$413$	−16.4722	+	28.5307i	−0.810544	+	1.40390i
$414$		0			0
$415$	−6.34847	+	10.9959i	−0.311634	+	0.539766i
$416$	2.17423	+	1.25529i	0.106601	+	0.0615459i
$417$		0			0
$418$	−16.3485	−	22.0239i	−0.799630	−	1.07722i
$419$		−	24.5344i		−	1.19859i	−0.800530	−	0.599293i	$-0.795448\pi$
$419$		−	24.5344i		−	1.19859i	0.800530	−	0.599293i	$-0.204552\pi$
$420$		0			0
$421$	−13.3485	−	7.70674i	−0.650565	−	0.375604i	0.138108	−	0.990417i	$-0.455898\pi$
$421$	−13.3485	−	7.70674i	−0.650565	−	0.375604i	−0.788672	+	0.614814i	$0.789231\pi$
$422$	−17.8485	+	10.3048i	−0.868850	+	0.501631i
$423$		0			0
$424$	2.44949	+	4.24264i	0.118958	+	0.206041i
$425$		−	14.6349i		−	0.709899i
$426$		0			0
$427$	2.50000	+	4.33013i	0.120983	+	0.209550i
$428$	1.89898	+	3.28913i	0.0917906	+	0.158986i
$429$		0			0
$430$			8.34242i			0.402307i
$431$	14.0227	+	24.2880i	0.675450	+	1.16991i	0.976337	+	0.216254i	$0.0693839\pi$
$431$	14.0227	+	24.2880i	0.675450	+	1.16991i	−0.300887	+	0.953660i	$0.597283\pi$
$432$		0			0
$433$	−4.19694	+	2.42310i	−0.201692	+	0.116447i	−0.597444	−	0.801910i	$-0.703817\pi$
$433$	−4.19694	+	2.42310i	−0.201692	+	0.116447i	0.395752	+	0.918357i	$0.370484\pi$
$434$	28.1969	+	16.2795i	1.35350	+	0.781441i
$435$		0			0
$436$		−	16.9706i		−	0.812743i
$437$	−24.4949	+	2.82843i	−1.17175	+	0.135302i
$438$		0			0
$439$	9.52270	+	5.49794i	0.454494	+	0.262402i	0.709726	−	0.704478i	$-0.248819\pi$
$439$	9.52270	+	5.49794i	0.454494	+	0.262402i	−0.255232	+	0.966880i	$0.582152\pi$
$440$	−4.44949	+	7.70674i	−0.212121	+	0.367405i
$441$		0			0
$442$	6.12372	−	10.6066i	0.291276	−	0.504505i
$443$	−28.2247	+	16.2956i	−1.34100	+	0.774226i	−0.986954	−	0.161003i	$-0.948527\pi$
$443$	−28.2247	+	16.2956i	−1.34100	+	0.774226i	−0.354044	+	0.935229i	$0.615194\pi$
$444$		0			0
$445$			17.3205i			0.821071i
$446$	−5.17423	+	2.98735i	−0.245007	+	0.141455i
$447$		0			0
$448$	−3.44949			−0.162973
$449$	6.24745			0.294835			0.147418	−	0.989074i	$-0.452904\pi$
$449$	6.24745			0.294835			0.147418	+	0.989074i	$0.452904\pi$
$450$		0			0
$451$		0			0
$452$	−8.57321	−	14.8492i	−0.403250	−	0.698450i
$453$		0			0
$454$	−5.57321	+	9.65309i	−0.261564	+	0.453042i
$455$	12.2474			0.574169
$456$		0			0
$457$	−9.69694			−0.453604			−0.226802	−	0.973941i	$-0.572827\pi$
$457$	−9.69694			−0.453604			−0.226802	+	0.973941i	$0.572827\pi$
$458$	−2.62372	+	4.54442i	−0.122599	+	0.212347i
$459$		0			0
$460$	4.00000	+	6.92820i	0.186501	+	0.323029i
$461$	−3.12372	−	1.80348i	−0.145486	−	0.0839966i	0.425490	−	0.904963i	$-0.360102\pi$
$461$	−3.12372	−	1.80348i	−0.145486	−	0.0839966i	−0.570976	+	0.820967i	$0.693435\pi$
$462$		0			0
$463$	5.85357			0.272039			0.136019	−	0.990706i	$-0.456569\pi$
$463$	5.85357			0.272039			0.136019	+	0.990706i	$0.456569\pi$
$464$	2.44949			0.113715
$465$		0			0
$466$	−9.24745	+	5.33902i	−0.428380	+	0.247325i
$467$		−	7.21393i		−	0.333821i	−0.985972	−	0.166910i	$-0.946621\pi$
$467$		−	7.21393i		−	0.333821i	0.985972	−	0.166910i	$-0.0533791\pi$
$468$		0			0
$469$	−20.1742	+	11.6476i	−0.931560	+	0.537836i
$470$	3.44949	−	5.97469i	0.159113	−	0.275592i
$471$		0			0
$472$	4.77526	−	8.27098i	0.219799	−	0.380703i
$473$	32.1464	+	18.5597i	1.47809	+	0.853378i
$474$		0			0
$475$	−1.50000	−	12.9904i	−0.0688247	−	0.596040i
$476$			16.8277i			0.771296i
$477$		0			0
$478$	−7.47219	−	4.31407i	−0.341770	−	0.197321i
$479$	26.1464	−	15.0956i	1.19466	−	0.689738i	0.235301	−	0.971923i	$-0.424392\pi$
$479$	26.1464	−	15.0956i	1.19466	−	0.689738i	0.959360	+	0.282185i	$0.0910592\pi$
$480$		0			0
$481$	7.50000	+	12.9904i	0.341971	+	0.592310i
$482$			31.0019i			1.41210i
$483$		0			0
$484$	14.2980	+	24.7648i	0.649907	+	1.12567i
$485$	−1.34847	−	2.33562i	−0.0612308	−	0.106055i
$486$		0			0
$487$		−	22.6916i		−	1.02826i	−0.857713	−	0.514128i	$-0.828116\pi$
$487$		−	22.6916i		−	1.02826i	0.857713	−	0.514128i	$-0.171884\pi$
$488$	−0.724745	−	1.25529i	−0.0328077	−	0.0568245i
$489$		0			0
$490$	−6.00000	+	3.46410i	−0.271052	+	0.156492i
$491$	−8.14643	−	4.70334i	−0.367643	−	0.212259i	0.304785	−	0.952421i	$-0.401415\pi$
$491$	−8.14643	−	4.70334i	−0.367643	−	0.212259i	−0.672428	+	0.740162i	$0.734749\pi$
$492$		0			0
$493$		−	11.9494i		−	0.538173i
$494$	4.34847	−	10.0424i	0.195647	−	0.451827i
$495$		0			0
$496$	−8.17423	−	4.71940i	−0.367034	−	0.211907i
$497$	−10.3485	+	17.9241i	−0.464192	+	0.804005i
$498$		0			0
$499$	−2.74745	+	4.75872i	−0.122993	+	0.213030i	−0.920947	−	0.389689i	$-0.872583\pi$
$499$	−2.74745	+	4.75872i	−0.122993	+	0.213030i	0.797954	+	0.602719i	$0.205916\pi$
$500$	−9.79796	+	5.65685i	−0.438178	+	0.252982i
$501$		0			0
$502$		−	1.41421i		−	0.0631194i
$503$	35.5176	−	20.5061i	1.58365	−	0.914322i	0.589331	−	0.807891i	$-0.299391\pi$
$503$	35.5176	−	20.5061i	1.58365	−	0.914322i	0.994320	−	0.106430i	$-0.0339421\pi$
$504$		0			0
$505$	−10.6969			−0.476008
$506$	35.5959			1.58243
$507$		0			0
$508$	7.34847	+	4.24264i	0.326036	+	0.188237i
$509$	0.674235	+	1.16781i	0.0298849	+	0.0517622i	0.880581	−	0.473896i	$-0.157153\pi$
$509$	0.674235	+	1.16781i	0.0298849	+	0.0517622i	−0.850696	+	0.525658i	$0.823819\pi$
$510$		0			0
$511$	−20.5227	+	35.5464i	−0.907871	+	1.57248i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.0000			0.529297
$515$	7.77526	−	13.4671i	0.342619	−	0.593433i
$516$		0			0
$517$	−15.3485	−	26.5843i	−0.675025	−	1.16918i
$518$	−17.8485	−	10.3048i	−0.784217	−	0.452768i
$519$		0			0
$520$	−3.55051			−0.155700
$521$	−27.7980			−1.21785			−0.608925	−	0.793228i	$-0.708399\pi$
$521$	−27.7980			−1.21785			−0.608925	+	0.793228i	$0.708399\pi$
$522$		0			0
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	0.765222	+	0.643767i	$0.222629\pi$
$524$			7.84961i			0.342912i
$525$		0			0
$526$	18.7980	−	10.8530i	0.819630	−	0.473214i
$527$	−23.0227	+	39.8765i	−1.00288	+	1.73705i
$528$		0			0
$529$	4.50000	−	7.79423i	0.195652	−	0.338880i
$530$	−6.00000	−	3.46410i	−0.260623	−	0.150471i
$531$		0			0
$532$	1.72474	+	14.9367i	0.0747772	+	0.647589i
$533$		0			0
$534$		0			0
$535$	−4.65153	−	2.68556i	−0.201103	−	0.116107i
$536$	5.84847	−	3.37662i	0.252615	−	0.145848i
$537$		0			0
$538$	7.77526	+	13.4671i	0.335215	+	0.580610i
$539$			30.8270i			1.32781i
$540$		0			0
$541$	−7.82577	−	13.5546i	−0.336456	−	0.582759i	0.647307	−	0.762229i	$-0.275895\pi$
$541$	−7.82577	−	13.5546i	−0.336456	−	0.582759i	−0.983763	+	0.179470i	$0.942562\pi$
$542$	13.6969	+	23.7238i	0.588334	+	1.01902i
$543$		0			0
$544$		−	4.87832i		−	0.209156i
$545$	12.0000	+	20.7846i	0.514024	+	0.890315i
$546$		0			0
$547$	−31.1969	+	18.0116i	−1.33388	+	0.770119i	−0.985893	−	0.167379i	$-0.946470\pi$
$547$	−31.1969	+	18.0116i	−1.33388	+	0.770119i	−0.347992	+	0.937497i	$0.613136\pi$
$548$	0.550510	+	0.317837i	0.0235166	+	0.0135773i
$549$		0			0
$550$			18.8776i			0.804943i
$551$	−1.22474	−	10.6066i	−0.0521759	−	0.451856i
$552$		0			0
$553$	−28.1969	−	16.2795i	−1.19906	−	0.692275i
$554$	−9.44949	+	16.3670i	−0.401470	+	0.695367i
$555$		0			0
$556$	3.50000	−	6.06218i	0.148433	−	0.257094i
$557$	−16.5959	+	9.58166i	−0.703192	+	0.405988i	−0.808535	−	0.588448i	$-0.799739\pi$
$557$	−16.5959	+	9.58166i	−0.703192	+	0.405988i	0.105343	+	0.994436i	$0.466406\pi$
$558$		0			0
$559$			14.8099i			0.626393i
$560$	4.22474	−	2.43916i	0.178528	−	0.103073i
$561$		0			0
$562$	−11.1464			−0.470184
$563$	13.5959			0.573000			0.286500	−	0.958080i	$-0.407508\pi$
$563$	13.5959			0.573000			0.286500	+	0.958080i	$0.407508\pi$
$564$		0			0
$565$	21.0000	+	12.1244i	0.883477	+	0.510075i
$566$	2.55051	+	4.41761i	0.107206	+	0.185686i
$567$		0			0
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	40.8990			1.71457			0.857287	−	0.514838i	$-0.172148\pi$
$569$	40.8990			1.71457			0.857287	+	0.514838i	$0.172148\pi$
$570$		0			0
$571$	25.6969			1.07538			0.537692	−	0.843142i	$-0.319296\pi$
$571$	25.6969			1.07538			0.537692	+	0.843142i	$0.319296\pi$
$572$	−7.89898	+	13.6814i	−0.330273	+	0.572049i
$573$		0			0
$574$		0			0
$575$	14.6969	+	8.48528i	0.612905	+	0.353861i
$576$		0			0
$577$	−13.7980			−0.574417			−0.287208	−	0.957868i	$-0.592727\pi$
$577$	−13.7980			−0.574417			−0.287208	+	0.957868i	$0.592727\pi$
$578$	−6.79796			−0.282758
$579$		0			0
$580$	−3.00000	+	1.73205i	−0.124568	+	0.0719195i
$581$		−	30.9698i		−	1.28485i
$582$		0			0
$583$	−26.6969	+	15.4135i	−1.10567	+	0.638361i
$584$	5.94949	−	10.3048i	0.246192	−	0.426416i
$585$		0			0
$586$	12.6742	−	21.9524i	0.523568	−	0.906846i
$587$	11.8763	+	6.85677i	0.490186	+	0.283009i	0.724652	−	0.689115i	$-0.242001\pi$
$587$	11.8763	+	6.85677i	0.490186	+	0.283009i	−0.234465	+	0.972124i	$0.575334\pi$
$588$		0			0
$589$	−16.3485	+	37.7552i	−0.673627	+	1.55567i
$590$			13.5065i			0.556052i
$591$		0			0
$592$	5.17423	+	2.98735i	0.212660	+	0.122779i
$593$	13.4722	−	7.77817i	0.553237	−	0.319411i	−0.197190	−	0.980365i	$-0.563182\pi$
$593$	13.4722	−	7.77817i	0.553237	−	0.319411i	0.750426	+	0.660954i	$0.229848\pi$
$594$		0			0
$595$	−11.8990	−	20.6096i	−0.487811	−	0.844913i
$596$		−	14.4921i		−	0.593619i
$597$		0			0
$598$	7.10102	+	12.2993i	0.290382	+	0.502957i
$599$	−0.797959	−	1.38211i	−0.0326037	−	0.0564713i	0.849263	−	0.527970i	$-0.177047\pi$
$599$	−0.797959	−	1.38211i	−0.0326037	−	0.0564713i	−0.881867	+	0.471499i	$0.843713\pi$
$600$		0			0
$601$		−	6.75323i		−	0.275470i	−0.990469	−	0.137735i	$-0.956018\pi$
$601$		−	6.75323i		−	0.275470i	0.990469	−	0.137735i	$-0.0439822\pi$
$602$	−10.1742	−	17.6223i	−0.414671	−	0.718231i
$603$		0			0
$604$	−13.3485	+	7.70674i	−0.543142	+	0.313583i
$605$	−35.0227	−	20.2204i	−1.42388	−	0.822075i
$606$		0			0
$607$		−	40.2658i		−	1.63434i	−0.576399	−	0.817168i	$-0.695543\pi$
$607$		−	40.2658i		−	1.63434i	0.576399	−	0.817168i	$-0.304457\pi$
$608$	−0.500000	−	4.33013i	−0.0202777	−	0.175610i
$609$		0			0
$610$	1.77526	+	1.02494i	0.0718780	+	0.0414988i
$611$	6.12372	−	10.6066i	0.247739	−	0.429097i
$612$		0			0
$613$	−4.55051	+	7.88171i	−0.183793	+	0.318339i	−0.943169	−	0.332313i	$-0.892171\pi$
$613$	−4.55051	+	7.88171i	−0.183793	+	0.318339i	0.759376	+	0.650652i	$0.225504\pi$
$614$	−1.34847	+	0.778539i	−0.0544198	+	0.0314193i
$615$		0			0
$616$		−	21.7060i		−	0.874560i
$617$	−37.8990	+	21.8810i	−1.52576	+	0.880895i	−0.526222	+	0.850347i	$0.676392\pi$
$617$	−37.8990	+	21.8810i	−1.52576	+	0.880895i	−0.999533	+	0.0305482i	$0.990275\pi$
$618$		0			0
$619$	22.3939			0.900086			0.450043	−	0.893007i	$-0.351409\pi$
$619$	22.3939			0.900086			0.450043	+	0.893007i	$0.351409\pi$
$620$	13.3485			0.536087
$621$		0			0
$622$	−22.4722	−	12.9743i	−0.901053	−	0.520223i
$623$	−21.1237	−	36.5874i	−0.846304	−	1.46584i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−6.69694			−0.267663
$627$		0			0
$628$	−2.34847			−0.0937141
$629$	14.5732	−	25.2415i	0.581072	−	1.00645i
$630$		0			0
$631$	−9.72474	−	16.8438i	−0.387136	−	0.670539i	0.604927	−	0.796281i	$-0.293202\pi$
$631$	−9.72474	−	16.8438i	−0.387136	−	0.670539i	−0.992063	+	0.125742i	$0.959869\pi$
$632$	8.17423	+	4.71940i	0.325154	+	0.187728i
$633$		0			0
$634$	7.34847			0.291845
$635$	−12.0000			−0.476205
$636$		0			0
$637$	−10.6515	+	6.14966i	−0.422029	+	0.243659i
$638$			15.4135i			0.610226i
$639$		0			0
$640$	−1.22474	+	0.707107i	−0.0484123	+	0.0279508i
$641$	0.977296	−	1.69273i	0.0386009	−	0.0668587i	−0.846080	−	0.533057i	$-0.821043\pi$
$641$	0.977296	−	1.69273i	0.0386009	−	0.0668587i	0.884680	+	0.466198i	$0.154377\pi$
$642$		0			0
$643$	−1.70204	+	2.94802i	−0.0671219	+	0.116259i	−0.897633	−	0.440743i	$-0.854715\pi$
$643$	−1.70204	+	2.94802i	−0.0671219	+	0.116259i	0.830511	+	0.557002i	$0.188048\pi$
$644$	−16.8990	−	9.75663i	−0.665913	−	0.384465i
$645$		0			0
$646$	−21.1237	+	2.43916i	−0.831102	+	0.0959674i
$647$		−	16.8277i		−	0.661565i	−0.943707	−	0.330783i	$-0.892687\pi$
$647$		−	16.8277i		−	0.661565i	0.943707	−	0.330783i	$-0.107313\pi$
$648$		0			0
$649$	52.0454	+	30.0484i	2.04296	+	1.17950i
$650$	−6.52270	+	3.76588i	−0.255841	+	0.147710i
$651$		0			0
$652$	10.8485	+	18.7901i	0.424859	+	0.735877i
$653$			10.1066i			0.395501i	0.980252	+	0.197750i	$0.0633636\pi$
$653$			10.1066i			0.395501i	−0.980252	+	0.197750i	$0.936636\pi$
$654$		0			0
$655$	−5.55051	−	9.61377i	−0.216876	−	0.375641i
$656$		0			0
$657$		0			0
$658$			16.8277i			0.656012i
$659$	−23.6969	−	41.0443i	−0.923102	−	1.59886i	−0.794586	−	0.607151i	$-0.792312\pi$
$659$	−23.6969	−	41.0443i	−0.923102	−	1.59886i	−0.128516	−	0.991707i	$-0.541021\pi$
$660$		0			0
$661$	5.69694	−	3.28913i	0.221585	−	0.127932i	−0.385099	−	0.922875i	$-0.625833\pi$
$661$	5.69694	−	3.28913i	0.221585	−	0.127932i	0.606684	+	0.794943i	$0.292499\pi$
$662$	13.1969	+	7.61926i	0.512914	+	0.296131i
$663$		0			0
$664$			8.97809i			0.348418i
$665$	−12.6742	−	17.0741i	−0.491486	−	0.662105i
$666$		0			0
$667$	12.0000	+	6.92820i	0.464642	+	0.268261i
$668$	1.77526	−	3.07483i	0.0686867	−	0.118969i
$669$		0			0
$670$	−4.77526	+	8.27098i	−0.184484	+	0.319536i
$671$	7.89898	−	4.56048i	0.304937	−	0.176055i
$672$		0			0
$673$		−	19.0526i		−	0.734422i	−0.930138	−	0.367211i	$-0.880313\pi$
$673$		−	19.0526i		−	0.734422i	0.930138	−	0.367211i	$-0.119687\pi$
$674$	−31.1969	+	18.0116i	−1.20166	+	0.693779i
$675$		0			0
$676$	6.69694			0.257575
$677$	22.6515			0.870569			0.435285	−	0.900293i	$-0.356648\pi$
$677$	22.6515			0.870569			0.435285	+	0.900293i	$0.356648\pi$
$678$		0			0
$679$	5.69694	+	3.28913i	0.218628	+	0.126225i
$680$	3.44949	+	5.97469i	0.132282	+	0.229119i
$681$		0			0
$682$	29.6969	−	51.4366i	1.13715	−	1.96961i
$683$	16.0454			0.613960			0.306980	−	0.951716i	$-0.400681\pi$
$683$	16.0454			0.613960			0.306980	+	0.951716i	$0.400681\pi$
$684$		0			0
$685$	−0.898979			−0.0343482
$686$	−3.62372	+	6.27647i	−0.138354	+	0.239637i
$687$		0			0
$688$	2.94949	+	5.10867i	0.112448	+	0.194766i
$689$	−10.6515	−	6.14966i	−0.405791	−	0.234284i
$690$		0			0
$691$	28.6969			1.09168			0.545841	−	0.837888i	$-0.316210\pi$
$691$	28.6969			1.09168			0.545841	+	0.837888i	$0.316210\pi$
$692$	−12.2474			−0.465578
$693$		0			0
$694$	25.7753	−	14.8814i	0.978415	−	0.564888i
$695$			9.89949i			0.375509i
$696$		0			0
$697$		0			0
$698$	0.623724	−	1.08032i	0.0236083	−	0.0408908i
$699$		0			0
$700$	5.17423	−	8.96204i	0.195568	−	0.338733i
$701$	−13.4722	−	7.77817i	−0.508838	−	0.293778i	0.223518	−	0.974700i	$-0.428246\pi$
$701$	−13.4722	−	7.77817i	−0.508838	−	0.293778i	−0.732356	+	0.680922i	$0.761579\pi$
$702$		0			0
$703$	10.3485	−	23.8988i	0.390300	−	0.901359i
$704$			6.29253i			0.237159i
$705$		0			0
$706$	−15.1237	−	8.73169i	−0.569189	−	0.328621i
$707$	22.5959	−	13.0458i	0.849807	−	0.490636i
$708$		0			0
$709$	4.17423	+	7.22999i	0.156767	+	0.271528i	0.933701	−	0.358054i	$-0.116560\pi$
$709$	4.17423	+	7.22999i	0.156767	+	0.271528i	−0.776934	+	0.629582i	$0.783226\pi$
$710$			8.48528i			0.318447i
$711$		0			0
$712$	6.12372	+	10.6066i	0.229496	+	0.397499i
$713$	−26.6969	−	46.2405i	−0.999808	−	1.73172i
$714$		0			0
$715$		−	22.3417i		−	0.835532i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	9.79796	−	5.65685i	0.365657	−	0.211112i
$719$	−17.1464	−	9.89949i	−0.639454	−	0.369189i	0.144950	−	0.989439i	$-0.453698\pi$
$719$	−17.1464	−	9.89949i	−0.639454	−	0.369189i	−0.784404	+	0.620250i	$0.787031\pi$
$720$		0			0
$721$			37.9301i			1.41259i
$722$	−18.5000	+	4.33013i	−0.688499	+	0.161151i
$723$		0			0
$724$	19.3485	+	11.1708i	0.719080	+	0.415161i
$725$	−3.67423	+	6.36396i	−0.136458	+	0.236352i
$726$		0			0
$727$	−12.1742	+	21.0864i	−0.451517	+	0.782051i	−0.998481	−	0.0551057i	$-0.982450\pi$
$727$	−12.1742	+	21.0864i	−0.451517	+	0.782051i	0.546963	+	0.837157i	$0.315784\pi$
$728$	7.50000	−	4.33013i	0.277968	−	0.160485i
$729$		0			0
$730$			16.8277i			0.622821i
$731$	24.9217	−	14.3885i	0.921762	−	0.532179i
$732$		0			0
$733$	−1.30306			−0.0481297			−0.0240648	−	0.999710i	$-0.507661\pi$
$733$	−1.30306			−0.0481297			−0.0240648	+	0.999710i	$0.507661\pi$
$734$	0.348469			0.0128622
$735$		0			0
$736$	4.89898	+	2.82843i	0.180579	+	0.104257i
$737$	21.2474	+	36.8017i	0.782660	+	1.35561i
$738$		0			0
$739$	6.19694	−	10.7334i	0.227958	−	0.394835i	−0.729245	−	0.684253i	$-0.760128\pi$
$739$	6.19694	−	10.7334i	0.227958	−	0.394835i	0.957203	+	0.289418i	$0.0934618\pi$
$740$	−8.44949			−0.310609
$741$		0			0
$742$	16.8990			0.620381
$743$	5.69694	−	9.86739i	0.209000	−	0.361999i	−0.742400	−	0.669957i	$-0.766312\pi$
$743$	5.69694	−	9.86739i	0.209000	−	0.361999i	0.951400	+	0.307958i	$0.0996457\pi$
$744$		0			0
$745$	10.2474	+	17.7491i	0.375437	+	0.650277i
$746$	−25.3485	−	14.6349i	−0.928073	−	0.535823i
$747$		0			0
$748$	30.6969			1.12239
$749$	13.1010			0.478701
$750$		0			0
$751$	−27.2196	+	15.7153i	−0.993259	+	0.573458i	−0.906247	−	0.422749i	$-0.861065\pi$
$751$	−27.2196	+	15.7153i	−0.993259	+	0.573458i	−0.0870120	+	0.996207i	$0.527732\pi$
$752$		−	4.87832i		−	0.177894i
$753$		0			0
$754$	−5.32577	+	3.07483i	−0.193953	+	0.111979i
$755$	10.8990	−	18.8776i	0.396654	−	0.687026i
$756$		0			0
$757$	−4.82577	+	8.35847i	−0.175395	+	0.303794i	−0.940298	−	0.340352i	$-0.889454\pi$
$757$	−4.82577	+	8.35847i	−0.175395	+	0.303794i	0.764903	+	0.644146i	$0.222787\pi$
$758$	16.5000	+	9.52628i	0.599307	+	0.346010i
$759$		0			0
$760$	3.67423	+	4.94975i	0.133278	+	0.179546i
$761$			3.25702i			0.118067i	0.998256	+	0.0590335i	$0.0188019\pi$
$761$			3.25702i			0.118067i	−0.998256	+	0.0590335i	$0.981198\pi$
$762$		0			0
$763$	−50.6969	−	29.2699i	−1.83535	−	1.05964i
$764$	10.7753	−	6.22110i	0.389835	−	0.225071i
$765$		0			0
$766$	−0.550510	−	0.953512i	−0.0198907	−	0.0344518i
$767$			23.9774i			0.865774i
$768$		0			0
$769$	−18.2980	−	31.6930i	−0.659841	−	1.14288i	−0.980656	−	0.195737i	$-0.937290\pi$
$769$	−18.2980	−	31.6930i	−0.659841	−	1.14288i	0.320815	−	0.947142i	$-0.396043\pi$
$770$	15.3485	+	26.5843i	0.553120	+	0.958033i
$771$		0			0
$772$		−	0.174973i		−	0.00629740i
$773$	−22.4722	−	38.9230i	−0.808269	−	1.39996i	−0.914062	−	0.405574i	$-0.867072\pi$
$773$	−22.4722	−	38.9230i	−0.808269	−	1.39996i	0.105793	−	0.994388i	$-0.466262\pi$
$774$		0			0
$775$	24.5227	−	14.1582i	0.880882	−	0.508577i
$776$	−1.65153	−	0.953512i	−0.0592865	−	0.0342291i
$777$		0			0
$778$			15.1278i			0.542356i
$779$		0			0
$780$		0			0
$781$	32.6969	+	18.8776i	1.16999	+	0.675493i
$782$	13.7980	−	23.8988i	0.493414	−	0.854618i
$783$		0			0
$784$	−2.44949	+	4.24264i	−0.0874818	+	0.151523i
$785$	2.87628	−	1.66062i	0.102659	−	0.0592700i
$786$		0			0
$787$		−	7.10318i		−	0.253201i	−0.991954	−	0.126600i	$-0.959593\pi$
$787$		−	7.10318i		−	0.253201i	0.991954	−	0.126600i	$-0.0404066\pi$
$788$	0.426786	−	0.246405i	0.0152036	−	0.00877781i
$789$		0			0
$790$	−13.3485			−0.474917
$791$	−59.1464			−2.10300
$792$		0			0
$793$	3.15153	+	1.81954i	0.111914	+	0.0646137i
$794$	−18.1742	−	31.4787i	−0.644979	−	1.11714i
$795$		0			0
$796$	3.62372	−	6.27647i	0.128440	−	0.222464i
$797$	−50.0908			−1.77431			−0.887154	−	0.461474i	$-0.847321\pi$
$797$	−50.0908			−1.77431			−0.887154	+	0.461474i	$0.847321\pi$
$798$		0			0
$799$	−23.7980			−0.841911
$800$	−1.50000	+	2.59808i	−0.0530330	+	0.0918559i
$801$		0			0
$802$	−12.1237	−	20.9989i	−0.428104	−	0.741497i
$803$	64.8434	+	37.4373i	2.28827	+	1.32113i
$804$		0			0
$805$	27.5959			0.972628
$806$	23.6969			0.834689
$807$		0			0
$808$	−6.55051	+	3.78194i	−0.230446	+	0.133048i
$809$			25.9487i			0.912306i	0.889901	+	0.456153i	$0.150773\pi$
$809$			25.9487i			0.912306i	−0.889901	+	0.456153i	$0.849227\pi$
$810$		0			0
$811$	−11.6969	+	6.75323i	−0.410735	+	0.237138i	−0.691106	−	0.722754i	$-0.742876\pi$
$811$	−11.6969	+	6.75323i	−0.410735	+	0.237138i	0.280370	+	0.959892i	$0.409543\pi$
$812$	4.22474	−	7.31747i	0.148259	−	0.256793i
$813$		0			0
$814$	−18.7980	+	32.5590i	−0.658868	+	1.14119i
$815$	−26.5732	−	15.3421i	−0.930819	−	0.537409i
$816$		0			0
$817$	20.6464	−	15.3260i	0.722327	−	0.536189i
$818$			21.9917i			0.768923i
$819$		0			0
$820$		0			0
$821$	22.1691	−	12.7994i	0.773708	−	0.446701i	−0.0604877	−	0.998169i	$-0.519266\pi$
$821$	22.1691	−	12.7994i	0.773708	−	0.446701i	0.834196	+	0.551468i	$0.185932\pi$
$822$		0			0
$823$	−2.65153	−	4.59259i	−0.0924266	−	0.160087i	0.816105	−	0.577903i	$-0.196129\pi$
$823$	−2.65153	−	4.59259i	−0.0924266	−	0.160087i	−0.908532	+	0.417816i	$0.862796\pi$
$824$		−	10.9959i		−	0.383059i
$825$		0			0
$826$	−16.4722	−	28.5307i	−0.573141	−	0.992709i
$827$	17.8207	+	30.8663i	0.619685	+	1.07333i	0.989543	+	0.144238i	$0.0460730\pi$
$827$	17.8207	+	30.8663i	0.619685	+	1.07333i	−0.369858	+	0.929088i	$0.620594\pi$
$828$		0			0
$829$		−	14.4600i		−	0.502216i	−0.967959	−	0.251108i	$-0.919205\pi$
$829$		−	14.4600i		−	0.502216i	0.967959	−	0.251108i	$-0.0807949\pi$
$830$	−6.34847	−	10.9959i	−0.220359	−	0.381672i
$831$		0			0
$832$	−2.17423	+	1.25529i	−0.0753780	+	0.0435195i
$833$	20.6969	+	11.9494i	0.717106	+	0.414022i
$834$		0			0
$835$			5.02118i			0.173765i
$836$	27.2474	−	3.14626i	0.942373	−	0.108816i
$837$		0			0
$838$	21.2474	+	12.2672i	0.733981	+	0.423764i
$839$	17.0227	−	29.4842i	0.587689	−	1.01791i	−0.406845	−	0.913497i	$-0.633371\pi$
$839$	17.0227	−	29.4842i	0.587689	−	1.01791i	0.994534	−	0.104410i	$-0.0332955\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$	13.3485	−	7.70674i	0.460019	−	0.265592i
$843$		0			0
$844$		−	20.6096i		−	0.709413i
$845$	−8.20204	+	4.73545i	−0.282159	+	0.162904i
$846$		0			0
$847$	98.6413			3.38936
$848$	−4.89898			−0.168232
$849$		0			0
$850$	12.6742	+	7.31747i	0.434723	+	0.250987i
$851$	16.8990	+	29.2699i	0.579290	+	1.00336i
$852$		0			0
$853$	22.1742	−	38.4069i	0.759231	−	1.31503i	−0.184012	−	0.982924i	$-0.558908\pi$
$853$	22.1742	−	38.4069i	0.759231	−	1.31503i	0.943243	−	0.332103i	$-0.107758\pi$
$854$	−5.00000			−0.171096
$855$		0			0
$856$	−3.79796			−0.129812
$857$	20.5732	−	35.6339i	0.702768	−	1.21723i	−0.264724	−	0.964324i	$-0.585281\pi$
$857$	20.5732	−	35.6339i	0.702768	−	1.21723i	0.967491	−	0.252905i	$-0.0813860\pi$
$858$		0			0
$859$	2.94949	+	5.10867i	0.100635	+	0.174305i	0.911947	−	0.410309i	$-0.134579\pi$
$859$	2.94949	+	5.10867i	0.100635	+	0.174305i	−0.811311	+	0.584614i	$0.801246\pi$
$860$	−7.22474	−	4.17121i	−0.246362	−	0.142237i
$861$		0			0
$862$	−28.0454			−0.955230
$863$	22.6515			0.771067			0.385534	−	0.922694i	$-0.374017\pi$
$863$	22.6515			0.771067			0.385534	+	0.922694i	$0.374017\pi$
$864$		0			0
$865$	15.0000	−	8.66025i	0.510015	−	0.294457i
$866$		−	4.84621i		−	0.164681i
$867$		0			0
$868$	−28.1969	+	16.2795i	−0.957066	+	0.552563i
$869$	−29.6969	+	51.4366i	−1.00740	+	1.74487i
$870$		0			0
$871$	−8.47730	+	14.6831i	−0.287242	+	0.497518i
$872$	14.6969	+	8.48528i	0.497701	+	0.287348i
$873$		0			0
$874$	9.79796	−	22.6274i	0.331421	−	0.765384i
$875$			39.0265i			1.31934i
$876$		0			0
$877$	2.47730	+	1.43027i	0.0836523	+	0.0482967i	0.541243	−	0.840866i	$-0.317954\pi$
$877$	2.47730	+	1.43027i	0.0836523	+	0.0482967i	−0.457590	+	0.889163i	$0.651287\pi$
$878$	−9.52270	+	5.49794i	−0.321376	+	0.185546i
$879$		0			0
$880$	−4.44949	−	7.70674i	−0.149992	−	0.259794i
$881$		−	4.87832i		−	0.164355i	−0.996618	−	0.0821773i	$-0.973813\pi$
$881$		−	4.87832i		−	0.164355i	0.996618	−	0.0821773i	$-0.0261874\pi$
$882$		0			0
$883$	−1.94949	−	3.37662i	−0.0656056	−	0.113632i	0.831357	−	0.555739i	$-0.187565\pi$
$883$	−1.94949	−	3.37662i	−0.0656056	−	0.113632i	−0.896962	+	0.442107i	$0.854231\pi$
$884$	6.12372	+	10.6066i	0.205963	+	0.356739i
$885$		0			0
$886$		−	32.5911i		−	1.09492i
$887$	−18.6742	−	32.3447i	−0.627019	−	1.08603i	−0.988147	−	0.153513i	$-0.950941\pi$
$887$	−18.6742	−	32.3447i	−0.627019	−	1.08603i	0.361127	−	0.932517i	$-0.382392\pi$
$888$		0			0
$889$	25.3485	−	14.6349i	0.850160	−	0.490840i
$890$	−15.0000	−	8.66025i	−0.502801	−	0.290292i
$891$		0			0
$892$		−	5.97469i		−	0.200047i
$893$	−21.1237	+	2.43916i	−0.706878	+	0.0816233i
$894$		0			0
$895$	−14.6969	−	8.48528i	−0.491264	−	0.283632i
$896$	1.72474	−	2.98735i	0.0576197	−	0.0998002i
$897$		0			0
$898$	−3.12372	+	5.41045i	−0.104240	+	0.180549i
$899$	20.0227	−	11.5601i	0.667795	−	0.385551i
$900$		0			0
$901$			23.8988i			0.796183i
$902$		0			0
$903$		0			0
$904$	17.1464			0.570282
$905$	−31.5959			−1.05028
$906$		0			0
$907$	6.30306	+	3.63907i	0.209290	+	0.120833i	0.600981	−	0.799263i	$-0.294777\pi$
$907$	6.30306	+	3.63907i	0.209290	+	0.120833i	−0.391692	+	0.920097i	$0.628110\pi$
$908$	−5.57321	−	9.65309i	−0.184954	−	0.320349i
$909$		0			0
$910$	−6.12372	+	10.6066i	−0.202999	+	0.351605i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−56.4949			−1.86971
$914$	4.84847	−	8.39780i	0.160373	−	0.277774i
$915$		0			0
$916$	−2.62372	−	4.54442i	−0.0866903	−	0.150152i
$917$	23.4495	+	13.5386i	0.774370	+	0.447083i
$918$		0			0
$919$	−35.0454			−1.15604			−0.578021	−	0.816022i	$-0.696175\pi$
$919$	−35.0454			−1.15604			−0.578021	+	0.816022i	$0.696175\pi$
$920$	−8.00000			−0.263752
$921$		0			0
$922$	3.12372	−	1.80348i	0.102874	−	0.0593946i
$923$			15.0635i			0.495822i
$924$		0			0
$925$	−15.5227	+	8.96204i	−0.510383	+	0.294670i
$926$	−2.92679	+	5.06934i	−0.0961802	+	0.166589i
$927$		0			0
$928$	−1.22474	+	2.12132i	−0.0402042	+	0.0696358i
$929$	−18.4268	−	10.6387i	−0.604563	−	0.349045i	0.166271	−	0.986080i	$-0.446827\pi$
$929$	−18.4268	−	10.6387i	−0.604563	−	0.349045i	−0.770835	+	0.637035i	$0.780161\pi$
$930$		0			0
$931$	19.5959	+	8.48528i	0.642230	+	0.278094i
$932$		−	10.6780i		−	0.349771i
$933$		0			0
$934$	6.24745	+	3.60697i	0.204423	+	0.118024i
$935$	−37.5959	+	21.7060i	−1.22952	+	0.709863i
$936$		0			0
$937$	21.1969	+	36.7142i	0.692474	+	1.19940i	0.971025	+	0.238978i	$0.0768125\pi$
$937$	21.1969	+	36.7142i	0.692474	+	1.19940i	−0.278551	+	0.960421i	$0.589854\pi$
$938$		−	23.2952i		−	0.760615i
$939$		0			0
$940$	3.44949	+	5.97469i	0.112510	+	0.194873i
$941$	15.5505	+	26.9343i	0.506932	+	0.878032i	0.999968	+	0.00802314i	$0.00255387\pi$
$941$	15.5505	+	26.9343i	0.506932	+	0.878032i	−0.493036	+	0.870009i	$0.664113\pi$
$942$		0			0
$943$		0			0
$944$	4.77526	+	8.27098i	0.155421	+	0.269198i
$945$		0			0
$946$	−32.1464	+	18.5597i	−1.04517	+	0.603429i
$947$	−15.4949	−	8.94598i	−0.503517	−	0.290705i	0.226648	−	0.973977i	$-0.427223\pi$
$947$	−15.4949	−	8.94598i	−0.503517	−	0.290705i	−0.730165	+	0.683271i	$0.760557\pi$
$948$		0			0
$949$			29.8735i			0.969733i
$950$	12.0000	+	5.19615i	0.389331	+	0.168585i
$951$		0			0
$952$	−14.5732	−	8.41385i	−0.472321	−	0.272694i
$953$	−5.44949	+	9.43879i	−0.176526	+	0.305752i	−0.940688	−	0.339272i	$-0.889819\pi$
$953$	−5.44949	+	9.43879i	−0.176526	+	0.305752i	0.764162	+	0.645024i	$0.223153\pi$
$954$		0			0
$955$	−8.79796	+	15.2385i	−0.284695	+	0.493107i
$956$	7.47219	−	4.31407i	0.241668	−	0.139527i
$957$		0			0
$958$			30.1913i			0.975436i
$959$	1.89898	−	1.09638i	0.0613212	−	0.0354038i
$960$		0			0
$961$	−58.0908			−1.87390
$962$	−15.0000			−0.483619
$963$		0			0
$964$	−26.8485	−	15.5010i	−0.864731	−	0.499253i
$965$	0.123724	+	0.214297i	0.00398283	+	0.00689846i
$966$		0			0
$967$	1.17423	−	2.03383i	0.0377608	−	0.0654037i	−0.846527	−	0.532345i	$-0.821311\pi$
$967$	1.17423	−	2.03383i	0.0377608	−	0.0654037i	0.884288	+	0.466942i	$0.154644\pi$
$968$	−28.5959			−0.919108
$969$		0			0
$970$	2.69694			0.0865935
$971$	−26.8207	+	46.4548i	−0.860716	+	1.49080i	0.0105228	+	0.999945i	$0.496650\pi$
$971$	−26.8207	+	46.4548i	−0.860716	+	1.49080i	−0.871239	+	0.490859i	$0.836683\pi$
$972$		0			0
$973$	−12.0732	−	20.9114i	−0.387049	−	0.670389i
$974$	19.6515	+	11.3458i	0.629676	+	0.363543i
$975$		0			0
$976$	1.44949			0.0463970
$977$	24.2474			0.775745			0.387872	−	0.921713i	$-0.373210\pi$
$977$	24.2474			0.775745			0.387872	+	0.921713i	$0.373210\pi$
$978$		0			0
$979$	−66.7423	+	38.5337i	−2.13309	+	1.23154i
$980$		−	6.92820i		−	0.221313i
$981$		0			0
$982$	8.14643	−	4.70334i	0.259963	−	0.150090i
$983$	15.2474	−	26.4094i	0.486318	−	0.842328i	−0.513558	−	0.858055i	$-0.671673\pi$
$983$	15.2474	−	26.4094i	0.486318	−	0.842328i	0.999876	+	0.0157271i	$0.00500630\pi$
$984$		0			0
$985$	−0.348469	+	0.603566i	−0.0111032	+	0.0192312i
$986$	10.3485	+	5.97469i	0.329562	+	0.190273i
$987$		0			0
$988$	6.52270	+	8.78706i	0.207515	+	0.279554i
$989$			33.3697i			1.06109i
$990$		0			0
$991$	16.1288	+	9.31198i	0.512349	+	0.295805i	0.733799	−	0.679367i	$-0.237746\pi$
$991$	16.1288	+	9.31198i	0.512349	+	0.295805i	−0.221450	+	0.975172i	$0.571079\pi$
$992$	8.17423	−	4.71940i	0.259532	−	0.149841i
$993$		0			0
$994$	−10.3485	−	17.9241i	−0.328234	−	0.568517i
$995$			10.2494i			0.324929i
$996$		0			0
$997$	−1.52270	−	2.63740i	−0.0482245	−	0.0835273i	0.840906	−	0.541182i	$-0.182023\pi$
$997$	−1.52270	−	2.63740i	−0.0482245	−	0.0835273i	−0.889130	+	0.457655i	$0.848690\pi$
$998$	−2.74745	−	4.75872i	−0.0869690	−	0.150635i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.s.a.179.2	yes	4
3.2	odd	2		342.2.s.b.179.1	yes	4
4.3	odd	2		2736.2.dc.b.1889.2		4
12.11	even	2		2736.2.dc.a.1889.1		4
19.12	odd	6		342.2.s.b.107.1	yes	4
57.50	even	6	inner	342.2.s.a.107.2	✓	4
76.31	even	6		2736.2.dc.a.449.1		4
228.107	odd	6		2736.2.dc.b.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.s.a.107.2	✓	4	57.50	even	6	inner
342.2.s.a.179.2	yes	4	1.1	even	1	trivial
342.2.s.b.107.1	yes	4	19.12	odd	6
342.2.s.b.179.1	yes	4	3.2	odd	2
2736.2.dc.a.449.1		4	76.31	even	6
2736.2.dc.a.1889.1		4	12.11	even	2
2736.2.dc.b.449.2		4	228.107	odd	6
2736.2.dc.b.1889.2		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} -3.44949 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} -3.44949 q^{7} +1.00000 q^{8} +(-1.22474 + 0.707107i) q^{10} +6.29253i q^{11} +(-2.17423 + 1.25529i) q^{13} +(1.72474 - 2.98735i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.22474 + 2.43916i) q^{17} +(4.00000 + 1.73205i) q^{19} -1.41421i q^{20} +(-5.44949 - 3.14626i) q^{22} +(-4.89898 + 2.82843i) q^{23} +(-1.50000 - 2.59808i) q^{25} -2.51059i q^{26} +(1.72474 + 2.98735i) q^{28} +(-1.22474 - 2.12132i) q^{29} +9.43879i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.22474 + 2.43916i) q^{34} +(-4.22474 - 2.43916i) q^{35} -5.97469i q^{37} +(-3.50000 + 2.59808i) q^{38} +(1.22474 + 0.707107i) q^{40} +(2.94949 - 5.10867i) q^{43} +(5.44949 - 3.14626i) q^{44} -5.65685i q^{46} +(-4.22474 + 2.43916i) q^{47} +4.89898 q^{49} +3.00000 q^{50} +(2.17423 + 1.25529i) q^{52} +(2.44949 + 4.24264i) q^{53} +(-4.44949 + 7.70674i) q^{55} -3.44949 q^{56} +2.44949 q^{58} +(4.77526 - 8.27098i) q^{59} +(-0.724745 - 1.25529i) q^{61} +(-8.17423 - 4.71940i) q^{62} +1.00000 q^{64} -3.55051 q^{65} +(5.84847 - 3.37662i) q^{67} -4.87832i q^{68} +(4.22474 - 2.43916i) q^{70} +(3.00000 - 5.19615i) q^{71} +(5.94949 - 10.3048i) q^{73} +(5.17423 + 2.98735i) q^{74} +(-0.500000 - 4.33013i) q^{76} -21.7060i q^{77} +(8.17423 + 4.71940i) q^{79} +(-1.22474 + 0.707107i) q^{80} +8.97809i q^{83} +(3.44949 + 5.97469i) q^{85} +(2.94949 + 5.10867i) q^{86} +6.29253i q^{88} +(6.12372 + 10.6066i) q^{89} +(7.50000 - 4.33013i) q^{91} +(4.89898 + 2.82843i) q^{92} -4.87832i q^{94} +(3.67423 + 4.94975i) q^{95} +(-1.65153 - 0.953512i) q^{97} +(-2.44949 + 4.24264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 12 q^{17} + 16 q^{19} - 12 q^{22} - 6 q^{25} + 2 q^{28} - 2 q^{32} - 12 q^{34} - 12 q^{35} - 14 q^{38} + 2 q^{43} + 12 q^{44} - 12 q^{47} + 12 q^{50} - 6 q^{52} - 8 q^{55} - 4 q^{56} + 24 q^{59} + 2 q^{61} - 18 q^{62} + 4 q^{64} - 24 q^{65} - 6 q^{67} + 12 q^{70} + 12 q^{71} + 14 q^{73} + 6 q^{74} - 2 q^{76} + 18 q^{79} + 4 q^{85} + 2 q^{86} + 30 q^{91} - 36 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 12 * q^17 + 16 * q^19 - 12 * q^22 - 6 * q^25 + 2 * q^28 - 2 * q^32 - 12 * q^34 - 12 * q^35 - 14 * q^38 + 2 * q^43 + 12 * q^44 - 12 * q^47 + 12 * q^50 - 6 * q^52 - 8 * q^55 - 4 * q^56 + 24 * q^59 + 2 * q^61 - 18 * q^62 + 4 * q^64 - 24 * q^65 - 6 * q^67 + 12 * q^70 + 12 * q^71 + 14 * q^73 + 6 * q^74 - 2 * q^76 + 18 * q^79 + 4 * q^85 + 2 * q^86 + 30 * q^91 - 36 * q^97

Introduction

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