LMFDB - Embedded newform 572.2.n.a.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			521.1
Root			$-1.11876 - 0.812829i$ of defining polynomial
Character	$\chi$	$=$	572.521
Dual form			572.2.n.a.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.427329 + 1.31518i) q^{3} +(-1.65997 + 1.20604i) q^{5} +(0.287529 + 0.884923i) q^{7} +(0.879951 + 0.639322i) q^{9} +O(q^{10})$	\(q+(-0.427329 + 1.31518i) q^{3} +(-1.65997 + 1.20604i) q^{5} +(0.287529 + 0.884923i) q^{7} +(0.879951 + 0.639322i) q^{9} +(3.31376 - 0.137749i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.876810 - 2.69854i) q^{15} +(-3.76767 + 2.73738i) q^{17} +(-1.26429 + 3.89110i) q^{19} -1.28671 q^{21} -6.10938 q^{23} +(-0.244113 + 0.751301i) q^{25} +(-4.57314 + 3.32258i) q^{27} +(-2.15997 - 6.64769i) q^{29} +(-5.80583 - 4.21818i) q^{31} +(-1.23490 + 4.41707i) q^{33} +(-1.54454 - 1.12217i) q^{35} +(1.69788 + 5.22554i) q^{37} +(1.11876 - 0.812829i) q^{39} +(-3.56250 + 10.9643i) q^{41} +5.01724 q^{43} -2.23174 q^{45} +(2.43244 - 7.48627i) q^{47} +(4.96270 - 3.60562i) q^{49} +(-1.99012 - 6.12495i) q^{51} +(11.5119 + 8.36386i) q^{53} +(-5.33462 + 4.22519i) q^{55} +(-4.57724 - 3.32556i) q^{57} +(-4.17219 - 12.8407i) q^{59} +(2.00498 - 1.45670i) q^{61} +(-0.312739 + 0.962512i) q^{63} +2.05184 q^{65} +4.44388 q^{67} +(2.61072 - 8.03496i) q^{69} +(-3.28225 + 2.38470i) q^{71} +(3.68976 + 11.3559i) q^{73} +(-0.883783 - 0.642106i) q^{75} +(1.07470 + 2.89282i) q^{77} +(11.0809 + 8.05071i) q^{79} +(-1.40724 - 4.33103i) q^{81} +(-11.2012 + 8.13818i) q^{83} +(2.95285 - 9.08793i) q^{85} +9.66595 q^{87} -11.8872 q^{89} +(0.287529 - 0.884923i) q^{91} +(8.02869 - 5.83318i) q^{93} +(-2.59412 - 7.98389i) q^{95} +(3.86541 + 2.80838i) q^{97} +(3.00402 + 1.99735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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			0
$2$		0			0
$3$	−0.427329	+	1.31518i	−0.246719	+	0.759322i	0.748630	+	0.662988i	$0.230712\pi$
$3$	−0.427329	+	1.31518i	−0.246719	+	0.759322i	−0.995349	+	0.0963344i	$0.969288\pi$
$4$		0			0
$5$	−1.65997	+	1.20604i	−0.742362	+	0.539357i	−0.893450	−	0.449163i	$-0.851722\pi$
$5$	−1.65997	+	1.20604i	−0.742362	+	0.539357i	0.151088	+	0.988520i	$0.451722\pi$
$6$		0			0
$7$	0.287529	+	0.884923i	0.108676	+	0.334469i	0.990576	−	0.136967i	$-0.0437356\pi$
$7$	0.287529	+	0.884923i	0.108676	+	0.334469i	−0.881900	+	0.471437i	$0.843736\pi$
$8$		0			0
$9$	0.879951	+	0.639322i	0.293317	+	0.213107i
$10$		0			0
$11$	3.31376	−	0.137749i	0.999137	−	0.0415328i
$11$	3.31376	−	0.137749i	0.999137	−	0.0415328i
$12$		0			0
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$		0			0
$15$	−0.876810	−	2.69854i	−0.226391	−	0.696761i
$16$		0			0
$17$	−3.76767	+	2.73738i	−0.913795	+	0.663911i	−0.941972	−	0.335692i	$-0.891030\pi$
$17$	−3.76767	+	2.73738i	−0.913795	+	0.663911i	0.0281766	+	0.999603i	$0.491030\pi$
$18$		0			0
$19$	−1.26429	+	3.89110i	−0.290049	+	0.892679i	0.694791	+	0.719212i	$0.255497\pi$
$19$	−1.26429	+	3.89110i	−0.290049	+	0.892679i	−0.984840	+	0.173467i	$0.944503\pi$
$20$		0			0
$21$	−1.28671			−0.280782
$22$		0			0
$23$	−6.10938			−1.27389			−0.636947	−	0.770908i	$-0.719803\pi$
$23$	−6.10938			−1.27389			−0.636947	+	0.770908i	$0.719803\pi$
$24$		0			0
$25$	−0.244113	+	0.751301i	−0.0488225	+	0.150260i
$26$		0			0
$27$	−4.57314	+	3.32258i	−0.880102	+	0.639431i
$28$		0			0
$29$	−2.15997	−	6.64769i	−0.401095	−	1.23445i	−0.924112	−	0.382122i	$-0.875193\pi$
$29$	−2.15997	−	6.64769i	−0.401095	−	1.23445i	0.523016	−	0.852323i	$-0.324807\pi$
$30$		0			0
$31$	−5.80583	−	4.21818i	−1.04276	−	0.757608i	−0.0719356	−	0.997409i	$-0.522918\pi$
$31$	−5.80583	−	4.21818i	−1.04276	−	0.757608i	−0.970822	+	0.239802i	$0.922918\pi$
$32$		0			0
$33$	−1.23490	+	4.41707i	−0.214969	+	0.768914i
$34$		0			0
$35$	−1.54454	−	1.12217i	−0.261075	−	0.189682i
$36$		0			0
$37$	1.69788	+	5.22554i	0.279130	+	0.859074i	0.988097	+	0.153832i	$0.0491615\pi$
$37$	1.69788	+	5.22554i	0.279130	+	0.859074i	−0.708967	+	0.705242i	$0.750838\pi$
$38$		0			0
$39$	1.11876	−	0.812829i	0.179145	−	0.130157i
$40$		0			0
$41$	−3.56250	+	10.9643i	−0.556369	+	1.71233i	0.135930	+	0.990718i	$0.456598\pi$
$41$	−3.56250	+	10.9643i	−0.556369	+	1.71233i	−0.692300	+	0.721610i	$0.743402\pi$
$42$		0			0
$43$	5.01724			0.765122			0.382561	−	0.923930i	$-0.375042\pi$
$43$	5.01724			0.765122			0.382561	+	0.923930i	$0.375042\pi$
$44$		0			0
$45$	−2.23174			−0.332688
$46$		0			0
$47$	2.43244	−	7.48627i	0.354807	−	1.09198i	−0.601314	−	0.799013i	$-0.705356\pi$
$47$	2.43244	−	7.48627i	0.354807	−	1.09198i	0.956121	−	0.292972i	$-0.0946441\pi$
$48$		0			0
$49$	4.96270	−	3.60562i	0.708958	−	0.515088i
$50$		0			0
$51$	−1.99012	−	6.12495i	−0.278672	−	0.857664i
$52$		0			0
$53$	11.5119	+	8.36386i	1.58128	+	1.14886i	0.915214	+	0.402969i	$0.132022\pi$
$53$	11.5119	+	8.36386i	1.58128	+	1.14886i	0.666063	+	0.745896i	$0.267978\pi$
$54$		0			0
$55$	−5.33462	+	4.22519i	−0.719320	+	0.569724i
$56$		0			0
$57$	−4.57724	−	3.32556i	−0.606270	−	0.440481i
$58$		0			0
$59$	−4.17219	−	12.8407i	−0.543172	−	1.67171i	−0.725296	−	0.688437i	$-0.758297\pi$
$59$	−4.17219	−	12.8407i	−0.543172	−	1.67171i	0.182123	−	0.983276i	$-0.441703\pi$
$60$		0			0
$61$	2.00498	−	1.45670i	0.256711	−	0.186511i	−0.451985	−	0.892026i	$-0.649284\pi$
$61$	2.00498	−	1.45670i	0.256711	−	0.186511i	0.708696	+	0.705514i	$0.249284\pi$
$62$		0			0
$63$	−0.312739	+	0.962512i	−0.0394014	+	0.121265i
$64$		0			0
$65$	2.05184			0.254499
$66$		0			0
$67$	4.44388			0.542907			0.271453	−	0.962452i	$-0.412496\pi$
$67$	4.44388			0.542907			0.271453	+	0.962452i	$0.412496\pi$
$68$		0			0
$69$	2.61072	−	8.03496i	0.314293	−	0.967296i
$70$		0			0
$71$	−3.28225	+	2.38470i	−0.389532	+	0.283011i	−0.765264	−	0.643717i	$-0.777391\pi$
$71$	−3.28225	+	2.38470i	−0.389532	+	0.283011i	0.375732	+	0.926728i	$0.377391\pi$
$72$		0			0
$73$	3.68976	+	11.3559i	0.431854	+	1.32911i	0.896277	+	0.443496i	$0.146262\pi$
$73$	3.68976	+	11.3559i	0.431854	+	1.32911i	−0.464423	+	0.885614i	$0.653738\pi$
$74$		0			0
$75$	−0.883783	−	0.642106i	−0.102051	−	0.0741440i
$76$		0			0
$77$	1.07470	+	2.89282i	0.122473	+	0.329667i
$78$		0			0
$79$	11.0809	+	8.05071i	1.24669	+	0.905776i	0.998025	−	0.0628127i	$-0.0200071\pi$
$79$	11.0809	+	8.05071i	1.24669	+	0.905776i	0.248668	+	0.968589i	$0.420007\pi$
$80$		0			0
$81$	−1.40724	−	4.33103i	−0.156360	−	0.481226i
$82$		0			0
$83$	−11.2012	+	8.13818i	−1.22950	+	0.893282i	−0.996852	−	0.0792803i	$-0.974738\pi$
$83$	−11.2012	+	8.13818i	−1.22950	+	0.893282i	−0.232644	+	0.972562i	$0.574738\pi$
$84$		0			0
$85$	2.95285	−	9.08793i	0.320281	−	0.985724i
$86$		0			0
$87$	9.66595			1.03630
$88$		0			0
$89$	−11.8872			−1.26004			−0.630018	−	0.776580i	$-0.716953\pi$
$89$	−11.8872			−1.26004			−0.630018	+	0.776580i	$0.716953\pi$
$90$		0			0
$91$	0.287529	−	0.884923i	0.0301412	−	0.0927651i
$92$		0			0
$93$	8.02869	−	5.83318i	0.832536	−	0.604873i
$94$		0			0
$95$	−2.59412	−	7.98389i	−0.266152	−	0.819130i
$96$		0			0
$97$	3.86541	+	2.80838i	0.392473	+	0.285148i	0.766468	−	0.642282i	$-0.222012\pi$
$97$	3.86541	+	2.80838i	0.392473	+	0.285148i	−0.373995	+	0.927431i	$0.622012\pi$
$98$		0			0
$99$	3.00402	+	1.99735i	0.301915	+	0.200741i
$100$		0			0
$101$	13.5460	+	9.84175i	1.34788	+	0.979291i	0.999114	+	0.0420800i	$0.0133984\pi$
$101$	13.5460	+	9.84175i	1.34788	+	0.979291i	0.348764	+	0.937211i	$0.386602\pi$
$102$		0			0
$103$	−0.659553	−	2.02989i	−0.0649876	−	0.200011i	0.913290	−	0.407310i	$-0.133533\pi$
$103$	−0.659553	−	2.02989i	−0.0649876	−	0.200011i	−0.978278	+	0.207298i	$0.933533\pi$
$104$		0			0
$105$	2.13589	−	1.55182i	0.208442	−	0.151442i
$106$		0			0
$107$	0.557547	−	1.71595i	0.0539001	−	0.165887i	−0.920483	−	0.390783i	$-0.872204\pi$
$107$	0.557547	−	1.71595i	0.0539001	−	0.165887i	0.974383	+	0.224896i	$0.0722042\pi$
$108$		0			0
$109$	11.3081			1.08311			0.541557	−	0.840664i	$-0.317835\pi$
$109$	11.3081			1.08311			0.541557	+	0.840664i	$0.317835\pi$
$110$		0			0
$111$	−7.59811			−0.721180
$112$		0			0
$113$	−3.11199	+	9.57771i	−0.292751	+	0.900996i	0.691216	+	0.722648i	$0.257075\pi$
$113$	−3.11199	+	9.57771i	−0.292751	+	0.900996i	−0.983968	+	0.178348i	$0.942925\pi$
$114$		0			0
$115$	10.1414	−	7.36815i	0.945690	−	0.687084i
$116$		0			0
$117$	−0.336111	−	1.03444i	−0.0310735	−	0.0956344i
$118$		0			0
$119$	−3.50568	−	2.54703i	−0.321365	−	0.233486i
$120$		0			0
$121$	10.9621	−	0.912933i	0.996550	−	0.0829939i
$122$		0			0
$123$	−12.8977	−	9.37069i	−1.16294	−	0.844927i
$124$		0			0
$125$	−3.67114	−	11.2986i	−0.328357	−	1.01058i
$126$		0			0
$127$	−1.30493	+	0.948085i	−0.115794	+	0.0841290i	−0.644175	−	0.764878i	$-0.722799\pi$
$127$	−1.30493	+	0.948085i	−0.115794	+	0.0841290i	0.528381	+	0.849007i	$0.322799\pi$
$128$		0			0
$129$	−2.14401	+	6.59860i	−0.188770	+	0.580974i
$130$		0			0
$131$	15.3069			1.33737			0.668685	−	0.743545i	$-0.266857\pi$
$131$	15.3069			1.33737			0.668685	+	0.743545i	$0.266857\pi$
$132$		0			0
$133$	−3.80684			−0.330095
$134$		0			0
$135$	3.58412	−	11.0308i	0.308472	−	0.949379i
$136$		0			0
$137$	3.36915	−	2.44783i	0.287846	−	0.209132i	−0.434487	−	0.900678i	$-0.643070\pi$
$137$	3.36915	−	2.44783i	0.287846	−	0.209132i	0.722332	+	0.691546i	$0.243070\pi$
$138$		0			0
$139$	−4.79794	−	14.7666i	−0.406956	−	1.25248i	−0.919251	−	0.393673i	$-0.871204\pi$
$139$	−4.79794	−	14.7666i	−0.406956	−	1.25248i	0.512294	−	0.858810i	$-0.328796\pi$
$140$		0			0
$141$	8.80637	+	6.39820i	0.741630	+	0.538826i
$142$		0			0
$143$	−2.76186	−	1.83634i	−0.230958	−	0.153562i
$144$		0			0
$145$	11.6029	+	8.42997i	0.963565	+	0.700071i
$146$		0			0
$147$	2.62134	+	8.06766i	0.216205	+	0.665409i
$148$		0			0
$149$	−7.22693	+	5.25067i	−0.592053	+	0.430152i	−0.843049	−	0.537836i	$-0.819242\pi$
$149$	−7.22693	+	5.25067i	−0.592053	+	0.430152i	0.250996	+	0.967988i	$0.419242\pi$
$150$		0			0
$151$	−1.62179	+	4.99137i	−0.131980	+	0.406192i	−0.995108	−	0.0987928i	$-0.968502\pi$
$151$	−1.62179	+	4.99137i	−0.131980	+	0.406192i	0.863128	+	0.504985i	$0.168502\pi$
$152$		0			0
$153$	−5.06543			−0.409516
$154$		0			0
$155$	14.7248			1.18272
$156$		0			0
$157$	3.15891	−	9.72211i	0.252108	−	0.775909i	−0.742278	−	0.670093i	$-0.766254\pi$
$157$	3.15891	−	9.72211i	0.252108	−	0.775909i	0.994386	−	0.105816i	$-0.0337456\pi$
$158$		0			0
$159$	−15.9194	+	11.5661i	−1.26249	+	0.917252i
$160$		0			0
$161$	−1.75662	−	5.40633i	−0.138441	−	0.426078i
$162$		0			0
$163$	11.2172	+	8.14980i	0.878602	+	0.638342i	0.932881	−	0.360184i	$-0.117286\pi$
$163$	11.2172	+	8.14980i	0.878602	+	0.638342i	−0.0542794	+	0.998526i	$0.517286\pi$
$164$		0			0
$165$	−3.27726	−	8.82156i	−0.255134	−	0.686757i
$166$		0			0
$167$	−8.98515	−	6.52809i	−0.695292	−	0.505159i	0.183104	−	0.983094i	$-0.441386\pi$
$167$	−8.98515	−	6.52809i	−0.695292	−	0.505159i	−0.878395	+	0.477935i	$0.841386\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$		0			0
$171$	−3.60018	+	2.61568i	−0.275313	+	0.200026i
$172$		0			0
$173$	1.25471	−	3.86161i	0.0953941	−	0.293593i	−0.891962	−	0.452110i	$-0.850671\pi$
$173$	1.25471	−	3.86161i	0.0953941	−	0.293593i	0.987356	+	0.158517i	$0.0506714\pi$
$174$		0			0
$175$	−0.735033			−0.0555633
$176$		0			0
$177$	18.6707			1.40338
$178$		0			0
$179$	5.22117	−	16.0691i	0.390249	−	1.20106i	−0.542352	−	0.840151i	$-0.682466\pi$
$179$	5.22117	−	16.0691i	0.390249	−	1.20106i	0.932601	−	0.360910i	$-0.117534\pi$
$180$		0			0
$181$	15.1261	−	10.9898i	1.12432	−	0.816863i	0.139458	−	0.990228i	$-0.455464\pi$
$181$	15.1261	−	10.9898i	1.12432	−	0.816863i	0.984858	+	0.173365i	$0.0554640\pi$
$182$		0			0
$183$	1.05905	+	3.25941i	0.0782869	+	0.240942i
$184$		0			0
$185$	−9.12064	−	6.62654i	−0.670563	−	0.487193i
$186$		0			0
$187$	−12.1081	+	9.59001i	−0.885433	+	0.701291i
$188$		0			0
$189$	−4.25514	−	3.09154i	−0.309516	−	0.224876i
$190$		0			0
$191$	−0.618584	−	1.90381i	−0.0447592	−	0.137755i	0.926180	−	0.377083i	$-0.123073\pi$
$191$	−0.618584	−	1.90381i	−0.0447592	−	0.137755i	−0.970939	+	0.239328i	$0.923073\pi$
$192$		0			0
$193$	−8.75018	+	6.35738i	−0.629852	+	0.457614i	−0.856349	−	0.516398i	$-0.827273\pi$
$193$	−8.75018	+	6.35738i	−0.629852	+	0.457614i	0.226497	+	0.974012i	$0.427273\pi$
$194$		0			0
$195$	−0.876810	+	2.69854i	−0.0627897	+	0.193247i
$196$		0			0
$197$	−4.14884			−0.295593			−0.147796	−	0.989018i	$-0.547218\pi$
$197$	−4.14884			−0.295593			−0.147796	+	0.989018i	$0.547218\pi$
$198$		0			0
$199$	13.9330			0.987684			0.493842	−	0.869552i	$-0.335592\pi$
$199$	13.9330			0.987684			0.493842	+	0.869552i	$0.335592\pi$
$200$		0			0
$201$	−1.89900	+	5.84453i	−0.133945	+	0.412241i
$202$		0			0
$203$	5.26164	−	3.82280i	0.369295	−	0.268308i
$204$		0			0
$205$	−7.30967	−	22.4969i	−0.510530	−	1.57125i
$206$		0			0
$207$	−5.37596	−	3.90586i	−0.373655	−	0.271476i
$208$		0			0
$209$	−3.65358	+	13.0683i	−0.252723	+	0.903955i
$210$		0			0
$211$	−8.18897	−	5.94964i	−0.563752	−	0.409590i	0.269078	−	0.963118i	$-0.413281\pi$
$211$	−8.18897	−	5.94964i	−0.563752	−	0.409590i	−0.832830	+	0.553528i	$0.813281\pi$
$212$		0			0
$213$	−1.73371	−	5.33582i	−0.118792	−	0.365604i
$214$		0			0
$215$	−8.32848	+	6.05099i	−0.567997	+	0.412674i
$216$		0			0
$217$	2.06342	−	6.35056i	0.140074	−	0.431104i
$218$		0			0
$219$	−16.5119			−1.11577
$220$		0			0
$221$	4.65710			0.313271
$222$		0			0
$223$	−3.15564	+	9.71207i	−0.211317	+	0.650368i	0.788077	+	0.615576i	$0.211077\pi$
$223$	−3.15564	+	9.71207i	−0.211317	+	0.650368i	−0.999395	+	0.0347917i	$0.988923\pi$
$224$		0			0
$225$	−0.695131	+	0.505042i	−0.0463420	+	0.0336695i
$226$		0			0
$227$	1.65272	+	5.08654i	0.109695	+	0.337606i	0.990804	−	0.135308i	$-0.0432023\pi$
$227$	1.65272	+	5.08654i	0.109695	+	0.337606i	−0.881109	+	0.472914i	$0.843202\pi$
$228$		0			0
$229$	22.0989	+	16.0558i	1.46034	+	1.06100i	0.983274	+	0.182130i	$0.0582993\pi$
$229$	22.0989	+	16.0558i	1.46034	+	1.06100i	0.477065	+	0.878868i	$0.341701\pi$
$230$		0			0
$231$	−4.26384	+	0.177242i	−0.280540	+	0.0116617i
$232$		0			0
$233$	9.44133	+	6.85953i	0.618522	+	0.449383i	0.852405	−	0.522882i	$-0.175143\pi$
$233$	9.44133	+	6.85953i	0.618522	+	0.449383i	−0.233883	+	0.972265i	$0.575143\pi$
$234$		0			0
$235$	4.99096	+	15.3606i	0.325574	+	1.00202i
$236$		0			0
$237$	−15.3233	+	11.1331i	−0.995358	+	0.723170i
$238$		0			0
$239$	−2.15946	+	6.64614i	−0.139684	+	0.429903i	−0.996289	−	0.0860695i	$-0.972569\pi$
$239$	−2.15946	+	6.64614i	−0.139684	+	0.429903i	0.856605	+	0.515972i	$0.172569\pi$
$240$		0			0
$241$	−10.7789			−0.694330			−0.347165	−	0.937804i	$-0.612856\pi$
$241$	−10.7789			−0.694330			−0.347165	+	0.937804i	$0.612856\pi$
$242$		0			0
$243$	−10.6607			−0.683884
$244$		0			0
$245$	−3.88943	+	11.9704i	−0.248487	+	0.764763i
$246$		0			0
$247$	3.30996	−	2.40483i	0.210608	−	0.153016i
$248$		0			0
$249$	−5.91659	−	18.2094i	−0.374949	−	1.15397i
$250$		0			0
$251$	23.0730	+	16.7635i	1.45636	+	1.05811i	0.984293	+	0.176541i	$0.0564909\pi$
$251$	23.0730	+	16.7635i	1.45636	+	1.05811i	0.472064	+	0.881564i	$0.343509\pi$
$252$		0			0
$253$	−20.2450	+	0.841559i	−1.27279	+	0.0529084i
$254$		0			0
$255$	10.6905	+	7.76708i	0.669463	+	0.486393i
$256$		0			0
$257$	−1.47351	−	4.53501i	−0.0919153	−	0.282886i	0.894522	−	0.447023i	$-0.147516\pi$
$257$	−1.47351	−	4.53501i	−0.0919153	−	0.282886i	−0.986437	+	0.164137i	$0.947516\pi$
$258$		0			0
$259$	−4.13601	+	3.00499i	−0.256999	+	0.186721i
$260$		0			0
$261$	2.34935	−	7.23056i	0.145421	−	0.447560i
$262$		0			0
$263$	−8.65998			−0.533997			−0.266999	−	0.963697i	$-0.586032\pi$
$263$	−8.65998			−0.533997			−0.266999	+	0.963697i	$0.586032\pi$
$264$		0			0
$265$	−29.1965			−1.79353
$266$		0			0
$267$	5.07973	−	15.6338i	0.310875	−	0.956773i
$268$		0			0
$269$	3.55537	−	2.58313i	0.216775	−	0.157496i	−0.474099	−	0.880472i	$-0.657226\pi$
$269$	3.55537	−	2.58313i	0.216775	−	0.157496i	0.690874	+	0.722976i	$0.257226\pi$
$270$		0			0
$271$	−5.59654	−	17.2244i	−0.339965	−	1.04631i	−0.964224	−	0.265088i	$-0.914599\pi$
$271$	−5.59654	−	17.2244i	−0.339965	−	1.04631i	0.624259	−	0.781218i	$-0.285401\pi$
$272$		0			0
$273$	1.04097	+	0.756307i	0.0630022	+	0.0457738i
$274$		0			0
$275$	−0.705441	+	2.52326i	−0.0425397	+	0.152158i
$276$		0			0
$277$	−11.5685	−	8.40501i	−0.695084	−	0.505008i	0.183243	−	0.983068i	$-0.441340\pi$
$277$	−11.5685	−	8.40501i	−0.695084	−	0.505008i	−0.878328	+	0.478059i	$0.841340\pi$
$278$		0			0
$279$	−2.41207	−	7.42359i	−0.144407	−	0.444439i
$280$		0			0
$281$	−6.08476	+	4.42084i	−0.362987	+	0.263725i	−0.754297	−	0.656534i	$-0.772022\pi$
$281$	−6.08476	+	4.42084i	−0.362987	+	0.263725i	0.391310	+	0.920259i	$0.372022\pi$
$282$		0			0
$283$	−9.63612	+	29.6569i	−0.572808	+	1.76292i	0.0707178	+	0.997496i	$0.477471\pi$
$283$	−9.63612	+	29.6569i	−0.572808	+	1.76292i	−0.643526	+	0.765425i	$0.722529\pi$
$284$		0			0
$285$	11.6088			0.687648
$286$		0			0
$287$	−10.7268			−0.633185
$288$		0			0
$289$	1.44886	−	4.45912i	0.0852268	−	0.262301i
$290$		0			0
$291$	−5.34534	+	3.88362i	−0.313350	+	0.227662i
$292$		0			0
$293$	8.55827	+	26.3396i	0.499979	+	1.53878i	0.809051	+	0.587739i	$0.199982\pi$
$293$	8.55827	+	26.3396i	0.499979	+	1.53878i	−0.309071	+	0.951039i	$0.600018\pi$
$294$		0			0
$295$	22.4121	+	16.2833i	1.30488	+	0.948052i
$296$		0			0
$297$	−14.6966	+	11.6402i	−0.852785	+	0.675433i
$298$		0			0
$299$	4.94259	+	3.59100i	0.285837	+	0.207673i
$300$		0			0
$301$	1.44260	+	4.43987i	0.0831502	+	0.255910i
$302$		0			0
$303$	−18.7323	+	13.6098i	−1.07614	+	0.781864i
$304$		0			0
$305$	−1.57136	+	4.83616i	−0.0899761	+	0.276918i
$306$		0			0
$307$	20.8377			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$307$	20.8377			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$308$		0			0
$309$	2.95153			0.167907
$310$		0			0
$311$	−1.59956	+	4.92295i	−0.0907029	+	0.279155i	−0.986110	−	0.166094i	$-0.946885\pi$
$311$	−1.59956	+	4.92295i	−0.0907029	+	0.279155i	0.895407	+	0.445248i	$0.146885\pi$
$312$		0			0
$313$	22.7400	−	16.5215i	1.28534	−	0.933853i	0.285638	−	0.958338i	$-0.407794\pi$
$313$	22.7400	−	16.5215i	1.28534	−	0.933853i	0.999700	+	0.0244847i	$0.00779450\pi$
$314$		0			0
$315$	−0.641690	−	1.97492i	−0.0361551	−	0.111274i
$316$		0			0
$317$	−10.9985	−	7.99089i	−0.617738	−	0.448813i	0.234392	−	0.972142i	$-0.424690\pi$
$317$	−10.9985	−	7.99089i	−0.617738	−	0.448813i	−0.852131	+	0.523329i	$0.824690\pi$
$318$		0			0
$319$	−8.07332	−	21.7313i	−0.452019	−	1.21672i
$320$		0			0
$321$	2.01854	+	1.46655i	0.112664	+	0.0818551i
$322$		0			0
$323$	−5.88794	−	18.1212i	−0.327614	−	1.00829i
$324$		0			0
$325$	0.639095	−	0.464330i	0.0354506	−	0.0257564i
$326$		0			0
$327$	−4.83226	+	14.8722i	−0.267225	+	0.822433i
$328$		0			0
$329$	7.32416			0.403794
$330$		0			0
$331$	24.3495			1.33837			0.669184	−	0.743097i	$-0.266644\pi$
$331$	24.3495			1.33837			0.669184	+	0.743097i	$0.266644\pi$
$332$		0			0
$333$	−1.84675	+	5.68372i	−0.101201	+	0.311466i
$334$		0			0
$335$	−7.37672	+	5.35950i	−0.403033	+	0.292821i
$336$		0			0
$337$	8.22120	+	25.3023i	0.447837	+	1.37830i	0.879342	+	0.476191i	$0.157983\pi$
$337$	8.22120	+	25.3023i	0.447837	+	1.37830i	−0.431504	+	0.902111i	$0.642017\pi$
$338$		0			0
$339$	−11.2666	−	8.18568i	−0.611919	−	0.444585i
$340$		0			0
$341$	−19.8202	−	13.1783i	−1.07332	−	0.713645i
$342$		0			0
$343$	9.88693	+	7.18328i	0.533844	+	0.387860i
$344$		0			0
$345$	5.35677	+	16.4864i	0.288399	+	0.887600i
$346$		0			0
$347$	10.5171	−	7.64112i	0.564588	−	0.410197i	−0.268547	−	0.963266i	$-0.586544\pi$
$347$	10.5171	−	7.64112i	0.564588	−	0.410197i	0.833135	+	0.553069i	$0.186544\pi$
$348$		0			0
$349$	3.89384	−	11.9840i	0.208433	−	0.641490i	−0.791122	−	0.611658i	$-0.790503\pi$
$349$	3.89384	−	11.9840i	0.208433	−	0.641490i	0.999555	−	0.0298317i	$-0.00949715\pi$
$350$		0			0
$351$	5.65272			0.301720
$352$		0			0
$353$	0.124932			0.00664947			0.00332474	−	0.999994i	$-0.498942\pi$
$353$	0.124932			0.00664947			0.00332474	+	0.999994i	$0.498942\pi$
$354$		0			0
$355$	2.57241	−	7.91705i	0.136529	−	0.420193i
$356$		0			0
$357$	4.84789	−	3.52220i	0.256578	−	0.186414i
$358$		0			0
$359$	−3.88803	−	11.9661i	−0.205202	−	0.631548i	−0.999705	−	0.0242872i	$-0.992268\pi$
$359$	−3.88803	−	11.9661i	−0.205202	−	0.631548i	0.794503	−	0.607261i	$-0.207732\pi$
$360$		0			0
$361$	1.82913	+	1.32894i	0.0962702	+	0.0699444i
$362$		0			0
$363$	−3.48373	+	14.8072i	−0.182848	+	0.777179i
$364$		0			0
$365$	−19.8206	−	14.4005i	−1.03746	−	0.753756i
$366$		0			0
$367$	0.333616	+	1.02676i	0.0174146	+	0.0535966i	0.959386	−	0.282096i	$-0.0910297\pi$
$367$	0.333616	+	1.02676i	0.0174146	+	0.0535966i	−0.941972	+	0.335693i	$0.891030\pi$
$368$		0			0
$369$	−10.1445	+	7.37042i	−0.528102	+	0.383689i
$370$		0			0
$371$	−4.09138	+	12.5920i	−0.212414	+	0.653742i
$372$		0			0
$373$	−27.1650			−1.40655			−0.703274	−	0.710919i	$-0.748279\pi$
$373$	−27.1650			−1.40655			−0.703274	+	0.710919i	$0.748279\pi$
$374$		0			0
$375$	16.4285			0.848366
$376$		0			0
$377$	−2.15997	+	6.64769i	−0.111244	+	0.342373i
$378$		0			0
$379$	10.9597	−	7.96270i	0.562963	−	0.409016i	−0.269579	−	0.962978i	$-0.586885\pi$
$379$	10.9597	−	7.96270i	0.562963	−	0.409016i	0.832542	+	0.553962i	$0.186885\pi$
$380$		0			0
$381$	−0.689273	−	2.12136i	−0.0353125	−	0.108681i
$382$		0			0
$383$	−2.87029	−	2.08539i	−0.146665	−	0.106558i	0.512033	−	0.858966i	$-0.328892\pi$
$383$	−2.87029	−	2.08539i	−0.146665	−	0.106558i	−0.658698	+	0.752407i	$0.728892\pi$
$384$		0			0
$385$	−5.27282	−	3.50586i	−0.268728	−	0.178675i
$386$		0			0
$387$	4.41493	+	3.20763i	0.224423	+	0.163053i
$388$		0			0
$389$	−4.58255	−	14.1036i	−0.232344	−	0.715082i	−0.997463	−	0.0711926i	$-0.977320\pi$
$389$	−4.58255	−	14.1036i	−0.232344	−	0.715082i	0.765118	−	0.643890i	$-0.222680\pi$
$390$		0			0
$391$	23.0182	−	16.7237i	1.16408	−	0.845752i
$392$		0			0
$393$	−6.54109	+	20.1314i	−0.329954	+	1.01550i
$394$		0			0
$395$	−28.1034			−1.41403
$396$		0			0
$397$	−15.7679			−0.791367			−0.395684	−	0.918387i	$-0.629492\pi$
$397$	−15.7679			−0.791367			−0.395684	+	0.918387i	$0.629492\pi$
$398$		0			0
$399$	1.62677	−	5.00670i	0.0814406	−	0.250648i
$400$		0			0
$401$	−13.1547	+	9.55747i	−0.656916	+	0.477277i	−0.865620	−	0.500701i	$-0.833075\pi$
$401$	−13.1547	+	9.55747i	−0.656916	+	0.477277i	0.208704	+	0.977979i	$0.433075\pi$
$402$		0			0
$403$	2.21763	+	6.82516i	0.110468	+	0.339985i
$404$		0			0
$405$	7.55937	+	5.49220i	0.375628	+	0.272910i
$406$		0			0
$407$	6.34619	+	17.0823i	0.314569	+	0.846740i
$408$		0			0
$409$	−20.5591	−	14.9371i	−1.01658	−	0.738592i	−0.0510045	−	0.998698i	$-0.516242\pi$
$409$	−20.5591	−	14.9371i	−1.01658	−	0.738592i	−0.965580	+	0.260107i	$0.916242\pi$
$410$		0			0
$411$	1.77961	+	5.47708i	0.0877817	+	0.270164i
$412$		0			0
$413$	10.1634	−	7.38413i	0.500107	−	0.363349i
$414$		0			0
$415$	8.77878	−	27.0183i	0.430933	−	1.32628i
$416$		0			0
$417$	21.4710			1.05144
$418$		0			0
$419$	−36.3686			−1.77672			−0.888361	−	0.459145i	$-0.848156\pi$
$419$	−36.3686			−1.77672			−0.888361	+	0.459145i	$0.848156\pi$
$420$		0			0
$421$	−8.79858	+	27.0792i	−0.428817	+	1.31976i	0.470475	+	0.882413i	$0.344082\pi$
$421$	−8.79858	+	27.0792i	−0.428817	+	1.31976i	−0.899292	+	0.437349i	$0.855918\pi$
$422$		0			0
$423$	6.92656	−	5.03244i	0.336781	−	0.244686i
$424$		0			0
$425$	−1.13686	−	3.49889i	−0.0551457	−	0.169721i
$426$		0			0
$427$	1.86556	+	1.35541i	0.0902806	+	0.0655927i
$428$		0			0
$429$	3.59535	−	2.84763i	0.173585	−	0.137485i
$430$		0			0
$431$	−21.4481	−	15.5830i	−1.03312	−	0.750605i	−0.0641883	−	0.997938i	$-0.520446\pi$
$431$	−21.4481	−	15.5830i	−1.03312	−	0.750605i	−0.968931	+	0.247333i	$0.920446\pi$
$432$		0			0
$433$	−5.90912	−	18.1864i	−0.283974	−	0.873983i	−0.986704	−	0.162526i	$-0.948036\pi$
$433$	−5.90912	−	18.1864i	−0.283974	−	0.873983i	0.702730	−	0.711457i	$-0.251964\pi$
$434$		0			0
$435$	−16.0452	+	11.6575i	−0.769309	+	0.558935i
$436$		0			0
$437$	7.72405	−	23.7722i	0.369491	−	1.13718i
$438$		0			0
$439$	1.28718			0.0614339			0.0307169	−	0.999528i	$-0.490221\pi$
$439$	1.28718			0.0614339			0.0307169	+	0.999528i	$0.490221\pi$
$440$		0			0
$441$	6.67209			0.317718
$442$		0			0
$443$	6.24502	−	19.2202i	0.296710	−	0.913179i	−0.685932	−	0.727666i	$-0.740605\pi$
$443$	6.24502	−	19.2202i	0.296710	−	0.913179i	0.982642	−	0.185513i	$-0.0593948\pi$
$444$		0			0
$445$	19.7323	−	14.3364i	0.935403	−	0.679610i
$446$		0			0
$447$	−3.81732	−	11.7485i	−0.180553	−	0.555686i
$448$		0			0
$449$	15.0933	+	10.9659i	0.712297	+	0.517514i	0.883914	−	0.467650i	$-0.154899\pi$
$449$	15.0933	+	10.9659i	0.712297	+	0.517514i	−0.171617	+	0.985164i	$0.554899\pi$
$450$		0			0
$451$	−10.2950	+	36.8237i	−0.484771	+	1.73396i
$452$		0			0
$453$	−5.87153	−	4.26592i	−0.275869	−	0.200430i
$454$		0			0
$455$	0.589962	+	1.81572i	0.0276579	+	0.0851221i
$456$		0			0
$457$	14.4552	−	10.5023i	0.676187	−	0.491279i	−0.195904	−	0.980623i	$-0.562764\pi$
$457$	14.4552	−	10.5023i	0.676187	−	0.491279i	0.872091	+	0.489345i	$0.162764\pi$
$458$		0			0
$459$	8.13496	−	25.0368i	0.379707	−	1.16862i
$460$		0			0
$461$	−15.3279			−0.713890			−0.356945	−	0.934125i	$-0.616182\pi$
$461$	−15.3279			−0.713890			−0.356945	+	0.934125i	$0.616182\pi$
$462$		0			0
$463$	32.4079			1.50612			0.753062	−	0.657950i	$-0.228576\pi$
$463$	32.4079			1.50612			0.753062	+	0.657950i	$0.228576\pi$
$464$		0			0
$465$	−6.29234	+	19.3658i	−0.291800	+	0.898069i
$466$		0			0
$467$	18.1880	−	13.2144i	0.841641	−	0.611488i	−0.0811878	−	0.996699i	$-0.525871\pi$
$467$	18.1880	−	13.2144i	0.841641	−	0.611488i	0.922829	+	0.385211i	$0.125871\pi$
$468$		0			0
$469$	1.27774	+	3.93249i	0.0590007	+	0.181586i
$470$		0			0
$471$	11.4365	+	8.30909i	0.526965	+	0.382863i
$472$		0			0
$473$	16.6260	−	0.691119i	0.764462	−	0.0317777i
$474$		0			0
$475$	−2.61476	−	1.89973i	−0.119973	−	0.0871657i
$476$		0			0
$477$	4.78268	+	14.7196i	0.218984	+	0.673963i
$478$		0			0
$479$	12.0452	−	8.75134i	0.550359	−	0.399859i	−0.277559	−	0.960709i	$-0.589525\pi$
$479$	12.0452	−	8.75134i	0.550359	−	0.399859i	0.827918	+	0.560849i	$0.189525\pi$
$480$		0			0
$481$	1.69788	−	5.22554i	0.0774167	−	0.238264i
$482$		0			0
$483$	7.86098			0.357687
$484$		0			0
$485$	−9.80349			−0.445153
$486$		0			0
$487$	0.469960	−	1.44639i	0.0212959	−	0.0655422i	−0.939844	−	0.341605i	$-0.889030\pi$
$487$	0.469960	−	1.44639i	0.0212959	−	0.0655422i	0.961140	+	0.276062i	$0.0890296\pi$
$488$		0			0
$489$	−15.5119	+	11.2701i	−0.701474	+	0.509651i
$490$		0			0
$491$	0.171241	+	0.527027i	0.00772802	+	0.0237844i	0.954846	−	0.297101i	$-0.0960197\pi$
$491$	0.171241	+	0.527027i	0.00772802	+	0.0237844i	−0.947118	+	0.320885i	$0.896020\pi$
$492$		0			0
$493$	26.3353	+	19.1337i	1.18608	+	0.861738i
$494$		0			0
$495$	−7.39546	+	0.307419i	−0.332401	+	0.0138175i
$496$		0			0
$497$	−3.05401	−	2.21887i	−0.136991	−	0.0995299i
$498$		0			0
$499$	−9.70914	−	29.8816i	−0.434641	−	1.33769i	−0.893454	−	0.449154i	$-0.851726\pi$
$499$	−9.70914	−	29.8816i	−0.434641	−	1.33769i	0.458814	−	0.888532i	$-0.348274\pi$
$500$		0			0
$501$	12.4253	−	9.02748i	0.555120	−	0.403318i
$502$		0			0
$503$	−5.15956	+	15.8795i	−0.230053	+	0.708031i	0.767686	+	0.640826i	$0.221408\pi$
$503$	−5.15956	+	15.8795i	−0.230053	+	0.708031i	−0.997739	+	0.0672048i	$0.978592\pi$
$504$		0			0
$505$	−34.3555			−1.52880
$506$		0			0
$507$	−1.38287			−0.0614153
$508$		0			0
$509$	4.93919	−	15.2013i	0.218926	−	0.673784i	−0.779926	−	0.625872i	$-0.784743\pi$
$509$	4.93919	−	15.2013i	0.218926	−	0.673784i	0.998852	−	0.0479118i	$-0.0152567\pi$
$510$		0			0
$511$	−8.98819	+	6.53030i	−0.397614	+	0.288884i
$512$		0			0
$513$	−7.14669	−	21.9953i	−0.315534	−	0.971115i
$514$		0			0
$515$	3.54297	+	2.57412i	0.156122	+	0.113429i
$516$		0			0
$517$	7.02929	−	25.1428i	0.309148	−	1.10578i
$518$		0			0
$519$	4.54256	+	3.30036i	0.199396	+	0.144870i
$520$		0			0
$521$	−1.55819	−	4.79560i	−0.0682654	−	0.210099i	0.911104	−	0.412176i	$-0.135231\pi$
$521$	−1.55819	−	4.79560i	−0.0682654	−	0.210099i	−0.979370	+	0.202077i	$0.935231\pi$
$522$		0			0
$523$	−4.17205	+	3.03117i	−0.182431	+	0.132544i	−0.675253	−	0.737586i	$-0.735965\pi$
$523$	−4.17205	+	3.03117i	−0.182431	+	0.132544i	0.492822	+	0.870130i	$0.335965\pi$
$524$		0			0
$525$	0.314101	−	0.966704i	0.0137085	−	0.0421904i
$526$		0			0
$527$	33.4212			1.45585
$528$		0			0
$529$	14.3245			0.622805
$530$		0			0
$531$	4.53800	−	13.9665i	0.196933	−	0.606096i
$532$		0			0
$533$	9.32675	−	6.77628i	0.403986	−	0.293513i
$534$		0			0
$535$	1.14400	+	3.52086i	0.0494592	+	0.152220i
$536$		0			0
$537$	18.9027	+	13.7336i	0.815711	+	0.592649i
$538$		0			0
$539$	15.9486	−	12.6318i	0.686953	−	0.544088i
$540$		0			0
$541$	8.04419	+	5.84445i	0.345847	+	0.251272i	0.747125	−	0.664684i	$-0.231434\pi$
$541$	8.04419	+	5.84445i	0.345847	+	0.251272i	−0.401278	+	0.915956i	$0.631434\pi$
$542$		0			0
$543$	7.98974	+	24.5899i	0.342873	+	1.05525i
$544$		0			0
$545$	−18.7710	+	13.6380i	−0.804063	+	0.584186i
$546$		0			0
$547$	−11.2460	+	34.6118i	−0.480846	+	1.47989i	0.357062	+	0.934081i	$0.383778\pi$
$547$	−11.2460	+	34.6118i	−0.480846	+	1.47989i	−0.837908	+	0.545811i	$0.816222\pi$
$548$		0			0
$549$	2.69558			0.115045
$550$		0			0
$551$	28.5976			1.21830
$552$		0			0
$553$	−3.93819	+	12.1205i	−0.167469	+	0.515417i
$554$		0			0
$555$	12.6126	−	9.16362i	0.535377	−	0.388974i
$556$		0			0
$557$	−7.60951	−	23.4197i	−0.322425	−	0.992324i	−0.972589	−	0.232530i	$-0.925300\pi$
$557$	−7.60951	−	23.4197i	−0.322425	−	0.992324i	0.650164	−	0.759794i	$-0.274700\pi$
$558$		0			0
$559$	−4.05903	−	2.94906i	−0.171679	−	0.124732i
$560$		0			0
$561$	−7.43848	−	20.0225i	−0.314053	−	0.845350i
$562$		0			0
$563$	23.7965	+	17.2892i	1.00290	+	0.728651i	0.962709	−	0.270541i	$-0.0872025\pi$
$563$	23.7965	+	17.2892i	1.00290	+	0.728651i	0.0401938	+	0.999192i	$0.487202\pi$
$564$		0			0
$565$	−6.38529	−	19.6519i	−0.268631	−	0.826762i
$566$		0			0
$567$	3.42801	−	2.49059i	0.143963	−	0.104595i
$568$		0			0
$569$	−5.24273	+	16.1355i	−0.219787	+	0.676434i	0.778992	+	0.627033i	$0.215731\pi$
$569$	−5.24273	+	16.1355i	−0.219787	+	0.676434i	−0.998779	+	0.0494003i	$0.984269\pi$
$570$		0			0
$571$	27.6974			1.15910			0.579550	−	0.814936i	$-0.303228\pi$
$571$	27.6974			1.15910			0.579550	+	0.814936i	$0.303228\pi$
$572$		0			0
$573$	2.76820			0.115643
$574$		0			0
$575$	1.49138	−	4.58999i	0.0621947	−	0.191416i
$576$		0			0
$577$	11.9955	−	8.71521i	0.499378	−	0.362819i	−0.309402	−	0.950931i	$-0.600129\pi$
$577$	11.9955	−	8.71521i	0.499378	−	0.362819i	0.808779	+	0.588112i	$0.200129\pi$
$578$		0			0
$579$	−4.62192	−	14.2248i	−0.192080	−	0.591162i
$580$		0			0
$581$	−10.4223	−	7.57228i	−0.432392	−	0.314151i
$582$		0			0
$583$	39.2997	+	26.1301i	1.62763	+	1.08220i
$584$		0			0
$585$	1.80552	+	1.31178i	0.0746489	+	0.0542356i
$586$		0			0
$587$	1.82003	+	5.60148i	0.0751207	+	0.231198i	0.981565	−	0.191127i	$-0.0612142\pi$
$587$	1.82003	+	5.60148i	0.0751207	+	0.231198i	−0.906445	+	0.422325i	$0.861214\pi$
$588$		0			0
$589$	23.7536	−	17.2580i	0.978751	−	0.711104i
$590$		0			0
$591$	1.77292	−	5.45650i	0.0729283	−	0.224450i
$592$		0			0
$593$	13.1200			0.538773			0.269387	−	0.963032i	$-0.413179\pi$
$593$	13.1200			0.538773			0.269387	+	0.963032i	$0.413179\pi$
$594$		0			0
$595$	8.89114			0.364501
$596$		0			0
$597$	−5.95398	+	18.3245i	−0.243680	+	0.749970i
$598$		0			0
$599$	20.9410	−	15.2145i	0.855626	−	0.621649i	−0.0710653	−	0.997472i	$-0.522640\pi$
$599$	20.9410	−	15.2145i	0.855626	−	0.621649i	0.926692	+	0.375823i	$0.122640\pi$
$600$		0			0
$601$	5.11928	+	15.7555i	0.208820	+	0.642682i	0.999535	+	0.0304972i	$0.00970905\pi$
$601$	5.11928	+	15.7555i	0.208820	+	0.642682i	−0.790715	+	0.612185i	$0.790291\pi$
$602$		0			0
$603$	3.91040	+	2.84107i	0.159244	+	0.115697i
$604$		0			0
$605$	−17.0957	+	14.7361i	−0.695037	+	0.599108i
$606$		0			0
$607$	−4.03193	−	2.92937i	−0.163651	−	0.118899i	0.502946	−	0.864318i	$-0.332250\pi$
$607$	−4.03193	−	2.92937i	−0.163651	−	0.118899i	−0.666597	+	0.745419i	$0.732250\pi$
$608$		0			0
$609$	2.77924	+	8.55362i	0.112621	+	0.346610i
$610$		0			0
$611$	−6.36820	+	4.62677i	−0.257630	+	0.187179i
$612$		0			0
$613$	0.588429	−	1.81100i	0.0237664	−	0.0731455i	−0.938470	−	0.345361i	$-0.887756\pi$
$613$	0.588429	−	1.81100i	0.0237664	−	0.0731455i	0.962236	+	0.272216i	$0.0877564\pi$
$614$		0			0
$615$	32.7112			1.31904
$616$		0			0
$617$	−25.5194			−1.02737			−0.513686	−	0.857978i	$-0.671720\pi$
$617$	−25.5194			−1.02737			−0.513686	+	0.857978i	$0.671720\pi$
$618$		0			0
$619$	−4.86041	+	14.9588i	−0.195356	+	0.601245i	0.804616	+	0.593796i	$0.202371\pi$
$619$	−4.86041	+	14.9588i	−0.195356	+	0.601245i	−0.999972	+	0.00744933i	$0.997629\pi$
$620$		0			0
$621$	27.9391	−	20.2989i	1.12116	−	0.814568i
$622$		0			0
$623$	−3.41790	−	10.5192i	−0.136935	−	0.421443i
$624$		0			0
$625$	16.5251	+	12.0062i	0.661003	+	0.480247i
$626$		0			0
$627$	−15.6260	−	10.3896i	−0.624041	−	0.414921i
$628$		0			0
$629$	−20.7013	−	15.0404i	−0.825416	−	0.599700i
$630$		0			0
$631$	−0.392228	−	1.20715i	−0.0156144	−	0.0480561i	0.942946	−	0.332946i	$-0.108043\pi$
$631$	−0.392228	−	1.20715i	−0.0156144	−	0.0480561i	−0.958560	+	0.284890i	$0.908043\pi$
$632$		0			0
$633$	11.3243	−	8.22755i	0.450099	−	0.327016i
$634$		0			0
$635$	1.02271	−	3.14759i	0.0405851	−	0.124908i
$636$		0			0
$637$	−6.13424			−0.243047
$638$		0			0
$639$	−4.41281			−0.174568
$640$		0			0
$641$	−8.23795	+	25.3538i	−0.325379	+	1.00141i	0.645890	+	0.763431i	$0.276487\pi$
$641$	−8.23795	+	25.3538i	−0.325379	+	1.00141i	−0.971269	+	0.237984i	$0.923513\pi$
$642$		0			0
$643$	−24.7240	+	17.9631i	−0.975021	+	0.708394i	−0.956590	−	0.291436i	$-0.905867\pi$
$643$	−24.7240	+	17.9631i	−0.975021	+	0.708394i	−0.0184309	+	0.999830i	$0.505867\pi$
$644$		0			0
$645$	−4.39917	−	13.5392i	−0.173217	−	0.533107i
$646$		0			0
$647$	0.781875	+	0.568065i	0.0307387	+	0.0223329i	0.603049	−	0.797705i	$-0.293953\pi$
$647$	0.781875	+	0.568065i	0.0307387	+	0.0223329i	−0.572310	+	0.820037i	$0.693953\pi$
$648$		0			0
$649$	−15.5944	−	41.9762i	−0.612135	−	1.64771i
$650$		0			0
$651$	7.47039	+	5.42756i	0.292788	+	0.212723i
$652$		0			0
$653$	−8.97613	−	27.6257i	−0.351263	−	1.08108i	−0.958145	−	0.286285i	$-0.907580\pi$
$653$	−8.97613	−	27.6257i	−0.351263	−	1.08108i	0.606881	−	0.794792i	$-0.292420\pi$
$654$		0			0
$655$	−25.4090	+	18.4607i	−0.992813	+	0.721321i
$656$		0			0
$657$	−4.01328	+	12.3516i	−0.156573	+	0.481882i
$658$		0			0
$659$	18.0073			0.701463			0.350731	−	0.936476i	$-0.385933\pi$
$659$	18.0073			0.701463			0.350731	+	0.936476i	$0.385933\pi$
$660$		0			0
$661$	15.0556			0.585596			0.292798	−	0.956174i	$-0.405414\pi$
$661$	15.0556			0.585596			0.292798	+	0.956174i	$0.405414\pi$
$662$		0			0
$663$	−1.99012	+	6.12495i	−0.0772897	+	0.237873i
$664$		0			0
$665$	6.31924	−	4.59120i	0.245050	−	0.178039i
$666$		0			0
$667$	13.1960	+	40.6133i	0.510953	+	1.57255i
$668$		0			0
$669$	−11.4247	−	8.30050i	−0.441703	−	0.320916i
$670$		0			0
$671$	6.44336	−	5.10335i	0.248743	−	0.197012i
$672$		0			0
$673$	−20.5569	−	14.9354i	−0.792409	−	0.575719i	0.116268	−	0.993218i	$-0.462907\pi$
$673$	−20.5569	−	14.9354i	−0.792409	−	0.575719i	−0.908678	+	0.417499i	$0.862907\pi$
$674$		0			0
$675$	−1.37990	−	4.24689i	−0.0531124	−	0.163463i
$676$		0			0
$677$	34.3670	−	24.9691i	1.32083	−	0.959641i	0.320911	−	0.947110i	$-0.396011\pi$
$677$	34.3670	−	24.9691i	1.32083	−	0.959641i	0.999921	−	0.0125311i	$-0.00398888\pi$
$678$		0			0
$679$	−1.37379	+	4.22808i	−0.0527211	+	0.162259i
$680$		0			0
$681$	−7.39600			−0.283415
$682$		0			0
$683$	−23.2929			−0.891278			−0.445639	−	0.895213i	$-0.647023\pi$
$683$	−23.2929			−0.891278			−0.445639	+	0.895213i	$0.647023\pi$
$684$		0			0
$685$	−2.64051	+	8.12665i	−0.100889	+	0.310503i
$686$		0			0
$687$	−30.5599	+	22.2031i	−1.16593	+	0.847100i
$688$		0			0
$689$	−4.39714	−	13.5330i	−0.167518	−	0.515567i
$690$		0			0
$691$	−23.0326	−	16.7341i	−0.876200	−	0.636597i	0.0560430	−	0.998428i	$-0.482152\pi$
$691$	−23.0326	−	16.7341i	−0.876200	−	0.636597i	−0.932244	+	0.361831i	$0.882152\pi$
$692$		0			0
$693$	−0.903759	+	3.23262i	−0.0343310	+	0.122797i
$694$		0			0
$695$	25.7735	+	18.7255i	0.977644	+	0.710300i
$696$		0			0
$697$	−16.5909	−	51.0616i	−0.628426	−	1.93410i
$698$		0			0
$699$	−13.0561	+	9.48582i	−0.493827	+	0.358787i
$700$		0			0
$701$	−5.18163	+	15.9474i	−0.195707	+	0.602326i	0.804260	+	0.594277i	$0.202562\pi$
$701$	−5.18163	+	15.9474i	−0.195707	+	0.602326i	−0.999968	+	0.00804830i	$0.997438\pi$
$702$		0			0
$703$	−22.4797			−0.847838
$704$		0			0
$705$	−22.3348			−0.841178
$706$		0			0
$707$	−4.81432	+	14.8170i	−0.181061	+	0.557249i
$708$		0			0
$709$	−20.2432	+	14.7075i	−0.760249	+	0.552353i	−0.898987	−	0.437976i	$-0.855696\pi$
$709$	−20.2432	+	14.7075i	−0.760249	+	0.552353i	0.138737	+	0.990329i	$0.455696\pi$
$710$		0			0
$711$	4.60361	+	14.1685i	0.172649	+	0.531359i
$712$		0			0
$713$	35.4700	+	25.7705i	1.32836	+	0.965112i
$714$		0			0
$715$	6.79930	−	0.282638i	0.254279	−	0.0105701i
$716$		0			0
$717$	−7.81809	−	5.68018i	−0.291972	−	0.212130i
$718$		0			0
$719$	1.13883	+	3.50496i	0.0424713	+	0.130713i	0.970044	−	0.242930i	$-0.0781085\pi$
$719$	1.13883	+	3.50496i	0.0424713	+	0.130713i	−0.927573	+	0.373643i	$0.878109\pi$
$720$		0			0
$721$	1.60666	−	1.16731i	0.0598351	−	0.0434727i
$722$		0			0
$723$	4.60614	−	14.1762i	0.171304	−	0.527220i
$724$		0			0
$725$	5.52169			0.205071
$726$		0			0
$727$	−42.1131			−1.56189			−0.780945	−	0.624600i	$-0.785262\pi$
$727$	−42.1131			−1.56189			−0.780945	+	0.624600i	$0.785262\pi$
$728$		0			0
$729$	8.77734	−	27.0139i	0.325087	−	1.00051i
$730$		0			0
$731$	−18.9033	+	13.7341i	−0.699165	+	0.507973i
$732$		0			0
$733$	−1.37192	−	4.22234i	−0.0506731	−	0.155956i	0.922518	−	0.385954i	$-0.126128\pi$
$733$	−1.37192	−	4.22234i	−0.0506731	−	0.155956i	−0.973191	+	0.229999i	$0.926128\pi$
$734$		0			0
$735$	−14.0813	−	10.2306i	−0.519395	−	0.377363i
$736$		0			0
$737$	14.7260	−	0.612139i	0.542438	−	0.0225484i
$738$		0			0
$739$	−32.9576	−	23.9451i	−1.21236	−	0.880834i	−0.216920	−	0.976189i	$-0.569601\pi$
$739$	−32.9576	−	23.9451i	−1.21236	−	0.880834i	−0.995443	+	0.0953555i	$0.969601\pi$
$740$		0			0
$741$	1.74835	+	5.38087i	0.0642272	+	0.197671i
$742$		0			0
$743$	−7.58933	+	5.51397i	−0.278426	+	0.202288i	−0.718230	−	0.695805i	$-0.755048\pi$
$743$	−7.58933	+	5.51397i	−0.278426	+	0.202288i	0.439805	+	0.898093i	$0.355048\pi$
$744$		0			0
$745$	5.66398	−	17.4319i	0.207512	−	0.638656i
$746$		0			0
$747$	−15.0595			−0.550997
$748$		0			0
$749$	1.67880			0.0613419
$750$		0			0
$751$	−5.64412	+	17.3708i	−0.205957	+	0.633870i	0.793716	+	0.608289i	$0.208144\pi$
$751$	−5.64412	+	17.3708i	−0.205957	+	0.633870i	−0.999673	+	0.0255812i	$0.991856\pi$
$752$		0			0
$753$	−31.9069	+	23.1817i	−1.16275	+	0.844790i
$754$		0			0
$755$	−3.32766	−	10.2415i	−0.121106	−	0.372726i
$756$		0			0
$757$	−20.9910	−	15.2509i	−0.762931	−	0.554302i	0.136877	−	0.990588i	$-0.456293\pi$
$757$	−20.9910	−	15.2509i	−0.762931	−	0.554302i	−0.899808	+	0.436286i	$0.856293\pi$
$758$		0			0
$759$	7.54449	−	26.9856i	0.273848	−	0.979515i
$760$		0			0
$761$	17.7028	+	12.8618i	0.641725	+	0.466240i	0.860442	−	0.509548i	$-0.170187\pi$
$761$	17.7028	+	12.8618i	0.641725	+	0.466240i	−0.218718	+	0.975788i	$0.570187\pi$
$762$		0			0
$763$	3.25139	+	10.0068i	0.117708	+	0.362269i
$764$		0			0
$765$	8.40847	−	6.10911i	0.304009	−	0.220875i
$766$		0			0
$767$	−4.17219	+	12.8407i	−0.150649	+	0.463650i
$768$		0			0
$769$	−8.15062			−0.293919			−0.146960	−	0.989143i	$-0.546949\pi$
$769$	−8.15062			−0.293919			−0.146960	+	0.989143i	$0.546949\pi$
$770$		0			0
$771$	6.59405			0.237479
$772$		0			0
$773$	1.91141	−	5.88272i	0.0687487	−	0.211587i	−0.910780	−	0.412893i	$-0.864518\pi$
$773$	1.91141	−	5.88272i	0.0687487	−	0.211587i	0.979528	+	0.201306i	$0.0645185\pi$
$774$		0			0
$775$	4.58640	−	3.33222i	0.164748	−	0.119697i
$776$		0			0
$777$	−2.18467	−	6.72374i	−0.0783748	−	0.241213i
$778$		0			0
$779$	−38.1589	−	27.7241i	−1.36718	−	0.993318i
$780$		0			0
$781$	−10.5481	+	8.35444i	−0.377441	+	0.298945i
$782$		0			0
$783$	31.9653	+	23.2242i	1.14235	+	0.829964i
$784$		0			0
$785$	6.48156	+	19.9482i	0.231337	+	0.711981i
$786$		0			0
$787$	−20.5421	+	14.9247i	−0.732248	+	0.532009i	−0.890274	−	0.455426i	$-0.849487\pi$
$787$	−20.5421	+	14.9247i	−0.732248	+	0.532009i	0.158026	+	0.987435i	$0.449487\pi$
$788$		0			0
$789$	3.70066	−	11.3895i	0.131747	−	0.405476i
$790$		0			0
$791$	−9.37032			−0.333170
$792$		0			0
$793$	−2.47829			−0.0880066
$794$		0			0
$795$	12.4765	−	38.3988i	0.442497	−	1.36186i
$796$		0			0
$797$	−16.2555	+	11.8103i	−0.575799	+	0.418342i	−0.837207	−	0.546886i	$-0.815813\pi$
$797$	−16.2555	+	11.8103i	−0.575799	+	0.418342i	0.261408	+	0.965228i	$0.415813\pi$
$798$		0			0
$799$	11.3281	+	34.8643i	0.400759	+	1.23341i
$800$		0			0
$801$	−10.4601	−	7.59972i	−0.369590	−	0.268523i
$802$		0			0
$803$	13.7913	+	37.1225i	0.486683	+	1.31003i
$804$		0			0
$805$	9.43619	+	6.85579i	0.332582	+	0.241635i
$806$		0			0
$807$	1.87797	+	5.77981i	0.0661078	+	0.203459i
$808$		0			0
$809$	45.7709	−	33.2545i	1.60922	−	1.16917i	0.743339	−	0.668915i	$-0.233241\pi$
$809$	45.7709	−	33.2545i	1.60922	−	1.16917i	0.865880	−	0.500251i	$-0.166759\pi$
$810$		0			0
$811$	−0.121521	+	0.374004i	−0.00426719	+	0.0131331i	−0.953167	−	0.302443i	$-0.902198\pi$
$811$	−0.121521	+	0.374004i	−0.00426719	+	0.0131331i	0.948900	+	0.315576i	$0.102198\pi$
$812$		0			0
$813$	25.0448			0.878359
$814$		0			0
$815$	−28.4493			−0.996534
$816$		0			0
$817$	−6.34327	+	19.5226i	−0.221923	+	0.683008i
$818$		0			0
$819$	0.818762	−	0.594865i	0.0286099	−	0.0207863i
$820$		0			0
$821$	14.1146	+	43.4404i	0.492605	+	1.51608i	0.820657	+	0.571421i	$0.193608\pi$
$821$	14.1146	+	43.4404i	0.492605	+	1.51608i	−0.328052	+	0.944660i	$0.606392\pi$
$822$		0			0
$823$	−20.9609	−	15.2290i	−0.730652	−	0.530850i	0.159118	−	0.987260i	$-0.449135\pi$
$823$	−20.9609	−	15.2290i	−0.730652	−	0.530850i	−0.889770	+	0.456410i	$0.849135\pi$
$824$		0			0
$825$	−3.01710	−	2.00605i	−0.105042	−	0.0698416i
$826$		0			0
$827$	−13.0351	−	9.47056i	−0.453275	−	0.329324i	0.337612	−	0.941285i	$-0.390381\pi$
$827$	−13.0351	−	9.47056i	−0.453275	−	0.329324i	−0.790888	+	0.611962i	$0.790381\pi$
$828$		0			0
$829$	6.81921	+	20.9874i	0.236841	+	0.728921i	0.996872	+	0.0790345i	$0.0251837\pi$
$829$	6.81921	+	20.9874i	0.236841	+	0.728921i	−0.760031	+	0.649887i	$0.774816\pi$
$830$		0			0
$831$	15.9977	−	11.6230i	0.554954	−	0.403198i
$832$		0			0
$833$	−8.82793	+	27.1696i	−0.305870	+	0.941370i
$834$		0			0
$835$	22.7882			0.788619
$836$		0			0
$837$	40.5661			1.40217
$838$		0			0
$839$	4.88930	−	15.0477i	0.168797	−	0.519505i	−0.830499	−	0.557021i	$-0.811944\pi$
$839$	4.88930	−	15.0477i	0.168797	−	0.519505i	0.999296	+	0.0375158i	$0.0119445\pi$
$840$		0			0
$841$	−16.0648	+	11.6718i	−0.553960	+	0.402475i
$842$		0			0
$843$	−3.21402	−	9.89174i	−0.110697	−	0.340690i
$844$		0			0
$845$	−1.65997	−	1.20604i	−0.0571047	−	0.0414890i
$846$		0			0
$847$	3.95978	+	9.43807i	0.136060	+	0.324296i
$848$		0			0
$849$	−34.8865	−	25.3465i	−1.19730	−	0.869891i
$850$		0			0
$851$	−10.3730	−	31.9248i	−0.355582	−	1.09437i
$852$		0			0
$853$	−44.3995	+	32.2581i	−1.52021	+	1.10450i	−0.558825	+	0.829286i	$0.688748\pi$
$853$	−44.3995	+	32.2581i	−1.52021	+	1.10450i	−0.961384	+	0.275210i	$0.911252\pi$
$854$		0			0
$855$	2.82158	−	8.68392i	0.0964959	−	0.296984i
$856$		0			0
$857$	11.6817			0.399038			0.199519	−	0.979894i	$-0.436062\pi$
$857$	11.6817			0.399038			0.199519	+	0.979894i	$0.436062\pi$
$858$		0			0
$859$	1.72050			0.0587027			0.0293513	−	0.999569i	$-0.490656\pi$
$859$	1.72050			0.0587027			0.0293513	+	0.999569i	$0.490656\pi$
$860$		0			0
$861$	4.58389	−	14.1078i	0.156219	−	0.480792i
$862$		0			0
$863$	−1.70693	+	1.24015i	−0.0581045	+	0.0422154i	−0.616458	−	0.787388i	$-0.711433\pi$
$863$	−1.70693	+	1.24015i	−0.0581045	+	0.0422154i	0.558354	+	0.829603i	$0.311433\pi$
$864$		0			0
$865$	2.57447	+	7.92340i	0.0875346	+	0.269404i
$866$		0			0
$867$	5.24543	+	3.81103i	0.178144	+	0.129429i
$868$		0			0
$869$	37.8283	+	25.1518i	1.28324	+	0.853216i
$870$		0			0
$871$	−3.59518	−	2.61205i	−0.121818	−	0.0885059i
$872$		0			0
$873$	1.60591	+	4.94248i	0.0543518	+	0.167278i
$874$		0			0
$875$	8.94284	−	6.49735i	0.302323	−	0.219651i
$876$		0			0
$877$	11.7546	−	36.1768i	0.396923	−	1.22160i	−0.530531	−	0.847666i	$-0.678007\pi$
$877$	11.7546	−	36.1768i	0.396923	−	1.22160i	0.927454	−	0.373938i	$-0.121993\pi$
$878$		0			0
$879$	−38.2987			−1.29178
$880$		0			0
$881$	−30.1024			−1.01418			−0.507088	−	0.861894i	$-0.669278\pi$
$881$	−30.1024			−1.01418			−0.507088	+	0.861894i	$0.669278\pi$
$882$		0			0
$883$	9.89590	−	30.4564i	0.333023	−	1.02494i	−0.634664	−	0.772788i	$-0.718861\pi$
$883$	9.89590	−	30.4564i	0.333023	−	1.02494i	0.967687	−	0.252153i	$-0.0811385\pi$
$884$		0			0
$885$	−30.9929	+	22.5177i	−1.04181	+	0.756923i
$886$		0			0
$887$	11.8913	+	36.5976i	0.399270	+	1.22883i	0.925586	+	0.378537i	$0.123573\pi$
$887$	11.8913	+	36.5976i	0.399270	+	1.22883i	−0.526316	+	0.850289i	$0.676427\pi$
$888$		0			0
$889$	−1.21419	−	0.882158i	−0.0407225	−	0.0295866i
$890$		0			0
$891$	−5.25984	−	14.1582i	−0.176211	−	0.474316i
$892$		0			0
$893$	26.0545	+	18.9297i	0.871880	+	0.633458i
$894$		0			0
$895$	10.7130	+	32.9712i	0.358096	+	1.10211i
$896$		0			0
$897$	−6.83495	+	4.96588i	−0.228212	+	0.165806i
$898$		0			0
$899$	−15.5008	+	47.7065i	−0.516980	+	1.59110i
$900$		0			0
$901$	−66.2680			−2.20771
$902$		0			0
$903$	−6.45572			−0.214833
$904$		0			0
$905$	−11.8548	+	36.4854i	−0.394068	+	1.21282i
$906$		0			0
$907$	28.7408	−	20.8814i	0.954324	−	0.693357i	0.00249835	−	0.999997i	$-0.499205\pi$
$907$	28.7408	−	20.8814i	0.954324	−	0.693357i	0.951826	+	0.306640i	$0.0992047\pi$
$908$		0			0
$909$	5.62778	+	17.3205i	0.186662	+	0.574485i
$910$		0			0
$911$	−11.9243	−	8.66348i	−0.395068	−	0.287034i	0.372461	−	0.928048i	$-0.378514\pi$
$911$	−11.9243	−	8.66348i	−0.395068	−	0.287034i	−0.767529	+	0.641014i	$0.778514\pi$
$912$		0			0
$913$	−35.9973	+	28.5110i	−1.19134	+	0.943575i
$914$		0			0
$915$	−5.68896	−	4.13327i	−0.188071	−	0.136642i
$916$		0			0
$917$	4.40118	+	13.5454i	0.145340	+	0.447310i
$918$		0			0
$919$	−15.0152	+	10.9092i	−0.495306	+	0.359861i	−0.807221	−	0.590249i	$-0.799029\pi$
$919$	−15.0152	+	10.9092i	−0.495306	+	0.359861i	0.311915	+	0.950110i	$0.399029\pi$
$920$		0			0
$921$	−8.90456	+	27.4054i	−0.293415	+	0.903039i
$922$		0			0
$923$	4.05709			0.133541
$924$		0			0
$925$	−4.34043			−0.142713
$926$		0			0
$927$	0.717382	−	2.20787i	0.0235619	−	0.0725161i
$928$		0			0
$929$	22.0541	−	16.0232i	0.723572	−	0.525706i	−0.163952	−	0.986468i	$-0.552424\pi$
$929$	22.0541	−	16.0232i	0.723572	−	0.525706i	0.887523	+	0.460763i	$0.152424\pi$
$930$		0			0
$931$	7.75548	+	23.8689i	0.254176	+	0.782272i
$932$		0			0
$933$	−5.79105	−	4.20744i	−0.189590	−	0.137745i
$934$		0			0
$935$	8.53318	−	30.5220i	0.279065	−	0.998176i
$936$		0			0
$937$	17.4950	+	12.7108i	0.571535	+	0.415245i	0.835663	−	0.549243i	$-0.185084\pi$
$937$	17.4950	+	12.7108i	0.571535	+	0.415245i	−0.264127	+	0.964488i	$0.585084\pi$
$938$		0			0
$939$	12.0114	+	36.9674i	0.391978	+	1.20638i
$940$		0			0
$941$	−5.80284	+	4.21601i	−0.189167	+	0.137438i	−0.678338	−	0.734750i	$-0.737299\pi$
$941$	−5.80284	+	4.21601i	−0.189167	+	0.137438i	0.489171	+	0.872188i	$0.337299\pi$
$942$		0			0
$943$	21.7647	−	66.9848i	0.708755	−	2.18132i
$944$		0			0
$945$	10.7919			0.351061
$946$		0			0
$947$	13.6649			0.444049			0.222025	−	0.975041i	$-0.428733\pi$
$947$	13.6649			0.444049			0.222025	+	0.975041i	$0.428733\pi$
$948$		0			0
$949$	3.68976	−	11.3559i	0.119775	−	0.368629i
$950$		0			0
$951$	15.2095	−	11.0503i	0.493201	−	0.358332i
$952$		0			0
$953$	4.19467	+	12.9099i	0.135879	+	0.418192i	0.995726	−	0.0923602i	$-0.0294411\pi$
$953$	4.19467	+	12.9099i	0.135879	+	0.418192i	−0.859847	+	0.510552i	$0.829441\pi$
$954$		0			0
$955$	3.32290	+	2.41423i	0.107526	+	0.0781225i
$956$		0			0
$957$	32.0307	−	1.33147i	1.03540	−	0.0430404i
$958$		0			0
$959$	3.13487	+	2.27761i	0.101230	+	0.0735480i
$960$		0			0
$961$	6.33506	+	19.4973i	0.204357	+	0.628946i
$962$		0			0
$963$	1.58766	−	1.15350i	0.0511617	−	0.0371711i
$964$		0			0
$965$	6.85780	−	21.1061i	0.220760	−	0.679430i
$966$		0			0
$967$	−16.0623			−0.516528			−0.258264	−	0.966074i	$-0.583150\pi$
$967$	−16.0623			−0.516528			−0.258264	+	0.966074i	$0.583150\pi$
$968$		0			0
$969$	26.3489			0.846447
$970$		0			0
$971$	6.38365	−	19.6468i	0.204861	−	0.630497i	−0.794858	−	0.606795i	$-0.792455\pi$
$971$	6.38365	−	19.6468i	0.204861	−	0.630497i	0.999719	−	0.0237019i	$-0.00754527\pi$
$972$		0			0
$973$	11.6877	−	8.49162i	0.374691	−	0.272229i
$974$		0			0
$975$	0.337575	+	1.03895i	0.0108111	+	0.0332730i
$976$		0			0
$977$	−14.3688	−	10.4395i	−0.459698	−	0.333990i	0.333715	−	0.942674i	$-0.391698\pi$
$977$	−14.3688	−	10.4395i	−0.459698	−	0.333990i	−0.793413	+	0.608684i	$0.791698\pi$
$978$		0			0
$979$	−39.3912	+	1.63744i	−1.25895	+	0.0523328i
$980$		0			0
$981$	9.95053	+	7.22949i	0.317696	+	0.230820i
$982$		0			0
$983$	−1.99051	−	6.12616i	−0.0634874	−	0.195394i	0.914282	−	0.405079i	$-0.132756\pi$
$983$	−1.99051	−	6.12616i	−0.0634874	−	0.195394i	−0.977769	+	0.209685i	$0.932756\pi$
$984$		0			0
$985$	6.88696	−	5.00367i	0.219437	−	0.159430i
$986$		0			0
$987$	−3.12983	+	9.63263i	−0.0996236	+	0.306610i
$988$		0			0
$989$	−30.6522			−0.974684
$990$		0			0
$991$	−33.3401			−1.05908			−0.529542	−	0.848284i	$-0.677636\pi$
$991$	−33.3401			−1.05908			−0.529542	+	0.848284i	$0.677636\pi$
$992$		0			0
$993$	−10.4052	+	32.0240i	−0.330200	+	1.01625i
$994$		0			0
$995$	−23.1284	+	16.8037i	−0.733218	+	0.532714i
$996$		0			0
$997$	−12.3782	−	38.0962i	−0.392022	−	1.20652i	−0.931257	−	0.364364i	$-0.881286\pi$
$997$	−12.3782	−	38.0962i	−0.392022	−	1.20652i	0.539235	−	0.842155i	$-0.318714\pi$
$998$		0			0
$999$	−25.1270	−	18.2558i	−0.794982	−	0.577588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.521.1	yes	20
11.3	even	5	inner	572.2.n.a.157.1	✓	20
11.5	even	5		6292.2.a.w.1.3		10
11.6	odd	10		6292.2.a.x.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.157.1	✓	20	11.3	even	5	inner
572.2.n.a.521.1	yes	20	1.1	even	1	trivial
6292.2.a.w.1.3		10	11.5	even	5
6292.2.a.x.1.3		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.427329 + 1.31518i) q^{3} +(-1.65997 + 1.20604i) q^{5} +(0.287529 + 0.884923i) q^{7} +(0.879951 + 0.639322i) q^{9} +O(q^{10})\)	\(q+(-0.427329 + 1.31518i) q^{3} +(-1.65997 + 1.20604i) q^{5} +(0.287529 + 0.884923i) q^{7} +(0.879951 + 0.639322i) q^{9} +(3.31376 - 0.137749i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.876810 - 2.69854i) q^{15} +(-3.76767 + 2.73738i) q^{17} +(-1.26429 + 3.89110i) q^{19} -1.28671 q^{21} -6.10938 q^{23} +(-0.244113 + 0.751301i) q^{25} +(-4.57314 + 3.32258i) q^{27} +(-2.15997 - 6.64769i) q^{29} +(-5.80583 - 4.21818i) q^{31} +(-1.23490 + 4.41707i) q^{33} +(-1.54454 - 1.12217i) q^{35} +(1.69788 + 5.22554i) q^{37} +(1.11876 - 0.812829i) q^{39} +(-3.56250 + 10.9643i) q^{41} +5.01724 q^{43} -2.23174 q^{45} +(2.43244 - 7.48627i) q^{47} +(4.96270 - 3.60562i) q^{49} +(-1.99012 - 6.12495i) q^{51} +(11.5119 + 8.36386i) q^{53} +(-5.33462 + 4.22519i) q^{55} +(-4.57724 - 3.32556i) q^{57} +(-4.17219 - 12.8407i) q^{59} +(2.00498 - 1.45670i) q^{61} +(-0.312739 + 0.962512i) q^{63} +2.05184 q^{65} +4.44388 q^{67} +(2.61072 - 8.03496i) q^{69} +(-3.28225 + 2.38470i) q^{71} +(3.68976 + 11.3559i) q^{73} +(-0.883783 - 0.642106i) q^{75} +(1.07470 + 2.89282i) q^{77} +(11.0809 + 8.05071i) q^{79} +(-1.40724 - 4.33103i) q^{81} +(-11.2012 + 8.13818i) q^{83} +(2.95285 - 9.08793i) q^{85} +9.66595 q^{87} -11.8872 q^{89} +(0.287529 - 0.884923i) q^{91} +(8.02869 - 5.83318i) q^{93} +(-2.59412 - 7.98389i) q^{95} +(3.86541 + 2.80838i) q^{97} +(3.00402 + 1.99735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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