LMFDB - Embedded newform 1520.2.bq.q.31.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1520,2,Mod(31,1520)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1520.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1520, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-6,0,0,0,-4,0,0,0,18,0,0,0,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$12.1372611072$
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} + 8x^{10} + 53x^{8} + 86x^{6} + 113x^{4} + 11x^{2} + 1 $ x^12 + 8x^10 + 53x^8 + 86x^6 + 113x^4 + 11*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Root			$-0.156347 - 0.270800i$ of defining polynomial
Character	$\chi$	$=$	1520.31
Dual form			1520.2.bq.q.1471.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59901 + 2.76957i) q^{3} +(-0.500000 - 0.866025i) q^{5} -2.37033i q^{7} +(-3.61367 + 6.25906i) q^{9} +0.284720i q^{11} +(2.92290 + 1.68754i) q^{13} +(1.59901 - 2.76957i) q^{15} +(0.788551 + 1.36581i) q^{17} +(0.207178 + 4.35397i) q^{19} +(6.56478 - 3.79018i) q^{21} +(2.52180 + 1.45596i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.5191 q^{27} +(5.85333 + 3.37942i) q^{29} -5.59020 q^{31} +(-0.788551 + 0.455270i) q^{33} +(-2.05276 + 1.18516i) q^{35} +10.0449i q^{37} +10.7936i q^{39} +(-2.85333 + 1.64737i) q^{41} +(-6.82569 + 3.94081i) q^{43} +7.22734 q^{45} +(-5.66514 - 3.27077i) q^{47} +1.38155 q^{49} +(-2.52180 + 4.36789i) q^{51} +(-0.788551 - 0.455270i) q^{53} +(0.246575 - 0.142360i) q^{55} +(-11.7273 + 7.53584i) q^{57} +(4.65597 + 8.06438i) q^{59} +(7.30445 - 12.6517i) q^{61} +(14.8360 + 8.56559i) q^{63} -3.37507i q^{65} +(2.57264 - 4.45593i) q^{67} +9.31241i q^{69} +(6.09864 + 10.5631i) q^{71} +(-4.51589 - 7.82176i) q^{73} -3.19802 q^{75} +0.674879 q^{77} +(-3.01757 - 5.22658i) q^{79} +(-10.7762 - 18.6650i) q^{81} -7.16394i q^{83} +(0.788551 - 1.36581i) q^{85} +21.6149i q^{87} +(-3.00000 - 1.73205i) q^{89} +(4.00001 - 6.92822i) q^{91} +(-8.93879 - 15.4824i) q^{93} +(3.66706 - 2.35641i) q^{95} +(8.77623 - 5.06696i) q^{97} +(-1.78208 - 1.02888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} - 4 q^{9} + 18 q^{13} + 18 q^{17} + 24 q^{21} - 6 q^{25} + 24 q^{29} - 18 q^{33} + 12 q^{41} + 8 q^{45} - 28 q^{49} - 18 q^{53} - 62 q^{57} + 26 q^{61} + 16 q^{73} + 56 q^{77} - 66 q^{81}+ \cdots + 42 q^{97}+O(q^{100}) $ 12 * q - 6 * q^5 - 4 * q^9 + 18 * q^13 + 18 * q^17 + 24 * q^21 - 6 * q^25 + 24 * q^29 - 18 * q^33 + 12 * q^41 + 8 * q^45 - 28 * q^49 - 18 * q^53 - 62 * q^57 + 26 * q^61 + 16 * q^73 + 56 * q^77 - 66 * q^81 + 18 * q^85 - 36 * q^89 - 20 * q^93 + 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	1.59901	+	2.76957i	0.923189	+	1.59901i	0.794448	+	0.607333i	$0.207761\pi$
$3$	1.59901	+	2.76957i	0.923189	+	1.59901i	0.128742	+	0.991678i	$0.458906\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$		−	2.37033i		−	0.895900i	−0.894059	−	0.447950i	$-0.852154\pi$
$7$		−	2.37033i		−	0.895900i	0.894059	−	0.447950i	$-0.147846\pi$
$8$		0			0
$9$	−3.61367	+	6.25906i	−1.20456	+	2.08635i
$10$		0			0
$11$			0.284720i			0.0858463i	0.999078	+	0.0429231i	$0.0136671\pi$
$11$			0.284720i			0.0858463i	−0.999078	+	0.0429231i	$0.986333\pi$
$12$		0			0
$13$	2.92290	+	1.68754i	0.810666	+	0.468038i	0.847187	−	0.531295i	$-0.178294\pi$
$13$	2.92290	+	1.68754i	0.810666	+	0.468038i	−0.0365211	+	0.999333i	$0.511628\pi$
$14$		0			0
$15$	1.59901	−	2.76957i	0.412863	−	0.715099i
$16$		0			0
$17$	0.788551	+	1.36581i	0.191252	+	0.331258i	0.945665	−	0.325142i	$-0.105412\pi$
$17$	0.788551	+	1.36581i	0.191252	+	0.331258i	−0.754414	+	0.656399i	$0.772079\pi$
$18$		0			0
$19$	0.207178	+	4.35397i	0.0475299	+	0.998870i
$19$	0.207178	+	4.35397i	0.0475299	+	0.998870i
$20$		0			0
$21$	6.56478	−	3.79018i	1.43255	−	0.827085i
$22$		0			0
$23$	2.52180	+	1.45596i	0.525832	+	0.303589i	0.739318	−	0.673357i	$-0.235148\pi$
$23$	2.52180	+	1.45596i	0.525832	+	0.303589i	−0.213485	+	0.976946i	$0.568482\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−13.5191			−2.60176
$28$		0			0
$29$	5.85333	+	3.37942i	1.08694	+	0.627543i	0.932759	−	0.360500i	$-0.117394\pi$
$29$	5.85333	+	3.37942i	1.08694	+	0.627543i	0.154178	+	0.988043i	$0.450727\pi$
$30$		0			0
$31$	−5.59020			−1.00403			−0.502015	−	0.864859i	$-0.667408\pi$
$31$	−5.59020			−1.00403			−0.502015	+	0.864859i	$0.667408\pi$
$32$		0			0
$33$	−0.788551	+	0.455270i	−0.137269	+	0.0792524i
$34$		0			0
$35$	−2.05276	+	1.18516i	−0.346980	+	0.200329i
$36$		0			0
$37$			10.0449i			1.65137i	0.564132	+	0.825685i	$0.309211\pi$
$37$			10.0449i			1.65137i	−0.564132	+	0.825685i	$0.690789\pi$
$38$		0			0
$39$			10.7936i			1.72835i
$40$		0			0
$41$	−2.85333	+	1.64737i	−0.445616	+	0.257276i	−0.705977	−	0.708235i	$-0.749492\pi$
$41$	−2.85333	+	1.64737i	−0.445616	+	0.257276i	0.260361	+	0.965511i	$0.416158\pi$
$42$		0			0
$43$	−6.82569	+	3.94081i	−1.04091	+	0.600968i	−0.920090	−	0.391707i	$-0.871885\pi$
$43$	−6.82569	+	3.94081i	−1.04091	+	0.600968i	−0.120817	+	0.992675i	$0.538552\pi$
$44$		0			0
$45$	7.22734			1.07739
$46$		0			0
$47$	−5.66514	−	3.27077i	−0.826346	−	0.477091i	0.0262540	−	0.999655i	$-0.491642\pi$
$47$	−5.66514	−	3.27077i	−0.826346	−	0.477091i	−0.852600	+	0.522564i	$0.824975\pi$
$48$		0			0
$49$	1.38155			0.197364
$50$		0			0
$51$	−2.52180	+	4.36789i	−0.353123	+	0.611627i
$52$		0			0
$53$	−0.788551	−	0.455270i	−0.108316	−	0.0625362i	0.444863	−	0.895598i	$-0.353252\pi$
$53$	−0.788551	−	0.455270i	−0.108316	−	0.0625362i	−0.553179	+	0.833062i	$0.686586\pi$
$54$		0			0
$55$	0.246575	−	0.142360i	0.0332481	−	0.0191958i
$56$		0			0
$57$	−11.7273	+	7.53584i	−1.55332	+	0.998147i
$58$		0			0
$59$	4.65597	+	8.06438i	0.606156	+	1.04989i	0.991868	+	0.127274i	$0.0406227\pi$
$59$	4.65597	+	8.06438i	0.606156	+	1.04989i	−0.385712	+	0.922619i	$0.626044\pi$
$60$		0			0
$61$	7.30445	−	12.6517i	0.935238	−	1.61988i	0.161030	−	0.986949i	$-0.448518\pi$
$61$	7.30445	−	12.6517i	0.935238	−	1.61988i	0.774208	−	0.632931i	$-0.218148\pi$
$62$		0			0
$63$	14.8360	+	8.56559i	1.86916	+	1.07916i
$64$		0			0
$65$		−	3.37507i		−	0.418626i
$66$		0			0
$67$	2.57264	−	4.45593i	0.314297	−	0.544379i	−0.664990	−	0.746852i	$-0.731564\pi$
$67$	2.57264	−	4.45593i	0.314297	−	0.544379i	0.979288	+	0.202473i	$0.0648978\pi$
$68$		0			0
$69$			9.31241i			1.12108i
$70$		0			0
$71$	6.09864	+	10.5631i	0.723775	+	1.25362i	0.959476	+	0.281790i	$0.0909280\pi$
$71$	6.09864	+	10.5631i	0.723775	+	1.25362i	−0.235701	+	0.971826i	$0.575739\pi$
$72$		0			0
$73$	−4.51589	−	7.82176i	−0.528545	−	0.915468i	−0.999446	−	0.0332813i	$-0.989404\pi$
$73$	−4.51589	−	7.82176i	−0.528545	−	0.915468i	0.470901	−	0.882186i	$-0.343929\pi$
$74$		0			0
$75$	−3.19802			−0.369276
$76$		0			0
$77$	0.674879			0.0769096
$78$		0			0
$79$	−3.01757	−	5.22658i	−0.339503	−	0.588036i	0.644837	−	0.764320i	$-0.276925\pi$
$79$	−3.01757	−	5.22658i	−0.339503	−	0.588036i	−0.984339	+	0.176285i	$0.943592\pi$
$80$		0			0
$81$	−10.7762	−	18.6650i	−1.19736	−	2.07389i
$82$		0			0
$83$		−	7.16394i		−	0.786344i	−0.919465	−	0.393172i	$-0.871378\pi$
$83$		−	7.16394i		−	0.786344i	0.919465	−	0.393172i	$-0.128622\pi$
$84$		0			0
$85$	0.788551	−	1.36581i	0.0855304	−	0.148143i
$86$		0			0
$87$			21.6149i			2.31737i
$88$		0			0
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	0.332501	−	0.943103i	$-0.392107\pi$
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	−0.650500	+	0.759506i	$0.725441\pi$
$90$		0			0
$91$	4.00001	−	6.92822i	0.419315	−	0.726275i
$92$		0			0
$93$	−8.93879	−	15.4824i	−0.926910	−	1.60545i
$94$		0			0
$95$	3.66706	−	2.35641i	0.376233	−	0.241762i
$96$		0			0
$97$	8.77623	−	5.06696i	0.891091	−	0.514472i	0.0167920	−	0.999859i	$-0.494655\pi$
$97$	8.77623	−	5.06696i	0.891091	−	0.514472i	0.874299	+	0.485387i	$0.161321\pi$
$98$		0			0
$99$	−1.78208	−	1.02888i	−0.179106	−	0.103407i
$100$		0			0
$101$	4.53657	−	7.85757i	0.451406	−	0.781857i	−0.547068	−	0.837088i	$-0.684256\pi$
$101$	4.53657	−	7.85757i	0.451406	−	0.781857i	0.998474	+	0.0552308i	$0.0175895\pi$
$102$		0			0
$103$	5.30808			0.523021			0.261510	−	0.965201i	$-0.415779\pi$
$103$	5.30808			0.523021			0.261510	+	0.965201i	$0.415779\pi$
$104$		0			0
$105$	−6.56478	−	3.79018i	−0.640657	−	0.369884i
$106$		0			0
$107$	7.48401			0.723506			0.361753	−	0.932274i	$-0.382178\pi$
$107$	7.48401			0.723506			0.361753	+	0.932274i	$0.382178\pi$
$108$		0			0
$109$	−2.21899	+	1.28113i	−0.212540	+	0.122710i	−0.602492	−	0.798125i	$-0.705825\pi$
$109$	−2.21899	+	1.28113i	−0.212540	+	0.122710i	0.389951	+	0.920836i	$0.372492\pi$
$110$		0			0
$111$	−27.8200	+	16.0619i	−2.64056	+	1.52453i
$112$		0			0
$113$			20.0095i			1.88233i	0.337946	+	0.941166i	$0.390268\pi$
$113$			20.0095i			1.88233i	−0.337946	+	0.941166i	$0.609732\pi$
$114$		0			0
$115$		−	2.91193i		−	0.271539i
$116$		0			0
$117$	−21.1248	+	12.1964i	−1.95299	+	1.12756i
$118$		0			0
$119$	3.23742	−	1.86912i	0.296774	−	0.171342i
$120$		0			0
$121$	10.9189			0.992630
$122$		0			0
$123$	−9.12503	−	5.26834i	−0.822776	−	0.475030i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	5.90289	−	10.2241i	0.523797	−	0.907243i	−0.475819	−	0.879543i	$-0.657848\pi$
$127$	5.90289	−	10.2241i	0.523797	−	0.907243i	0.999616	−	0.0277001i	$-0.00881836\pi$
$128$		0			0
$129$	−21.8287	−	12.6028i	−1.92191	−	1.10961i
$130$		0			0
$131$	5.66514	−	3.27077i	0.494966	−	0.285769i	−0.231666	−	0.972795i	$-0.574418\pi$
$131$	5.66514	−	3.27077i	0.494966	−	0.285769i	0.726632	+	0.687027i	$0.241084\pi$
$132$		0			0
$133$	10.3203	−	0.491080i	0.894887	−	0.0425820i
$134$		0			0
$135$	6.75957	+	11.7079i	0.581771	+	1.00766i
$136$		0			0
$137$	−0.935217	+	1.61984i	−0.0799010	+	0.138393i	−0.903207	−	0.429205i	$-0.858794\pi$
$137$	−0.935217	+	1.61984i	−0.0799010	+	0.138393i	0.823306	+	0.567598i	$0.192127\pi$
$138$		0			0
$139$	−15.9507	−	9.20915i	−1.35292	−	0.781110i	−0.364264	−	0.931296i	$-0.618679\pi$
$139$	−15.9507	−	9.20915i	−1.35292	−	0.781110i	−0.988658	+	0.150186i	$0.952013\pi$
$140$		0			0
$141$		−	20.9200i		−	1.76178i
$142$		0			0
$143$	−0.480475	+	0.832207i	−0.0401793	+	0.0695927i
$144$		0			0
$145$		−	6.75885i		−	0.561292i
$146$		0			0
$147$	2.20911	+	3.82629i	0.182204	+	0.315587i
$148$		0			0
$149$	−4.61367	−	7.99111i	−0.377967	−	0.654658i	0.612800	−	0.790238i	$-0.290043\pi$
$149$	−4.61367	−	7.99111i	−0.377967	−	0.654658i	−0.990766	+	0.135581i	$0.956710\pi$
$150$		0			0
$151$	−20.0956			−1.63536			−0.817680	−	0.575673i	$-0.804740\pi$
$151$	−20.0956			−1.63536			−0.817680	+	0.575673i	$0.804740\pi$
$152$		0			0
$153$	−11.3983			−0.921495
$154$		0			0
$155$	2.79510	+	4.84126i	0.224508	+	0.388859i
$156$		0			0
$157$	−4.66256	−	8.07579i	−0.372113	−	0.644518i	0.617778	−	0.786353i	$-0.288033\pi$
$157$	−4.66256	−	8.07579i	−0.372113	−	0.644518i	−0.989890	+	0.141835i	$0.954700\pi$
$158$		0			0
$159$		−	2.91193i		−	0.230931i
$160$		0			0
$161$	3.45111	−	5.97750i	0.271986	−	0.471093i
$162$		0			0
$163$			3.91433i			0.306594i	0.988180	+	0.153297i	$0.0489892\pi$
$163$			3.91433i			0.306594i	−0.988180	+	0.153297i	$0.951011\pi$
$164$		0			0
$165$	0.788551	+	0.455270i	0.0613886	+	0.0354427i
$166$		0			0
$167$	−8.26835	+	14.3212i	−0.639824	+	1.10821i	0.345647	+	0.938365i	$0.387660\pi$
$167$	−8.26835	+	14.3212i	−0.639824	+	1.10821i	−0.985471	+	0.169843i	$0.945674\pi$
$168$		0			0
$169$	−0.804446	−	1.39334i	−0.0618804	−	0.107180i
$170$		0			0
$171$	−28.0005	−	14.4371i	−2.14125	−	1.10403i
$172$		0			0
$173$	16.2762	−	9.39709i	1.23746	−	0.714447i	0.268885	−	0.963172i	$-0.413345\pi$
$173$	16.2762	−	9.39709i	1.23746	−	0.714447i	0.968574	+	0.248725i	$0.0800115\pi$
$174$		0			0
$175$	2.05276	+	1.18516i	0.155174	+	0.0895900i
$176$		0			0
$177$	−14.8899	+	25.7901i	−1.11919	+	1.93850i
$178$		0			0
$179$	−17.5712			−1.31333			−0.656667	−	0.754180i	$-0.728034\pi$
$179$	−17.5712			−1.31333			−0.656667	+	0.754180i	$0.728034\pi$
$180$		0			0
$181$	12.7591	+	7.36649i	0.948379	+	0.547547i	0.892577	−	0.450895i	$-0.148895\pi$
$181$	12.7591	+	7.36649i	0.948379	+	0.547547i	0.0558019	+	0.998442i	$0.482228\pi$
$182$		0			0
$183$	46.7196			3.45361
$184$		0			0
$185$	8.69913	−	5.02244i	0.639573	−	0.369257i
$186$		0			0
$187$	−0.388873	+	0.224516i	−0.0284372	+	0.0164182i
$188$		0			0
$189$			32.0448i			2.33091i
$190$		0			0
$191$		−	9.99507i		−	0.723218i	−0.932330	−	0.361609i	$-0.882228\pi$
$191$		−	9.99507i		−	0.723218i	0.932330	−	0.361609i	$-0.117772\pi$
$192$		0			0
$193$	5.07232	−	2.92851i	0.365114	−	0.210799i	−0.306208	−	0.951965i	$-0.599060\pi$
$193$	5.07232	−	2.92851i	0.365114	−	0.210799i	0.671322	+	0.741166i	$0.265727\pi$
$194$		0			0
$195$	9.34749	−	5.39678i	0.669388	−	0.386471i
$196$		0			0
$197$	16.6653			1.18735			0.593677	−	0.804703i	$-0.297676\pi$
$197$	16.6653			1.18735			0.593677	+	0.804703i	$0.297676\pi$
$198$		0			0
$199$	−16.4680	−	9.50779i	−1.16738	−	0.673989i	−0.214321	−	0.976763i	$-0.568754\pi$
$199$	−16.4680	−	9.50779i	−1.16738	−	0.673989i	−0.953062	+	0.302774i	$0.902087\pi$
$200$		0			0
$201$	16.4547			1.16062
$202$		0			0
$203$	8.01034	−	13.8743i	0.562216	−	0.973786i
$204$		0			0
$205$	2.85333	+	1.64737i	0.199286	+	0.115058i
$206$		0			0
$207$	−18.2259	+	10.5228i	−1.26679	+	0.731382i
$208$		0			0
$209$	−1.23966	+	0.0589877i	−0.0857493	+	0.00408027i
$210$		0			0
$211$	3.06578	+	5.31009i	0.211057	+	0.365562i	0.952046	−	0.305956i	$-0.0989760\pi$
$211$	3.06578	+	5.31009i	0.211057	+	0.365562i	−0.740988	+	0.671518i	$0.765643\pi$
$212$		0			0
$213$	−19.5036	+	33.7812i	−1.33636	+	2.31465i
$214$		0			0
$215$	6.82569	+	3.94081i	0.465508	+	0.268761i
$216$		0			0
$217$			13.2506i			0.899510i
$218$		0			0
$219$	14.4419	−	25.0142i	0.975895	−	1.69030i
$220$		0			0
$221$			5.32283i			0.358052i
$222$		0			0
$223$	2.01337	+	3.48725i	0.134825	+	0.233524i	0.925531	−	0.378673i	$-0.123619\pi$
$223$	2.01337	+	3.48725i	0.134825	+	0.233524i	−0.790706	+	0.612197i	$0.790286\pi$
$224$		0			0
$225$	−3.61367	−	6.25906i	−0.240911	−	0.417271i
$226$		0			0
$227$	28.8533			1.91506			0.957530	−	0.288334i	$-0.0931013\pi$
$227$	28.8533			1.91506			0.957530	+	0.288334i	$0.0931013\pi$
$228$		0			0
$229$	17.7480			1.17282			0.586411	−	0.810014i	$-0.300540\pi$
$229$	17.7480			1.17282			0.586411	+	0.810014i	$0.300540\pi$
$230$		0			0
$231$	1.07914	+	1.86912i	0.0710022	+	0.122979i
$232$		0			0
$233$	11.3692	+	19.6921i	0.744823	+	1.29007i	0.950277	+	0.311405i	$0.100799\pi$
$233$	11.3692	+	19.6921i	0.744823	+	1.29007i	−0.205454	+	0.978667i	$0.565867\pi$
$234$		0			0
$235$			6.54154i			0.426723i
$236$		0			0
$237$	9.65024	−	16.7147i	0.626851	−	1.08574i
$238$		0			0
$239$			9.16875i			0.593077i	0.955021	+	0.296539i	$0.0958323\pi$
$239$			9.16875i			0.593077i	−0.955021	+	0.296539i	$0.904168\pi$
$240$		0			0
$241$	9.15420	+	5.28518i	0.589674	+	0.340449i	0.764969	−	0.644068i	$-0.222754\pi$
$241$	9.15420	+	5.28518i	0.589674	+	0.340449i	−0.175295	+	0.984516i	$0.556088\pi$
$242$		0			0
$243$	14.1839	−	24.5673i	0.909899	−	1.57599i
$244$		0			0
$245$	−0.690774	−	1.19646i	−0.0441319	−	0.0764388i
$246$		0			0
$247$	−6.74192	+	13.0758i	−0.428978	+	0.831996i
$248$		0			0
$249$	19.8410	−	11.4552i	1.25737	−	0.725945i
$250$		0			0
$251$	−19.8314	−	11.4497i	−1.25175	−	0.722697i	−0.280292	−	0.959915i	$-0.590431\pi$
$251$	−19.8314	−	11.4497i	−1.25175	−	0.722697i	−0.971456	+	0.237218i	$0.923764\pi$
$252$		0			0
$253$	−0.414542	+	0.718008i	−0.0260620	+	0.0451408i
$254$		0			0
$255$	5.04361			0.315843
$256$		0			0
$257$	14.3287	+	8.27268i	0.893800	+	0.516035i	0.875183	−	0.483791i	$-0.160741\pi$
$257$	14.3287	+	8.27268i	0.893800	+	0.516035i	0.0186161	+	0.999827i	$0.494074\pi$
$258$		0			0
$259$	23.8097			1.47946
$260$		0			0
$261$	−42.3041	+	24.4243i	−2.61856	+	1.51182i
$262$		0			0
$263$	−1.73622	+	1.00241i	−0.107060	+	0.0618110i	−0.552574	−	0.833464i	$-0.686354\pi$
$263$	−1.73622	+	1.00241i	−0.107060	+	0.0618110i	0.445514	+	0.895275i	$0.353021\pi$
$264$		0			0
$265$			0.910540i			0.0559341i
$266$		0			0
$267$		−	11.0783i		−	0.677979i
$268$		0			0
$269$	7.34580	−	4.24110i	0.447881	−	0.258584i	−0.259054	−	0.965863i	$-0.583411\pi$
$269$	7.34580	−	4.24110i	0.447881	−	0.258584i	0.706935	+	0.707279i	$0.250077\pi$
$270$		0			0
$271$	27.9966	−	16.1639i	1.70067	−	0.981884i	0.755595	−	0.655039i	$-0.227348\pi$
$271$	27.9966	−	16.1639i	1.70067	−	0.981884i	0.945078	−	0.326845i	$-0.105986\pi$
$272$		0			0
$273$	25.5843			1.54843
$274$		0			0
$275$	−0.246575	−	0.142360i	−0.0148690	−	0.00858463i
$276$		0			0
$277$	−4.45469			−0.267656			−0.133828	−	0.991005i	$-0.542727\pi$
$277$	−4.45469			−0.267656			−0.133828	+	0.991005i	$0.542727\pi$
$278$		0			0
$279$	20.2012	−	34.9894i	1.20941	−	2.09476i
$280$		0			0
$281$	−22.2468	−	12.8442i	−1.32713	−	0.766221i	−0.342278	−	0.939599i	$-0.611199\pi$
$281$	−22.2468	−	12.8442i	−1.32713	−	0.766221i	−0.984855	+	0.173378i	$0.944532\pi$
$282$		0			0
$283$	−4.12964	+	2.38425i	−0.245481	+	0.141729i	−0.617693	−	0.786419i	$-0.711933\pi$
$283$	−4.12964	+	2.38425i	−0.245481	+	0.141729i	0.372212	+	0.928148i	$0.378599\pi$
$284$		0			0
$285$	12.3899	+	6.38826i	0.733915	+	0.378408i
$286$		0			0
$287$	3.90481	+	6.76334i	0.230494	+	0.399227i
$288$		0			0
$289$	7.25637	−	12.5684i	0.426846	−	0.739318i
$290$		0			0
$291$	28.0666	+	16.2042i	1.64529	+	0.949910i
$292$		0			0
$293$		−	4.46367i		−	0.260771i	−0.991463	−	0.130385i	$-0.958379\pi$
$293$		−	4.46367i		−	0.260771i	0.991463	−	0.130385i	$-0.0416214\pi$
$294$		0			0
$295$	4.65597	−	8.06438i	0.271081	−	0.469526i
$296$		0			0
$297$		−	3.84917i		−	0.223351i
$298$		0			0
$299$	4.91398	+	8.51127i	0.284183	+	0.492219i
$300$		0			0
$301$	9.34102	+	16.1791i	0.538407	+	0.932549i
$302$		0			0
$303$	29.0161			1.66693
$304$		0			0
$305$	−14.6089			−0.836503
$306$		0			0
$307$	−14.2894	−	24.7500i	−0.815541	−	1.41256i	−0.908939	−	0.416930i	$-0.863106\pi$
$307$	−14.2894	−	24.7500i	−0.815541	−	1.41256i	0.0933976	−	0.995629i	$-0.470227\pi$
$308$		0			0
$309$	8.48768	+	14.7011i	0.482847	+	0.836316i
$310$		0			0
$311$			7.16666i			0.406384i	0.979139	+	0.203192i	$0.0651316\pi$
$311$			7.16666i			0.406384i	−0.979139	+	0.203192i	$0.934868\pi$
$312$		0			0
$313$	−14.6455	+	25.3667i	−0.827810	+	1.43381i	0.0719419	+	0.997409i	$0.477080\pi$
$313$	−14.6455	+	25.3667i	−0.827810	+	1.43381i	−0.899752	+	0.436401i	$0.856253\pi$
$314$		0			0
$315$		−	17.1312i		−	0.965232i
$316$		0			0
$317$	−16.9257	−	9.77203i	−0.950640	−	0.548852i	−0.0573600	−	0.998354i	$-0.518268\pi$
$317$	−16.9257	−	9.77203i	−0.950640	−	0.548852i	−0.893280	+	0.449502i	$0.851602\pi$
$318$		0			0
$319$	−0.962189	+	1.66656i	−0.0538723	+	0.0933095i
$320$		0			0
$321$	11.9670	+	20.7275i	0.667933	+	1.15689i
$322$		0			0
$323$	−5.78333	+	3.71630i	−0.321793	+	0.206780i
$324$		0			0
$325$	−2.92290	+	1.68754i	−0.162133	+	0.0936076i
$326$		0			0
$327$	−7.09637	−	4.09709i	−0.392430	−	0.226570i
$328$		0			0
$329$	−7.75280	+	13.4282i	−0.427426	+	0.740323i
$330$		0			0
$331$	−14.5360			−0.798971			−0.399486	−	0.916739i	$-0.630811\pi$
$331$	−14.5360			−0.798971			−0.399486	+	0.916739i	$0.630811\pi$
$332$		0			0
$333$	−62.8716	−	36.2989i	−3.44534	−	1.98917i
$334$		0			0
$335$	−5.14527			−0.281116
$336$		0			0
$337$	10.7313	−	6.19572i	0.584572	−	0.337503i	−0.178377	−	0.983962i	$-0.557085\pi$
$337$	10.7313	−	6.19572i	0.584572	−	0.337503i	0.762948	+	0.646460i	$0.223751\pi$
$338$		0			0
$339$	−55.4175	+	31.9953i	−3.00987	+	1.73775i
$340$		0			0
$341$		−	1.59164i		−	0.0861922i
$342$		0			0
$343$		−	19.8670i		−	1.07272i
$344$		0			0
$345$	8.06478	−	4.65620i	0.434193	−	0.250682i
$346$		0			0
$347$	−16.9611	+	9.79251i	−0.910521	+	0.525689i	−0.880599	−	0.473863i	$-0.842859\pi$
$347$	−16.9611	+	9.79251i	−0.910521	+	0.525689i	−0.0299220	+	0.999552i	$0.509526\pi$
$348$		0			0
$349$	−20.4300			−1.09360			−0.546798	−	0.837265i	$-0.684153\pi$
$349$	−20.4300			−1.09360			−0.546798	+	0.837265i	$0.684153\pi$
$350$		0			0
$351$	−39.5151	−	22.8140i	−2.10916	−	1.21772i
$352$		0			0
$353$	28.5692			1.52058			0.760292	−	0.649582i	$-0.225056\pi$
$353$	28.5692			1.52058			0.760292	+	0.649582i	$0.225056\pi$
$354$		0			0
$355$	6.09864	−	10.5631i	0.323682	−	0.560634i
$356$		0			0
$357$	10.3533	+	5.97750i	0.547957	+	0.316363i
$358$		0			0
$359$	8.87845	−	5.12598i	0.468587	−	0.270539i	−0.247061	−	0.969000i	$-0.579465\pi$
$359$	8.87845	−	5.12598i	0.468587	−	0.270539i	0.715648	+	0.698461i	$0.246132\pi$
$360$		0			0
$361$	−18.9142	+	1.80410i	−0.995482	+	0.0949524i
$362$		0			0
$363$	17.4595	+	30.2407i	0.916386	+	1.58723i
$364$		0			0
$365$	−4.51589	+	7.82176i	−0.236373	+	0.409410i
$366$		0			0
$367$	−5.46679	−	3.15625i	−0.285364	−	0.164755i	0.350485	−	0.936568i	$-0.386017\pi$
$367$	−5.46679	−	3.15625i	−0.285364	−	0.164755i	−0.635849	+	0.771813i	$0.719350\pi$
$368$		0			0
$369$		−	23.8123i		−	1.23962i
$370$		0			0
$371$	−1.07914	+	1.86912i	−0.0560261	+	0.0970401i
$372$		0			0
$373$		−	10.9554i		−	0.567251i	−0.958935	−	0.283625i	$-0.908463\pi$
$373$		−	10.9554i		−	0.567251i	0.958935	−	0.283625i	$-0.0915372\pi$
$374$		0			0
$375$	1.59901	+	2.76957i	0.0825726	+	0.143020i
$376$		0			0
$377$	11.4058	+	19.7554i	0.587429	+	1.01746i
$378$		0			0
$379$	8.80587			0.452327			0.226164	−	0.974089i	$-0.427382\pi$
$379$	8.80587			0.452327			0.226164	+	0.974089i	$0.427382\pi$
$380$		0			0
$381$	37.7552			1.93426
$382$		0			0
$383$	−1.26606	−	2.19288i	−0.0646927	−	0.112051i	0.831865	−	0.554978i	$-0.187273\pi$
$383$	−1.26606	−	2.19288i	−0.0646927	−	0.112051i	−0.896558	+	0.442927i	$0.853940\pi$
$384$		0			0
$385$	−0.337440	−	0.584463i	−0.0171975	−	0.0297870i
$386$		0			0
$387$		−	56.9632i		−	2.89560i
$388$		0			0
$389$	10.5807	−	18.3263i	0.536462	−	0.929179i	−0.462629	−	0.886552i	$-0.653094\pi$
$389$	10.5807	−	18.3263i	0.536462	−	0.929179i	0.999091	−	0.0426271i	$-0.0135727\pi$
$390$		0			0
$391$			4.59241i			0.232248i
$392$		0			0
$393$	18.1172	+	10.4600i	0.913894	+	0.527637i
$394$		0			0
$395$	−3.01757	+	5.22658i	−0.151830	+	0.262978i
$396$		0			0
$397$	−9.85333	−	17.0665i	−0.494525	−	0.856542i	0.505455	−	0.862853i	$-0.331325\pi$
$397$	−9.85333	−	17.0665i	−0.494525	−	0.856542i	−0.999980	+	0.00631086i	$0.997991\pi$
$398$		0			0
$399$	17.8624	+	27.7976i	0.894239	+	1.39162i
$400$		0			0
$401$	11.3581	−	6.55761i	0.567197	−	0.327471i	−0.188832	−	0.982009i	$-0.560470\pi$
$401$	11.3581	−	6.55761i	0.567197	−	0.327471i	0.756029	+	0.654538i	$0.227137\pi$
$402$		0			0
$403$	−16.3396	−	9.43366i	−0.813933	−	0.469924i
$404$		0			0
$405$	−10.7762	+	18.6650i	−0.535475	+	0.927470i
$406$		0			0
$407$	−2.85998			−0.141764
$408$		0			0
$409$	−30.4181	−	17.5619i	−1.50408	−	0.868380i	−0.999989	−	0.00472953i	$-0.998495\pi$
$409$	−30.4181	−	17.5619i	−1.50408	−	0.868380i	−0.504090	−	0.863651i	$-0.668172\pi$
$410$		0			0
$411$	−5.98169			−0.295055
$412$		0			0
$413$	19.1152	−	11.0362i	0.940599	−	0.543055i
$414$		0			0
$415$	−6.20415	+	3.58197i	−0.304550	+	0.175832i
$416$		0			0
$417$		−	58.9021i		−	2.88445i
$418$		0			0
$419$			5.62265i			0.274685i	0.990524	+	0.137342i	$0.0438560\pi$
$419$			5.62265i			0.274685i	−0.990524	+	0.137342i	$0.956144\pi$
$420$		0			0
$421$	−26.0203	+	15.0228i	−1.26815	+	0.732167i	−0.974638	−	0.223788i	$-0.928158\pi$
$421$	−26.0203	+	15.0228i	−1.26815	+	0.732167i	−0.293513	+	0.955955i	$0.594824\pi$
$422$		0			0
$423$	40.9439	−	23.6390i	1.99076	−	1.14937i
$424$		0			0
$425$	−1.57710			−0.0765007
$426$		0			0
$427$	−29.9886	−	17.3139i	−1.45125	−	0.837880i
$428$		0			0
$429$	−3.07314			−0.148373
$430$		0			0
$431$	−1.27750	+	2.21269i	−0.0615348	+	0.106581i	−0.895152	−	0.445762i	$-0.852933\pi$
$431$	−1.27750	+	2.21269i	−0.0615348	+	0.106581i	0.833617	+	0.552343i	$0.186266\pi$
$432$		0			0
$433$	33.4432	+	19.3084i	1.60718	+	0.927904i	0.989998	+	0.141081i	$0.0450578\pi$
$433$	33.4432	+	19.3084i	1.60718	+	0.927904i	0.617179	+	0.786823i	$0.288275\pi$
$434$		0			0
$435$	18.7191	−	10.8075i	0.897512	−	0.518179i
$436$		0			0
$437$	−5.81676	+	11.2815i	−0.278254	+	0.539668i
$438$		0			0
$439$	−1.31689	−	2.28092i	−0.0628518	−	0.108863i	0.832887	−	0.553443i	$-0.186686\pi$
$439$	−1.31689	−	2.28092i	−0.0628518	−	0.108863i	−0.895739	+	0.444580i	$0.853353\pi$
$440$		0			0
$441$	−4.99246	+	8.64720i	−0.237736	+	0.411771i
$442$		0			0
$443$	34.0506	+	19.6591i	1.61779	+	0.934034i	0.987489	+	0.157686i	$0.0504034\pi$
$443$	34.0506	+	19.6591i	1.61779	+	0.934034i	0.630305	+	0.776348i	$0.282930\pi$
$444$		0			0
$445$			3.46410i			0.164214i
$446$		0			0
$447$	14.7546	−	25.5558i	0.697870	−	1.20875i
$448$		0			0
$449$		−	24.8922i		−	1.17473i	−0.809321	−	0.587367i	$-0.800165\pi$
$449$		−	24.8922i		−	1.17473i	0.809321	−	0.587367i	$-0.199835\pi$
$450$		0			0
$451$	−0.469040	−	0.812401i	−0.0220862	−	0.0382545i
$452$		0			0
$453$	−32.1331	−	55.6562i	−1.50975	−	2.61496i
$454$		0			0
$455$	−8.00002			−0.375047
$456$		0			0
$457$	17.5771			0.822222			0.411111	−	0.911585i	$-0.365141\pi$
$457$	17.5771			0.822222			0.411111	+	0.911585i	$0.365141\pi$
$458$		0			0
$459$	−10.6605	−	18.4646i	−0.497591	−	0.861853i
$460$		0			0
$461$	−5.33266	−	9.23644i	−0.248367	−	0.430184i	0.714706	−	0.699425i	$-0.246560\pi$
$461$	−5.33266	−	9.23644i	−0.248367	−	0.430184i	−0.963073	+	0.269241i	$0.913227\pi$
$462$		0			0
$463$		−	18.7309i		−	0.870497i	−0.900310	−	0.435248i	$-0.856661\pi$
$463$		−	18.7309i		−	0.870497i	0.900310	−	0.435248i	$-0.143339\pi$
$464$		0			0
$465$	−8.93879	+	15.4824i	−0.414527	+	0.717981i
$466$		0			0
$467$			4.25201i			0.196760i	0.995149	+	0.0983798i	$0.0313660\pi$
$467$			4.25201i			0.196760i	−0.995149	+	0.0983798i	$0.968634\pi$
$468$		0			0
$469$	−10.5620	−	6.09799i	−0.487709	−	0.281579i
$470$		0			0
$471$	14.9110	−	25.8266i	0.687061	−	1.19002i
$472$		0			0
$473$	−1.12203	−	1.94341i	−0.0515909	−	0.0893580i
$474$		0			0
$475$	−3.87424	−	1.99756i	−0.177762	−	0.0916546i
$476$		0			0
$477$	5.69913	−	3.29039i	0.260945	−	0.150657i
$478$		0			0
$479$	31.8291	+	18.3765i	1.45431	+	0.839645i	0.998722	−	0.0505459i	$-0.0160961\pi$
$479$	31.8291	+	18.3765i	1.45431	+	0.839645i	0.455587	+	0.890191i	$0.349429\pi$
$480$		0			0
$481$	−16.9511	+	29.3602i	−0.772904	+	1.33871i
$482$		0			0
$483$	22.0735			1.00438
$484$		0			0
$485$	−8.77623	−	5.06696i	−0.398508	−	0.230079i
$486$		0			0
$487$	2.52442			0.114392			0.0571961	−	0.998363i	$-0.481784\pi$
$487$	2.52442			0.114392			0.0571961	+	0.998363i	$0.481784\pi$
$488$		0			0
$489$	−10.8410	+	6.25906i	−0.490248	+	0.283045i
$490$		0			0
$491$	12.4691	−	7.19902i	0.562722	−	0.324887i	−0.191516	−	0.981490i	$-0.561340\pi$
$491$	12.4691	−	7.19902i	0.562722	−	0.324887i	0.754237	+	0.656602i	$0.228007\pi$
$492$		0			0
$493$			10.6594i			0.480075i
$494$		0			0
$495$			2.05777i			0.0924898i
$496$		0			0
$497$	25.0381	−	14.4558i	1.12311	−	0.648430i
$498$		0			0
$499$	−11.8211	+	6.82490i	−0.529184	+	0.305525i	−0.740684	−	0.671853i	$-0.765498\pi$
$499$	−11.8211	+	6.82490i	−0.529184	+	0.305525i	0.211500	+	0.977378i	$0.432165\pi$
$500$		0			0
$501$	−52.8847			−2.36272
$502$		0			0
$503$	−1.23287	−	0.711800i	−0.0549711	−	0.0317376i	0.472263	−	0.881458i	$-0.343437\pi$
$503$	−1.23287	−	0.711800i	−0.0549711	−	0.0317376i	−0.527234	+	0.849720i	$0.676771\pi$
$504$		0			0
$505$	−9.07314			−0.403749
$506$		0			0
$507$	2.57264	−	4.45593i	0.114255	−	0.197895i
$508$		0			0
$509$	7.77899	+	4.49120i	0.344798	+	0.199069i	0.662392	−	0.749158i	$-0.269542\pi$
$509$	7.77899	+	4.49120i	0.344798	+	0.199069i	−0.317594	+	0.948227i	$0.602875\pi$
$510$		0			0
$511$	−18.5401	+	10.7041i	−0.820167	+	0.473524i
$512$		0			0
$513$	−2.80087	−	58.8620i	−0.123661	−	2.59882i
$514$		0			0
$515$	−2.65404	−	4.59693i	−0.116951	−	0.202565i
$516$		0			0
$517$	0.931254	−	1.61298i	0.0409565	−	0.0709387i
$518$		0			0
$519$	52.0517	+	30.0521i	2.28482	+	1.31914i
$520$		0			0
$521$			37.3850i			1.63787i	0.573888	+	0.818934i	$0.305434\pi$
$521$			37.3850i			1.63787i	−0.573888	+	0.818934i	$0.694566\pi$
$522$		0			0
$523$	8.54165	−	14.7946i	0.373500	−	0.646921i	−0.616601	−	0.787276i	$-0.711491\pi$
$523$	8.54165	−	14.7946i	0.373500	−	0.646921i	0.990101	+	0.140354i	$0.0448242\pi$
$524$		0			0
$525$			7.58036i			0.330834i
$526$		0			0
$527$	−4.40816	−	7.63516i	−0.192022	−	0.332593i
$528$		0			0
$529$	−7.26034	−	12.5753i	−0.315667	−	0.546751i
$530$		0			0
$531$	−67.3006			−2.92060
$532$		0			0
$533$	−11.1200			−0.481661
$534$		0			0
$535$	−3.74200	−	6.48134i	−0.161781	−	0.280213i
$536$		0			0
$537$	−28.0966	−	48.6647i	−1.21246	−	2.10004i
$538$		0			0
$539$			0.393354i			0.0169430i
$540$		0			0
$541$	17.6172	−	30.5140i	0.757425	−	1.31190i	−0.186735	−	0.982410i	$-0.559791\pi$
$541$	17.6172	−	30.5140i	0.757425	−	1.31190i	0.944160	−	0.329488i	$-0.106876\pi$
$542$		0			0
$543$			47.1164i			2.02196i
$544$		0			0
$545$	2.21899	+	1.28113i	0.0950510	+	0.0548777i
$546$		0			0
$547$	13.0146	−	22.5419i	0.556462	−	0.963821i	−0.441326	−	0.897347i	$-0.645492\pi$
$547$	13.0146	−	22.5419i	0.556462	−	0.963821i	0.997788	−	0.0664738i	$-0.0211749\pi$
$548$		0			0
$549$	52.7917	+	91.4380i	2.25310	+	3.90248i
$550$		0			0
$551$	−13.5012	+	26.1854i	−0.575172	+	1.11554i
$552$		0			0
$553$	−12.3887	+	7.15262i	−0.526821	+	0.304160i
$554$		0			0
$555$	27.8200	+	16.0619i	1.18089	+	0.681789i
$556$		0			0
$557$	0.487681	−	0.844688i	0.0206637	−	0.0357906i	−0.855509	−	0.517789i	$-0.826755\pi$
$557$	0.487681	−	0.844688i	0.0206637	−	0.0357906i	0.876172	+	0.481998i	$0.160089\pi$
$558$		0			0
$559$	−26.6010			−1.12510
$560$		0			0
$561$	−1.24363	−	0.718008i	−0.0525059	−	0.0303143i
$562$		0			0
$563$	15.0115			0.632660			0.316330	−	0.948649i	$-0.397549\pi$
$563$	15.0115			0.632660			0.316330	+	0.948649i	$0.397549\pi$
$564$		0			0
$565$	17.3287	−	10.0047i	0.729024	−	0.420902i
$566$		0			0
$567$	−44.2421	+	25.5432i	−1.85799	+	1.07271i
$568$		0			0
$569$		−	16.1089i		−	0.675321i	−0.941268	−	0.337660i	$-0.890364\pi$
$569$		−	16.1089i		−	0.675321i	0.941268	−	0.337660i	$-0.109636\pi$
$570$		0			0
$571$			8.07105i			0.337763i	0.985636	+	0.168882i	$0.0540155\pi$
$571$			8.07105i			0.337763i	−0.985636	+	0.168882i	$0.945984\pi$
$572$		0			0
$573$	27.6820	−	15.9822i	1.15643	−	0.667667i
$574$		0			0
$575$	−2.52180	+	1.45596i	−0.105166	+	0.0607179i
$576$		0			0
$577$	−27.4451			−1.14256			−0.571278	−	0.820757i	$-0.693552\pi$
$577$	−27.4451			−1.14256			−0.571278	+	0.820757i	$0.693552\pi$
$578$		0			0
$579$	16.2214	+	9.36543i	0.674138	+	0.389214i
$580$		0			0
$581$	−16.9809			−0.704486
$582$		0			0
$583$	0.129624	−	0.224516i	0.00536850	−	0.00929851i
$584$		0			0
$585$	21.1248	+	12.1964i	0.873402	+	0.504259i
$586$		0			0
$587$	−21.9830	+	12.6919i	−0.907335	+	0.523850i	−0.879573	−	0.475765i	$-0.842171\pi$
$587$	−21.9830	+	12.6919i	−0.907335	+	0.523850i	−0.0277619	+	0.999615i	$0.508838\pi$
$588$		0			0
$589$	−1.15817	−	24.3396i	−0.0477215	−	1.00290i
$590$		0			0
$591$	26.6480	+	46.1557i	1.09615	+	1.89859i
$592$		0			0
$593$	−16.4960	+	28.5720i	−0.677411	+	1.17331i	0.298347	+	0.954458i	$0.403565\pi$
$593$	−16.4960	+	28.5720i	−0.677411	+	1.17331i	−0.975758	+	0.218853i	$0.929769\pi$
$594$		0			0
$595$	−3.23742	−	1.86912i	−0.132721	−	0.0766266i
$596$		0			0
$597$		−	60.8122i		−	2.48888i
$598$		0			0
$599$	22.4255	−	38.8422i	0.916283	−	1.58705i	0.111271	−	0.993790i	$-0.464508\pi$
$599$	22.4255	−	38.8422i	0.916283	−	1.58705i	0.805012	−	0.593259i	$-0.202159\pi$
$600$		0			0
$601$			6.41143i			0.261528i	0.991414	+	0.130764i	$0.0417430\pi$
$601$			6.41143i			0.261528i	−0.991414	+	0.130764i	$0.958257\pi$
$602$		0			0
$603$	18.5933	+	32.2046i	0.757178	+	1.31147i
$604$		0			0
$605$	−5.45947	−	9.45607i	−0.221959	−	0.384444i
$606$		0			0
$607$	6.32967			0.256913			0.128457	−	0.991715i	$-0.458998\pi$
$607$	6.32967			0.256913			0.128457	+	0.991715i	$0.458998\pi$
$608$		0			0
$609$	51.2345			2.07613
$610$		0			0
$611$	−11.0391	−	19.1203i	−0.446594	−	0.773523i
$612$		0			0
$613$	8.84102	+	15.3131i	0.357085	+	0.618490i	0.987473	−	0.157791i	$-0.0504372\pi$
$613$	8.84102	+	15.3131i	0.357085	+	0.618490i	−0.630387	+	0.776281i	$0.717104\pi$
$614$		0			0
$615$			10.5367i			0.424880i
$616$		0			0
$617$	15.0366	−	26.0441i	0.605349	−	1.04850i	−0.386647	−	0.922228i	$-0.626367\pi$
$617$	15.0366	−	26.0441i	0.605349	−	1.04850i	0.991996	−	0.126268i	$-0.0403000\pi$
$618$		0			0
$619$		−	28.6730i		−	1.15246i	−0.817286	−	0.576232i	$-0.804522\pi$
$619$		−	28.6730i		−	1.15246i	0.817286	−	0.576232i	$-0.195478\pi$
$620$		0			0
$621$	−34.0926	−	19.6834i	−1.36809	−	0.789867i
$622$		0			0
$623$	−4.10553	+	7.11098i	−0.164484	+	0.284895i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−2.14560	−	3.33901i	−0.0856872	−	0.133347i
$628$		0			0
$629$	−13.7194	+	7.92091i	−0.547029	+	0.315827i
$630$		0			0
$631$	−24.7249	−	14.2749i	−0.984282	−	0.568276i	−0.0807220	−	0.996737i	$-0.525723\pi$
$631$	−24.7249	−	14.2749i	−0.984282	−	0.568276i	−0.903560	+	0.428461i	$0.859056\pi$
$632$		0			0
$633$	−9.80445	+	16.9818i	−0.389692	+	0.674966i
$634$		0			0
$635$	−11.8058			−0.468498
$636$		0			0
$637$	4.03812	+	2.33141i	0.159996	+	0.0923739i
$638$		0			0
$639$	−88.1539			−3.48731
$640$		0			0
$641$	−41.9086	+	24.1959i	−1.65529	+	0.955681i	−0.680443	+	0.732801i	$0.738212\pi$
$641$	−41.9086	+	24.1959i	−1.65529	+	0.955681i	−0.974846	+	0.222880i	$0.928454\pi$
$642$		0			0
$643$	20.3510	−	11.7497i	0.802566	−	0.463362i	−0.0418014	−	0.999126i	$-0.513310\pi$
$643$	20.3510	−	11.7497i	0.802566	−	0.463362i	0.844368	+	0.535764i	$0.179976\pi$
$644$		0			0
$645$			25.2056i			0.992470i
$646$		0			0
$647$			45.2320i			1.77825i	0.457662	+	0.889126i	$0.348687\pi$
$647$			45.2320i			1.77825i	−0.457662	+	0.889126i	$0.651313\pi$
$648$		0			0
$649$	−2.29609	+	1.32565i	−0.0901294	+	0.0520362i
$650$		0			0
$651$	−36.6985	+	21.1879i	−1.43833	+	0.830418i
$652$		0			0
$653$	−30.4618			−1.19206			−0.596032	−	0.802961i	$-0.703257\pi$
$653$	−30.4618			−1.19206			−0.596032	+	0.802961i	$0.703257\pi$
$654$		0			0
$655$	−5.66514	−	3.27077i	−0.221355	−	0.127800i
$656$		0			0
$657$	65.2758			2.54665
$658$		0			0
$659$	20.9829	−	36.3434i	0.817377	−	1.41574i	−0.0902312	−	0.995921i	$-0.528761\pi$
$659$	20.9829	−	36.3434i	0.817377	−	1.41574i	0.907608	−	0.419818i	$-0.137906\pi$
$660$		0			0
$661$	22.2762	+	12.8612i	0.866445	+	0.500242i	0.866165	−	0.499758i	$-0.166578\pi$
$661$	22.2762	+	12.8612i	0.866445	+	0.500242i	0.000279760		1.00000i	$0.499911\pi$
$662$		0			0
$663$	−14.7419	+	8.51127i	−0.572530	+	0.330550i
$664$		0			0
$665$	−5.58546	−	8.69214i	−0.216595	−	0.337067i
$666$		0			0
$667$	9.84064	+	17.0445i	0.381031	+	0.659965i
$668$		0			0
$669$	−6.43879	+	11.1523i	−0.248938	+	0.431173i
$670$		0			0
$671$	3.60218	+	2.07972i	0.139061	+	0.0802867i
$672$		0			0
$673$			24.7605i			0.954445i	0.878782	+	0.477223i	$0.158357\pi$
$673$			24.7605i			0.954445i	−0.878782	+	0.477223i	$0.841643\pi$
$674$		0			0
$675$	6.75957	−	11.7079i	0.260176	−	0.450638i
$676$		0			0
$677$			6.18702i			0.237786i	0.992907	+	0.118893i	$0.0379346\pi$
$677$			6.18702i			0.237786i	−0.992907	+	0.118893i	$0.962065\pi$
$678$		0			0
$679$	−12.0104	−	20.8025i	−0.460915	−	0.798328i
$680$		0			0
$681$	46.1367	+	79.9111i	1.76796	+	3.06220i
$682$		0			0
$683$	−17.2866			−0.661454			−0.330727	−	0.943726i	$-0.607294\pi$
$683$	−17.2866			−0.661454			−0.330727	+	0.943726i	$0.607294\pi$
$684$		0			0
$685$	1.87043			0.0714656
$686$		0			0
$687$	28.3793	+	49.1543i	1.08274	+	1.87536i
$688$		0			0
$689$	−1.53657	−	2.66142i	−0.0585386	−	0.101392i
$690$		0			0
$691$		−	27.1514i		−	1.03289i	−0.856321	−	0.516443i	$-0.827256\pi$
$691$		−	27.1514i		−	1.03289i	0.856321	−	0.516443i	$-0.172744\pi$
$692$		0			0
$693$	−2.43879	+	4.22411i	−0.0926421	+	0.160461i
$694$		0			0
$695$			18.4183i			0.698646i
$696$		0			0
$697$	−4.50000	−	2.59808i	−0.170450	−	0.0984092i
$698$		0			0
$699$	−36.3590	+	62.9757i	−1.37523	+	2.38196i
$700$		0			0
$701$	20.4829	+	35.4774i	0.773628	+	1.33996i	0.935562	+	0.353162i	$0.114894\pi$
$701$	20.4829	+	35.4774i	0.773628	+	1.33996i	−0.161934	+	0.986802i	$0.551773\pi$
$702$		0			0
$703$	−43.7352	+	2.08108i	−1.64950	+	0.0784895i
$704$		0			0
$705$	−18.1172	+	10.4600i	−0.682335	+	0.393946i
$706$		0			0
$707$	−18.6250	−	10.7532i	−0.700466	−	0.404414i
$708$		0			0
$709$	11.6578	−	20.1919i	0.437817	−	0.758322i	−0.559704	−	0.828693i	$-0.689085\pi$
$709$	11.6578	−	20.1919i	0.437817	−	0.758322i	0.997521	+	0.0703713i	$0.0224184\pi$
$710$		0			0
$711$	43.6180			1.63580
$712$		0			0
$713$	−14.0974	−	8.13913i	−0.527951	−	0.304813i
$714$		0			0
$715$	0.960950			0.0359375
$716$		0			0
$717$	−25.3935	+	14.6609i	−0.948337	+	0.547523i
$718$		0			0
$719$	−12.7833	+	7.38042i	−0.476735	+	0.275243i	−0.719055	−	0.694953i	$-0.755425\pi$
$719$	−12.7833	+	7.38042i	−0.476735	+	0.275243i	0.242320	+	0.970196i	$0.422092\pi$
$720$		0			0
$721$		−	12.5819i		−	0.468574i
$722$		0			0
$723$			33.8043i			1.25719i
$724$		0			0
$725$	−5.85333	+	3.37942i	−0.217387	+	0.125509i
$726$		0			0
$727$	13.6055	−	7.85515i	0.504601	−	0.291331i	−0.226011	−	0.974125i	$-0.572568\pi$
$727$	13.6055	−	7.85515i	0.504601	−	0.291331i	0.730611	+	0.682794i	$0.239235\pi$
$728$		0			0
$729$	26.0636			0.965318
$730$		0			0
$731$	−10.7648	−	6.21506i	−0.398151	−	0.229872i
$732$		0			0
$733$	−10.8529			−0.400863			−0.200431	−	0.979708i	$-0.564234\pi$
$733$	−10.8529			−0.400863			−0.200431	+	0.979708i	$0.564234\pi$
$734$		0			0
$735$	2.20911	−	3.82629i	0.0814843	−	0.141135i
$736$		0			0
$737$	1.26869	+	0.732480i	0.0467329	+	0.0269813i
$738$		0			0
$739$	−4.18805	+	2.41797i	−0.154060	+	0.0889466i	−0.575048	−	0.818120i	$-0.695017\pi$
$739$	−4.18805	+	2.41797i	−0.154060	+	0.0889466i	0.420988	+	0.907066i	$0.361683\pi$
$740$		0			0
$741$	−46.9948	+	2.23619i	−1.72640	+	0.0821484i
$742$		0			0
$743$	−13.0895	−	22.6717i	−0.480207	−	0.831743i	0.519535	−	0.854449i	$-0.326105\pi$
$743$	−13.0895	−	22.6717i	−0.480207	−	0.831743i	−0.999742	+	0.0227062i	$0.992772\pi$
$744$		0			0
$745$	−4.61367	+	7.99111i	−0.169032	+	0.292772i
$746$		0			0
$747$	44.8395	+	25.8881i	1.64059	+	0.947197i
$748$		0			0
$749$		−	17.7395i		−	0.648189i
$750$		0			0
$751$	−7.27683	+	12.6038i	−0.265535	+	0.459920i	−0.967704	−	0.252090i	$-0.918882\pi$
$751$	−7.27683	+	12.6038i	−0.265535	+	0.459920i	0.702169	+	0.712011i	$0.252215\pi$
$752$		0			0
$753$		−	73.2326i		−	2.66874i
$754$		0			0
$755$	10.0478	+	17.4033i	0.365678	+	0.633372i
$756$		0			0
$757$	6.34580	+	10.9912i	0.230642	+	0.399483i	0.957997	−	0.286778i	$-0.0925841\pi$
$757$	6.34580	+	10.9912i	0.230642	+	0.399483i	−0.727355	+	0.686261i	$0.759251\pi$
$758$		0			0
$759$	−2.65143			−0.0962407
$760$		0			0
$761$	30.6971			1.11277			0.556385	−	0.830925i	$-0.312188\pi$
$761$	30.6971			1.11277			0.556385	+	0.830925i	$0.312188\pi$
$762$		0			0
$763$	3.03671	+	5.25973i	0.109936	+	0.190415i
$764$		0			0
$765$	5.69913	+	9.87118i	0.206052	+	0.356893i
$766$		0			0
$767$			31.4285i			1.13482i
$768$		0			0
$769$	−13.4388	+	23.2767i	−0.484615	+	0.839378i	−0.999844	−	0.0176746i	$-0.994374\pi$
$769$	−13.4388	+	23.2767i	−0.484615	+	0.839378i	0.515229	+	0.857053i	$0.327707\pi$
$770$		0			0
$771$			52.9124i			1.90559i
$772$		0			0
$773$	17.5155	+	10.1126i	0.629989	+	0.363724i	0.780748	−	0.624846i	$-0.214838\pi$
$773$	17.5155	+	10.1126i	0.629989	+	0.363724i	−0.150759	+	0.988571i	$0.548172\pi$
$774$		0			0
$775$	2.79510	−	4.84126i	0.100403	−	0.173903i
$776$		0			0
$777$	38.0719	+	65.9425i	1.36582	+	2.36567i
$778$		0			0
$779$	−7.76377	−	12.0820i	−0.278166	−	0.432884i
$780$		0			0
$781$	−3.00754	+	1.73640i	−0.107618	+	0.0621334i
$782$		0			0
$783$	−79.1320	−	45.6869i	−2.82795	−	1.63272i
$784$		0			0
$785$	−4.66256	+	8.07579i	−0.166414	+	0.288237i
$786$		0			0
$787$	−7.46636			−0.266147			−0.133074	−	0.991106i	$-0.542485\pi$
$787$	−7.46636			−0.266147			−0.133074	+	0.991106i	$0.542485\pi$
$788$		0			0
$789$	−5.55246	−	3.20572i	−0.197673	−	0.114127i
$790$		0			0
$791$	47.4290			1.68638
$792$		0			0
$793$	42.7003	−	24.6530i	1.51633	−	0.875455i
$794$		0			0
$795$	−2.52180	+	1.45596i	−0.0894392	+	0.0516377i
$796$		0			0
$797$			27.6151i			0.978176i	0.872234	+	0.489088i	$0.162670\pi$
$797$			27.6151i			0.978176i	−0.872234	+	0.489088i	$0.837330\pi$
$798$		0			0
$799$		−	10.3167i		−	0.364978i
$800$		0			0
$801$	21.6820	−	12.5181i	0.766097	−	0.442306i
$802$		0			0
$803$	2.22701	−	1.28577i	0.0785895	−	0.0453737i
$804$		0			0
$805$	−6.90222			−0.243271
$806$		0			0
$807$	23.4920	+	13.5631i	0.826958	+	0.477444i
$808$		0			0
$809$	−26.0318			−0.915229			−0.457614	−	0.889151i	$-0.651296\pi$
$809$	−26.0318			−0.915229			−0.457614	+	0.889151i	$0.651296\pi$
$810$		0			0
$811$	5.44914	−	9.43819i	0.191345	−	0.331420i	−0.754351	−	0.656471i	$-0.772048\pi$
$811$	5.44914	−	9.43819i	0.191345	−	0.331420i	0.945696	+	0.325052i	$0.105382\pi$
$812$		0			0
$813$	89.5338	+	51.6923i	3.14009	+	1.81293i
$814$		0			0
$815$	3.38991	−	1.95717i	0.118743	−	0.0685566i
$816$		0			0
$817$	−18.5723	−	28.9024i	−0.649763	−	1.01117i
$818$		0			0
$819$	28.9095	+	50.0727i	1.01018	+	1.74968i
$820$		0			0
$821$	10.9877	−	19.0312i	0.383473	−	0.664194i	−0.608083	−	0.793873i	$-0.708061\pi$
$821$	10.9877	−	19.0312i	0.383473	−	0.664194i	0.991556	+	0.129679i	$0.0413947\pi$
$822$		0			0
$823$	−25.9680	−	14.9926i	−0.905186	−	0.522609i	−0.0263069	−	0.999654i	$-0.508375\pi$
$823$	−25.9680	−	14.9926i	−0.905186	−	0.522609i	−0.878879	+	0.477044i	$0.841708\pi$
$824$		0			0
$825$		−	0.910540i		−	0.0317009i
$826$		0			0
$827$	−17.2282	+	29.8401i	−0.599083	+	1.03764i	0.393873	+	0.919165i	$0.371135\pi$
$827$	−17.2282	+	29.8401i	−0.599083	+	1.03764i	−0.992957	+	0.118478i	$0.962198\pi$
$828$		0			0
$829$			10.2606i			0.356365i	0.983997	+	0.178183i	$0.0570218\pi$
$829$			10.2606i			0.356365i	−0.983997	+	0.178183i	$0.942978\pi$
$830$		0			0
$831$	−7.12309	−	12.3376i	−0.247097	−	0.427985i
$832$		0			0
$833$	1.08942	+	1.88693i	0.0377462	+	0.0653784i
$834$		0			0
$835$	16.5367			0.572276
$836$		0			0
$837$	75.5747			2.61224
$838$		0			0
$839$	−10.5207	−	18.2224i	−0.363215	−	0.629107i	0.625273	−	0.780406i	$-0.284988\pi$
$839$	−10.5207	−	18.2224i	−0.363215	−	0.629107i	−0.988488	+	0.151299i	$0.951654\pi$
$840$		0			0
$841$	8.34102	+	14.4471i	0.287621	+	0.498175i
$842$		0			0
$843$		−	82.1521i		−	2.82947i
$844$		0			0
$845$	−0.804446	+	1.39334i	−0.0276738	+	0.0479324i
$846$		0			0
$847$		−	25.8814i		−	0.889297i
$848$		0			0
$849$	−13.2067	−	7.62487i	−0.453252	−	0.261685i
$850$		0			0
$851$	−14.6250	+	25.3312i	−0.501338	+	0.868344i
$852$		0			0
$853$	0.767876	+	1.33000i	0.0262916	+	0.0455384i	0.878872	−	0.477058i	$-0.158297\pi$
$853$	0.767876	+	1.33000i	0.0262916	+	0.0455384i	−0.852580	+	0.522596i	$0.824963\pi$
$854$		0			0
$855$	1.49735	+	31.4677i	0.0512082	+	1.07617i
$856$		0			0
$857$	−29.7794	+	17.1932i	−1.01725	+	0.587307i	−0.913305	−	0.407276i	$-0.866479\pi$
$857$	−29.7794	+	17.1932i	−1.01725	+	0.587307i	−0.103941	+	0.994583i	$0.533145\pi$
$858$		0			0
$859$	29.7661	+	17.1855i	1.01561	+	0.586361i	0.912829	−	0.408343i	$-0.133893\pi$
$859$	29.7661	+	17.1855i	1.01561	+	0.586361i	0.102779	+	0.994704i	$0.467227\pi$
$860$		0			0
$861$	−12.4877	+	21.6293i	−0.425579	+	0.737125i
$862$		0			0
$863$	49.1652			1.67360			0.836801	−	0.547507i	$-0.184423\pi$
$863$	49.1652			1.67360			0.836801	+	0.547507i	$0.184423\pi$
$864$		0			0
$865$	−16.2762	−	9.39709i	−0.553408	−	0.319511i
$866$		0			0
$867$	46.4121			1.57624
$868$		0			0
$869$	1.48811	−	0.859161i	0.0504807	−	0.0291450i
$870$		0			0
$871$	15.0391	−	8.68283i	0.509580	−	0.294206i
$872$		0			0
$873$			73.2413i			2.47884i
$874$		0			0
$875$		−	2.37033i		−	0.0801317i
$876$		0			0
$877$	−4.13711	+	2.38856i	−0.139700	+	0.0806559i	−0.568221	−	0.822876i	$-0.692368\pi$
$877$	−4.13711	+	2.38856i	−0.139700	+	0.0806559i	0.428521	+	0.903532i	$0.359035\pi$
$878$		0			0
$879$	12.3624	−	7.13746i	0.416975	−	0.240741i
$880$		0			0
$881$	−22.7965			−0.768034			−0.384017	−	0.923326i	$-0.625460\pi$
$881$	−22.7965			−0.768034			−0.384017	+	0.923326i	$0.625460\pi$
$882$		0			0
$883$	28.7846	+	16.6188i	0.968677	+	0.559266i	0.898833	−	0.438292i	$-0.144416\pi$
$883$	28.7846	+	16.6188i	0.968677	+	0.559266i	0.0698446	+	0.997558i	$0.477750\pi$
$884$		0			0
$885$	29.7798			1.00104
$886$		0			0
$887$	1.47821	−	2.56033i	0.0496334	−	0.0859676i	−0.840141	−	0.542368i	$-0.817528\pi$
$887$	1.47821	−	2.56033i	0.0496334	−	0.0859676i	0.889775	+	0.456400i	$0.150861\pi$
$888$		0			0
$889$	−24.2345	−	13.9918i	−0.812799	−	0.469270i
$890$		0			0
$891$	5.31429	−	3.06821i	0.178035	−	0.102789i
$892$		0			0
$893$	13.0672	−	25.3435i	0.437276	−	0.848088i
$894$		0			0
$895$	8.78561	+	15.2171i	0.293671	+	0.508652i
$896$		0			0
$897$	−15.7150	+	27.2192i	−0.524709	+	0.908823i
$898$		0			0
$899$	−32.7213	−	18.8917i	−1.09132	−	0.630072i
$900$		0			0
$901$		−	1.43602i		−	0.0478406i
$902$		0			0
$903$	−29.8728	+	51.7412i	−0.994104	+	1.72184i
$904$		0			0
$905$		−	14.7330i		−	0.489741i
$906$		0			0
$907$	25.3731	+	43.9476i	0.842501	+	1.45926i	0.887773	+	0.460281i	$0.152251\pi$
$907$	25.3731	+	43.9476i	0.842501	+	1.45926i	−0.0452721	+	0.998975i	$0.514415\pi$
$908$		0			0
$909$	32.7873	+	56.7894i	1.08749	+	1.88358i
$910$		0			0
$911$	51.4152			1.70346			0.851730	−	0.523980i	$-0.175553\pi$
$911$	51.4152			1.70346			0.851730	+	0.523980i	$0.175553\pi$
$912$		0			0
$913$	2.03972			0.0675047
$914$		0			0
$915$	−23.3598	−	40.4603i	−0.772250	−	1.33758i
$916$		0			0
$917$	−7.75280	−	13.4282i	−0.256020	−	0.443440i
$918$		0			0
$919$			21.2071i			0.699558i	0.936832	+	0.349779i	$0.113743\pi$
$919$			21.2071i			0.699558i	−0.936832	+	0.349779i	$0.886257\pi$
$920$		0			0
$921$	45.6979	−	79.1511i	1.50580	−	2.60812i
$922$		0			0
$923$			41.1667i			1.35502i
$924$		0			0
$925$	−8.69913	−	5.02244i	−0.286026	−	0.165137i
$926$		0			0
$927$	−19.1817	+	33.2236i	−0.630009	+	1.09121i
$928$		0			0
$929$	−21.8032	−	37.7643i	−0.715341	−	1.23901i	−0.962828	−	0.270116i	$-0.912938\pi$
$929$	−21.8032	−	37.7643i	−0.715341	−	1.23901i	0.247487	−	0.968891i	$-0.420395\pi$
$930$		0			0
$931$	0.286227	+	6.01522i	0.00938070	+	0.197141i
$932$		0			0
$933$	−19.8486	+	11.4596i	−0.649812	+	0.375169i
$934$		0			0
$935$	0.388873	+	0.224516i	0.0127175	+	0.00734246i
$936$		0			0
$937$	−14.5330	+	25.1719i	−0.474772	+	0.822330i	−0.999583	−	0.0288896i	$-0.990803\pi$
$937$	−14.5330	+	25.1719i	−0.474772	+	0.822330i	0.524810	+	0.851219i	$0.324136\pi$
$938$		0			0
$939$	−93.6730			−3.05690
$940$		0			0
$941$	25.3641	+	14.6439i	0.826845	+	0.477379i	0.852771	−	0.522285i	$-0.174920\pi$
$941$	25.3641	+	14.6439i	0.826845	+	0.477379i	−0.0259264	+	0.999664i	$0.508254\pi$
$942$		0			0
$943$	−9.59407			−0.312426
$944$		0			0
$945$	27.7516	−	16.0224i	0.902759	−	0.521208i
$946$		0			0
$947$	−28.6181	+	16.5227i	−0.929965	+	0.536915i	−0.886800	−	0.462153i	$-0.847077\pi$
$947$	−28.6181	+	16.5227i	−0.929965	+	0.536915i	−0.0431643	+	0.999068i	$0.513744\pi$
$948$		0			0
$949$		−	30.4829i		−	0.989518i
$950$		0			0
$951$		−	62.5023i		−	2.02678i
$952$		0			0
$953$	−42.6275	+	24.6110i	−1.38084	+	0.797229i	−0.992259	−	0.124185i	$-0.960368\pi$
$953$	−42.6275	+	24.6110i	−1.38084	+	0.797229i	−0.388583	+	0.921414i	$0.627035\pi$
$954$		0			0
$955$	−8.65599	+	4.99754i	−0.280101	+	0.161716i
$956$		0			0
$957$	−6.15420			−0.198937
$958$		0			0
$959$	3.83956	+	2.21677i	0.123986	+	0.0715832i
$960$		0			0
$961$	0.250348			0.00807573
$962$		0			0
$963$	−27.0447	+	46.8429i	−0.871505	+	1.50949i
$964$		0			0
$965$	−5.07232	−	2.92851i	−0.163284	−	0.0942720i
$966$		0			0
$967$	−18.2983	+	10.5645i	−0.588433	+	0.339732i	−0.764478	−	0.644650i	$-0.777003\pi$
$967$	−18.2983	+	10.5645i	−0.588433	+	0.339732i	0.176045	+	0.984382i	$0.443670\pi$
$968$		0			0
$969$	−19.5401	−	10.0749i	−0.627720	−	0.323653i
$970$		0			0
$971$	8.46906	+	14.6689i	0.271785	+	0.470746i	0.969319	−	0.245806i	$-0.0790526\pi$
$971$	8.46906	+	14.6689i	0.271785	+	0.470746i	−0.697534	+	0.716552i	$0.745719\pi$
$972$		0			0
$973$	−21.8287	+	37.8084i	−0.699796	+	1.21208i
$974$		0			0
$975$	−9.34749	−	5.39678i	−0.299359	−	0.172835i
$976$		0			0
$977$		−	4.78497i		−	0.153085i	−0.997066	−	0.0765424i	$-0.975612\pi$
$977$		−	4.78497i		−	0.153085i	0.997066	−	0.0765424i	$-0.0243881\pi$
$978$		0			0
$979$	0.493149	−	0.854160i	0.0157611	−	0.0272991i
$980$		0			0
$981$		−	18.5184i		−	0.591246i
$982$		0			0
$983$	−4.92666	−	8.53322i	−0.157136	−	0.272167i	0.776699	−	0.629872i	$-0.216893\pi$
$983$	−4.92666	−	8.53322i	−0.157136	−	0.272167i	−0.933835	+	0.357705i	$0.883559\pi$
$984$		0			0
$985$	−8.33266	−	14.4326i	−0.265501	−	0.459861i
$986$		0			0
$987$	−49.5872			−1.57838
$988$		0			0
$989$	−22.9507			−0.729791
$990$		0			0
$991$	−28.3907	−	49.1742i	−0.901861	−	1.56207i	−0.825077	−	0.565021i	$-0.808868\pi$
$991$	−28.3907	−	49.1742i	−0.901861	−	1.56207i	−0.0767839	−	0.997048i	$-0.524465\pi$
$992$		0			0
$993$	−23.2432	−	40.2585i	−0.737602	−	1.27756i
$994$		0			0
$995$			19.0156i			0.602834i
$996$		0			0
$997$	17.3609	−	30.0699i	0.549824	−	0.952324i	−0.448462	−	0.893802i	$-0.648028\pi$
$997$	17.3609	−	30.0699i	0.549824	−	0.952324i	0.998286	−	0.0585217i	$-0.0186387\pi$
$998$		0			0
$999$		−	135.798i		−	4.29647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.bq.q.31.6	yes	12
4.3	odd	2	inner	1520.2.bq.q.31.1	✓	12
19.8	odd	6	inner	1520.2.bq.q.1471.1	yes	12
76.27	even	6	inner	1520.2.bq.q.1471.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1520.2.bq.q.31.1	✓	12	4.3	odd	2	inner
1520.2.bq.q.31.6	yes	12	1.1	even	1	trivial
1520.2.bq.q.1471.1	yes	12	19.8	odd	6	inner
1520.2.bq.q.1471.6	yes	12	76.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59901 + 2.76957i) q^{3} +(-0.500000 - 0.866025i) q^{5} -2.37033i q^{7} +(-3.61367 + 6.25906i) q^{9} +0.284720i q^{11} +(2.92290 + 1.68754i) q^{13} +(1.59901 - 2.76957i) q^{15} +(0.788551 + 1.36581i) q^{17} +(0.207178 + 4.35397i) q^{19} +(6.56478 - 3.79018i) q^{21} +(2.52180 + 1.45596i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.5191 q^{27} +(5.85333 + 3.37942i) q^{29} -5.59020 q^{31} +(-0.788551 + 0.455270i) q^{33} +(-2.05276 + 1.18516i) q^{35} +10.0449i q^{37} +10.7936i q^{39} +(-2.85333 + 1.64737i) q^{41} +(-6.82569 + 3.94081i) q^{43} +7.22734 q^{45} +(-5.66514 - 3.27077i) q^{47} +1.38155 q^{49} +(-2.52180 + 4.36789i) q^{51} +(-0.788551 - 0.455270i) q^{53} +(0.246575 - 0.142360i) q^{55} +(-11.7273 + 7.53584i) q^{57} +(4.65597 + 8.06438i) q^{59} +(7.30445 - 12.6517i) q^{61} +(14.8360 + 8.56559i) q^{63} -3.37507i q^{65} +(2.57264 - 4.45593i) q^{67} +9.31241i q^{69} +(6.09864 + 10.5631i) q^{71} +(-4.51589 - 7.82176i) q^{73} -3.19802 q^{75} +0.674879 q^{77} +(-3.01757 - 5.22658i) q^{79} +(-10.7762 - 18.6650i) q^{81} -7.16394i q^{83} +(0.788551 - 1.36581i) q^{85} +21.6149i q^{87} +(-3.00000 - 1.73205i) q^{89} +(4.00001 - 6.92822i) q^{91} +(-8.93879 - 15.4824i) q^{93} +(3.66706 - 2.35641i) q^{95} +(8.77623 - 5.06696i) q^{97} +(-1.78208 - 1.02888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} - 4 q^{9} + 18 q^{13} + 18 q^{17} + 24 q^{21} - 6 q^{25} + 24 q^{29} - 18 q^{33} + 12 q^{41} + 8 q^{45} - 28 q^{49} - 18 q^{53} - 62 q^{57} + 26 q^{61} + 16 q^{73} + 56 q^{77} - 66 q^{81}+ \cdots + 42 q^{97}+O(q^{100}) \) 12 * q - 6 * q^5 - 4 * q^9 + 18 * q^13 + 18 * q^17 + 24 * q^21 - 6 * q^25 + 24 * q^29 - 18 * q^33 + 12 * q^41 + 8 * q^45 - 28 * q^49 - 18 * q^53 - 62 * q^57 + 26 * q^61 + 16 * q^73 + 56 * q^77 - 66 * q^81 + 18 * q^85 - 36 * q^89 - 20 * q^93 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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