LMFDB - Embedded newform 1080.2.b.a.971.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1080,2,Mod(971,1080)] 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("1080.971"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1080, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + x^{14} + 2 x^{13} - 6 x^{12} + 8 x^{11} - 6 x^{10} - 8 x^{9} + 32 x^{8} - 16 x^{7} + \cdots + 256 $ x^16 - 2x^15 + x^14 + 2x^13 - 6x^12 + 8x^11 - 6x^10 - 8x^9 + 32x^8 - 16x^7 - 24x^6 + 64x^5 - 96x^4 + 64x^3 + 64x^2 - 256x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.14
Root			$-1.23596 + 0.687323i$ of defining polynomial
Character	$\chi$	$=$	1080.971
Dual form			1080.2.b.a.971.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23596 + 0.687323i) q^{2} +(1.05517 + 1.69900i) q^{4} +1.00000 q^{5} +0.920206i q^{7} +(0.136384 + 2.82514i) q^{8} +(1.23596 + 0.687323i) q^{10} +0.482221i q^{11} +2.01753i q^{13} +(-0.632479 + 1.13733i) q^{14} +(-1.77322 + 3.58548i) q^{16} +0.701532i q^{17} +0.782948 q^{19} +(1.05517 + 1.69900i) q^{20} +(-0.331442 + 0.596004i) q^{22} +1.44101 q^{23} +1.00000 q^{25} +(-1.38669 + 2.49357i) q^{26} +(-1.56343 + 0.970977i) q^{28} +2.14505 q^{29} +6.59164i q^{31} +(-4.65601 + 3.21273i) q^{32} +(-0.482179 + 0.867062i) q^{34} +0.920206i q^{35} -2.33837i q^{37} +(0.967689 + 0.538138i) q^{38} +(0.136384 + 2.82514i) q^{40} -7.36833i q^{41} -7.06978 q^{43} +(-0.819295 + 0.508827i) q^{44} +(1.78103 + 0.990441i) q^{46} +0.294304 q^{47} +6.15322 q^{49} +(1.23596 + 0.687323i) q^{50} +(-3.42778 + 2.12884i) q^{52} +10.5190 q^{53} +0.482221i q^{55} +(-2.59971 + 0.125502i) q^{56} +(2.65119 + 1.47434i) q^{58} -10.8042i q^{59} +8.65852i q^{61} +(-4.53059 + 8.14697i) q^{62} +(-7.96280 + 0.770608i) q^{64} +2.01753i q^{65} -11.2157 q^{67} +(-1.19190 + 0.740238i) q^{68} +(-0.632479 + 1.13733i) q^{70} +5.57514 q^{71} +1.01962 q^{73} +(1.60722 - 2.89013i) q^{74} +(0.826146 + 1.33023i) q^{76} -0.443743 q^{77} +1.86662i q^{79} +(-1.77322 + 3.58548i) q^{80} +(5.06442 - 9.10693i) q^{82} -1.75905i q^{83} +0.701532i q^{85} +(-8.73794 - 4.85922i) q^{86} +(-1.36234 + 0.0657674i) q^{88} -11.9152i q^{89} -1.85654 q^{91} +(1.52052 + 2.44828i) q^{92} +(0.363747 + 0.202282i) q^{94} +0.782948 q^{95} +3.93818 q^{97} +(7.60511 + 4.22925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} + 16 q^{5} + 4 q^{8} - 2 q^{10} - 6 q^{14} + 10 q^{16} - 8 q^{19} + 2 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{25} + 16 q^{26} + 20 q^{28} + 8 q^{32} + 18 q^{34} + 14 q^{38} + 4 q^{40}+ \cdots + 32 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 + 16 * q^5 + 4 * q^8 - 2 * q^10 - 6 * q^14 + 10 * q^16 - 8 * q^19 + 2 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^25 + 16 * q^26 + 20 * q^28 + 8 * q^32 + 18 * q^34 + 14 * q^38 + 4 * q^40 - 6 * q^44 + 2 * q^46 + 16 * q^47 - 8 * q^49 - 2 * q^50 - 20 * q^52 - 32 * q^53 - 12 * q^56 - 16 * q^58 - 16 * q^62 + 14 * q^64 + 32 * q^67 + 8 * q^68 - 6 * q^70 - 24 * q^71 + 8 * q^73 - 34 * q^74 + 36 * q^76 + 10 * q^80 - 8 * q^82 + 34 * q^86 + 16 * q^88 + 48 * q^91 + 32 * q^92 + 10 * q^94 - 8 * q^95 - 8 * q^97 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.23596	+	0.687323i	0.873953	+	0.486011i
$2$	1.23596	+	0.687323i	0.873953	+	0.486011i
$3$		0			0
$3$		0			0
$4$	1.05517	+	1.69900i	0.527587	+	0.849501i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$			0.920206i			0.347805i	0.984763	+	0.173903i	$0.0556378\pi$
$7$			0.920206i			0.347805i	−0.984763	+	0.173903i	$0.944362\pi$
$8$	0.136384	+	2.82514i	0.0482191	+	0.998837i
$9$		0			0
$10$	1.23596	+	0.687323i	0.390844	+	0.217351i
$11$			0.482221i			0.145395i	0.997354	+	0.0726976i	$0.0231608\pi$
$11$			0.482221i			0.145395i	−0.997354	+	0.0726976i	$0.976839\pi$
$12$		0			0
$13$			2.01753i			0.559561i	0.960064	+	0.279781i	$0.0902617\pi$
$13$			2.01753i			0.559561i	−0.960064	+	0.279781i	$0.909738\pi$
$14$	−0.632479	+	1.13733i	−0.169037	+	0.303965i
$15$		0			0
$16$	−1.77322	+	3.58548i	−0.443304	+	0.896371i
$17$			0.701532i			0.170146i	0.996375	+	0.0850732i	$0.0271124\pi$
$17$			0.701532i			0.170146i	−0.996375	+	0.0850732i	$0.972888\pi$
$18$		0			0
$19$	0.782948			0.179621			0.0898103	−	0.995959i	$-0.471374\pi$
$19$	0.782948			0.179621			0.0898103	+	0.995959i	$0.471374\pi$
$20$	1.05517	+	1.69900i	0.235944	+	0.379908i
$21$		0			0
$22$	−0.331442	+	0.596004i	−0.0706637	+	0.127069i
$23$	1.44101			0.300472			0.150236	−	0.988650i	$-0.451997\pi$
$23$	1.44101			0.300472			0.150236	+	0.988650i	$0.451997\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.38669	+	2.49357i	−0.271953	+	0.489030i
$27$		0			0
$28$	−1.56343	+	0.970977i	−0.295461	+	0.183497i
$29$	2.14505			0.398326			0.199163	−	0.979966i	$-0.436178\pi$
$29$	2.14505			0.398326			0.199163	+	0.979966i	$0.436178\pi$
$30$		0			0
$31$			6.59164i			1.18389i	0.805977	+	0.591946i	$0.201640\pi$
$31$			6.59164i			1.18389i	−0.805977	+	0.591946i	$0.798360\pi$
$32$	−4.65601	+	3.21273i	−0.823073	+	0.567935i
$33$		0			0
$34$	−0.482179	+	0.867062i	−0.0826930	+	0.148700i
$35$			0.920206i			0.155543i
$36$		0			0
$37$		−	2.33837i		−	0.384426i	−0.981353	−	0.192213i	$-0.938433\pi$
$37$		−	2.33837i		−	0.384426i	0.981353	−	0.192213i	$-0.0615665\pi$
$38$	0.967689	+	0.538138i	0.156980	+	0.0872975i
$39$		0			0
$40$	0.136384	+	2.82514i	0.0215642	+	0.446693i
$41$		−	7.36833i		−	1.15074i	−0.817893	−	0.575370i	$-0.804858\pi$
$41$		−	7.36833i		−	1.15074i	0.817893	−	0.575370i	$-0.195142\pi$
$42$		0			0
$43$	−7.06978			−1.07813			−0.539066	−	0.842264i	$-0.681223\pi$
$43$	−7.06978			−1.07813			−0.539066	+	0.842264i	$0.681223\pi$
$44$	−0.819295	+	0.508827i	−0.123513	+	0.0767086i
$45$		0			0
$46$	1.78103	+	0.990441i	0.262598	+	0.146033i
$47$	0.294304			0.0429287			0.0214643	−	0.999770i	$-0.493167\pi$
$47$	0.294304			0.0429287			0.0214643	+	0.999770i	$0.493167\pi$
$48$		0			0
$49$	6.15322			0.879031
$50$	1.23596	+	0.687323i	0.174791	+	0.0972022i
$51$		0			0
$52$	−3.42778	+	2.12884i	−0.475348	+	0.295217i
$53$	10.5190			1.44489			0.722445	−	0.691428i	$-0.243018\pi$
$53$	10.5190			1.44489			0.722445	+	0.691428i	$0.243018\pi$
$54$		0			0
$55$			0.482221i			0.0650227i
$56$	−2.59971	+	0.125502i	−0.347401	+	0.0167709i
$57$		0			0
$58$	2.65119	+	1.47434i	0.348118	+	0.193591i
$59$		−	10.8042i		−	1.40659i	−0.710899	−	0.703295i	$-0.751712\pi$
$59$		−	10.8042i		−	1.40659i	0.710899	−	0.703295i	$-0.248288\pi$
$60$		0			0
$61$			8.65852i			1.10861i	0.832313	+	0.554305i	$0.187016\pi$
$61$			8.65852i			1.10861i	−0.832313	+	0.554305i	$0.812984\pi$
$62$	−4.53059	+	8.14697i	−0.575385	+	1.03467i
$63$		0			0
$64$	−7.96280	+	0.770608i	−0.995350	+	0.0963260i
$65$			2.01753i			0.250243i
$66$		0			0
$67$	−11.2157			−1.37022			−0.685110	−	0.728439i	$-0.740246\pi$
$67$	−11.2157			−1.37022			−0.685110	+	0.728439i	$0.740246\pi$
$68$	−1.19190	+	0.740238i	−0.144540	+	0.0897670i
$69$		0			0
$70$	−0.632479	+	1.13733i	−0.0755957	+	0.135937i
$71$	5.57514			0.661647			0.330824	−	0.943693i	$-0.392673\pi$
$71$	5.57514			0.661647			0.330824	+	0.943693i	$0.392673\pi$
$72$		0			0
$73$	1.01962			0.119337			0.0596686	−	0.998218i	$-0.480996\pi$
$73$	1.01962			0.119337			0.0596686	+	0.998218i	$0.480996\pi$
$74$	1.60722	−	2.89013i	0.186835	−	0.335970i
$75$		0			0
$76$	0.826146	+	1.33023i	0.0947654	+	0.152588i
$77$	−0.443743			−0.0505692
$78$		0			0
$79$			1.86662i			0.210012i	0.994472	+	0.105006i	$0.0334861\pi$
$79$			1.86662i			0.210012i	−0.994472	+	0.105006i	$0.966514\pi$
$80$	−1.77322	+	3.58548i	−0.198252	+	0.400869i
$81$		0			0
$82$	5.06442	−	9.10693i	0.559272	−	1.00569i
$83$		−	1.75905i		−	0.193081i	−0.995329	−	0.0965404i	$-0.969222\pi$
$83$		−	1.75905i		−	0.193081i	0.995329	−	0.0965404i	$-0.0307777\pi$
$84$		0			0
$85$			0.701532i			0.0760918i
$86$	−8.73794	−	4.85922i	−0.942236	−	0.523984i
$87$		0			0
$88$	−1.36234	+	0.0657674i	−0.145226	+	0.00701082i
$89$		−	11.9152i		−	1.26301i	−0.775373	−	0.631503i	$-0.782438\pi$
$89$		−	11.9152i		−	1.26301i	0.775373	−	0.631503i	$-0.217562\pi$
$90$		0			0
$91$	−1.85654			−0.194618
$92$	1.52052	+	2.44828i	0.158525	+	0.255251i
$93$		0			0
$94$	0.363747	+	0.202282i	0.0375176	+	0.0208638i
$95$	0.782948			0.0803287
$96$		0			0
$97$	3.93818			0.399862			0.199931	−	0.979810i	$-0.435928\pi$
$97$	3.93818			0.399862			0.199931	+	0.979810i	$0.435928\pi$
$98$	7.60511	+	4.22925i	0.768232	+	0.427219i
$99$		0			0
$100$	1.05517	+	1.69900i	0.105517	+	0.169900i
$101$	−8.11015			−0.806990			−0.403495	−	0.914982i	$-0.632205\pi$
$101$	−8.11015			−0.806990			−0.403495	+	0.914982i	$0.632205\pi$
$102$		0			0
$103$			14.0930i			1.38863i	0.719672	+	0.694314i	$0.244292\pi$
$103$			14.0930i			1.38863i	−0.719672	+	0.694314i	$0.755708\pi$
$104$	−5.69979	+	0.275159i	−0.558910	+	0.0269815i
$105$		0			0
$106$	13.0010	+	7.22993i	1.26277	+	0.702233i
$107$		−	2.23739i		−	0.216297i	−0.994135	−	0.108149i	$-0.965508\pi$
$107$		−	2.23739i		−	0.216297i	0.994135	−	0.108149i	$-0.0344922\pi$
$108$		0			0
$109$		−	14.7481i		−	1.41261i	−0.707907	−	0.706306i	$-0.750360\pi$
$109$		−	14.7481i		−	1.41261i	0.707907	−	0.706306i	$-0.249640\pi$
$110$	−0.331442	+	0.596004i	−0.0316017	+	0.0568268i
$111$		0			0
$112$	−3.29939	−	1.63173i	−0.311763	−	0.154184i
$113$		−	17.3371i		−	1.63094i	−0.578802	−	0.815468i	$-0.696480\pi$
$113$		−	17.3371i		−	1.63094i	0.578802	−	0.815468i	$-0.303520\pi$
$114$		0			0
$115$	1.44101			0.134375
$116$	2.26340	+	3.64444i	0.210151	+	0.338378i
$117$		0			0
$118$	7.42599	−	13.3535i	0.683618	−	1.22929i
$119$	−0.645554			−0.0591778
$120$		0			0
$121$	10.7675			0.978860
$122$	−5.95121	+	10.7016i	−0.538797	+	0.968873i
$123$		0			0
$124$	−11.1992	+	6.95532i	−1.00572	+	0.624606i
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	3.45636i		−	0.306702i	−0.988172	−	0.153351i	$-0.950993\pi$
$127$		−	3.45636i		−	0.306702i	0.988172	−	0.153351i	$-0.0490066\pi$
$128$	−10.3713	−	4.52058i	−0.916704	−	0.399566i
$129$		0			0
$130$	−1.38669	+	2.49357i	−0.121621	+	0.218701i
$131$		−	17.4536i		−	1.52493i	−0.647032	−	0.762463i	$-0.723990\pi$
$131$		−	17.4536i		−	1.52493i	0.647032	−	0.762463i	$-0.276010\pi$
$132$		0			0
$133$			0.720473i			0.0624730i
$134$	−13.8622	−	7.70884i	−1.19751	−	0.665942i
$135$		0			0
$136$	−1.98192	+	0.0956778i	−0.169948	+	0.00820430i
$137$			9.15998i			0.782590i	0.920265	+	0.391295i	$0.127973\pi$
$137$			9.15998i			0.782590i	−0.920265	+	0.391295i	$0.872027\pi$
$138$		0			0
$139$	−8.97927			−0.761611			−0.380806	−	0.924655i	$-0.624353\pi$
$139$	−8.97927			−0.761611			−0.380806	+	0.924655i	$0.624353\pi$
$140$	−1.56343	+	0.970977i	−0.132134	+	0.0820626i
$141$		0			0
$142$	6.89063	+	3.83192i	0.578249	+	0.321568i
$143$	−0.972894			−0.0813575
$144$		0			0
$145$	2.14505			0.178137
$146$	1.26020	+	0.700807i	0.104295	+	0.0579992i
$147$		0			0
$148$	3.97290	−	2.46739i	0.326571	−	0.202818i
$149$	5.27614			0.432238			0.216119	−	0.976367i	$-0.430660\pi$
$149$	5.27614			0.432238			0.216119	+	0.976367i	$0.430660\pi$
$150$		0			0
$151$			16.8834i			1.37395i	0.726681	+	0.686975i	$0.241062\pi$
$151$			16.8834i			1.37395i	−0.726681	+	0.686975i	$0.758938\pi$
$152$	0.106782	+	2.21193i	0.00866114	+	0.179412i
$153$		0			0
$154$	−0.548447	−	0.304995i	−0.0441951	−	0.0245772i
$155$			6.59164i			0.529453i
$156$		0			0
$157$		−	14.2642i		−	1.13841i	−0.822196	−	0.569204i	$-0.807251\pi$
$157$		−	14.2642i		−	1.13841i	0.822196	−	0.569204i	$-0.192749\pi$
$158$	−1.28297	+	2.30706i	−0.102068	+	0.183540i
$159$		0			0
$160$	−4.65601	+	3.21273i	−0.368090	+	0.253988i
$161$			1.32603i			0.104506i
$162$		0			0
$163$	−2.68674			−0.210442			−0.105221	−	0.994449i	$-0.533555\pi$
$163$	−2.68674			−0.210442			−0.105221	+	0.994449i	$0.533555\pi$
$164$	12.5188	−	7.77487i	0.977555	−	0.607115i
$165$		0			0
$166$	1.20904	−	2.17411i	0.0938394	−	0.168744i
$167$	7.28504			0.563733			0.281867	−	0.959454i	$-0.409046\pi$
$167$	7.28504			0.563733			0.281867	+	0.959454i	$0.409046\pi$
$168$		0			0
$169$	8.92959			0.686891
$170$	−0.482179	+	0.867062i	−0.0369814	+	0.0665006i
$171$		0			0
$172$	−7.45985	−	12.0116i	−0.568808	−	0.915874i
$173$	−6.06567			−0.461164			−0.230582	−	0.973053i	$-0.574063\pi$
$173$	−6.06567			−0.461164			−0.230582	+	0.973053i	$0.574063\pi$
$174$		0			0
$175$			0.920206i			0.0695611i
$176$	−1.72900	−	0.855083i	−0.130328	−	0.0644543i
$177$		0			0
$178$	8.18958	−	14.7266i	0.613835	−	1.10381i
$179$		−	18.1969i		−	1.36010i	−0.733165	−	0.680050i	$-0.761958\pi$
$179$		−	18.1969i		−	1.36010i	0.733165	−	0.680050i	$-0.238042\pi$
$180$		0			0
$181$		−	5.60765i		−	0.416813i	−0.978042	−	0.208407i	$-0.933172\pi$
$181$		−	5.60765i		−	0.416813i	0.978042	−	0.208407i	$-0.0668278\pi$
$182$	−2.29460	−	1.27604i	−0.170087	−	0.0945866i
$183$		0			0
$184$	0.196531	+	4.07106i	0.0144885	+	0.300122i
$185$		−	2.33837i		−	0.171921i
$186$		0			0
$187$	−0.338293			−0.0247385
$188$	0.310542	+	0.500023i	0.0226486	+	0.0364680i
$189$		0			0
$190$	0.967689	+	0.538138i	0.0702035	+	0.0390406i
$191$	8.21210			0.594206			0.297103	−	0.954845i	$-0.403979\pi$
$191$	8.21210			0.594206			0.297103	+	0.954845i	$0.403979\pi$
$192$		0			0
$193$	14.2696			1.02715			0.513573	−	0.858046i	$-0.328322\pi$
$193$	14.2696			1.02715			0.513573	+	0.858046i	$0.328322\pi$
$194$	4.86742	+	2.70680i	0.349460	+	0.194337i
$195$		0			0
$196$	6.49272	+	10.4543i	0.463765	+	0.746738i
$197$	3.98477			0.283903			0.141952	−	0.989874i	$-0.454662\pi$
$197$	3.98477			0.283903			0.141952	+	0.989874i	$0.454662\pi$
$198$		0			0
$199$		−	27.7090i		−	1.96424i	−0.188264	−	0.982118i	$-0.560286\pi$
$199$		−	27.7090i		−	1.96424i	0.188264	−	0.982118i	$-0.439714\pi$
$200$	0.136384	+	2.82514i	0.00964382	+	0.199767i
$201$		0			0
$202$	−10.0238	−	5.57429i	−0.705271	−	0.392206i
$203$			1.97389i			0.138540i
$204$		0			0
$205$		−	7.36833i		−	0.514626i
$206$	−9.68647	+	17.4184i	−0.674888	+	1.21359i
$207$		0			0
$208$	−7.23381	−	3.57751i	−0.501574	−	0.248056i
$209$			0.377554i			0.0261160i
$210$		0			0
$211$	−17.5428			−1.20769			−0.603847	−	0.797100i	$-0.706366\pi$
$211$	−17.5428			−1.20769			−0.603847	+	0.797100i	$0.706366\pi$
$212$	11.0993	+	17.8717i	0.762305	+	1.22744i
$213$		0			0
$214$	1.53781	−	2.76532i	0.105123	−	0.189033i
$215$	−7.06978			−0.482155
$216$		0			0
$217$	−6.06567			−0.411764
$218$	10.1367	−	18.2280i	0.686545	−	1.23456i
$219$		0			0
$220$	−0.819295	+	0.508827i	−0.0552369	+	0.0343051i
$221$	−1.41536			−0.0952073
$222$		0			0
$223$			0.406159i			0.0271984i	0.999908	+	0.0135992i	$0.00432890\pi$
$223$			0.406159i			0.0271984i	−0.999908	+	0.0135992i	$0.995671\pi$
$224$	−2.95637	−	4.28449i	−0.197531	−	0.286269i
$225$		0			0
$226$	11.9162	−	21.4279i	0.792653	−	1.42536i
$227$			17.6015i			1.16825i	0.811663	+	0.584126i	$0.198563\pi$
$227$			17.6015i			1.16825i	−0.811663	+	0.584126i	$0.801437\pi$
$228$		0			0
$229$		−	25.2194i		−	1.66655i	−0.552860	−	0.833274i	$-0.686464\pi$
$229$		−	25.2194i		−	1.66655i	0.552860	−	0.833274i	$-0.313536\pi$
$230$	1.78103	+	0.990441i	0.117437	+	0.0653078i
$231$		0			0
$232$	0.292551	+	6.06006i	0.0192069	+	0.397862i
$233$		−	12.9599i		−	0.849034i	−0.905420	−	0.424517i	$-0.860444\pi$
$233$		−	12.9599i		−	0.849034i	0.905420	−	0.424517i	$-0.139556\pi$
$234$		0			0
$235$	0.294304			0.0191983
$236$	18.3564	−	11.4003i	1.19490	−	0.742098i
$237$		0			0
$238$	−0.797876	−	0.443704i	−0.0517186	−	0.0287611i
$239$	12.1176			0.783821			0.391911	−	0.920003i	$-0.371814\pi$
$239$	12.1176			0.783821			0.391911	+	0.920003i	$0.371814\pi$
$240$		0			0
$241$	6.52697			0.420439			0.210220	−	0.977654i	$-0.432582\pi$
$241$	6.52697			0.420439			0.210220	+	0.977654i	$0.432582\pi$
$242$	13.3081	+	7.40073i	0.855478	+	0.475737i
$243$		0			0
$244$	−14.7109	+	9.13625i	−0.941766	+	0.584888i
$245$	6.15322			0.393115
$246$		0			0
$247$			1.57962i			0.100509i
$248$	−18.6223	+	0.898995i	−1.18252	+	0.0570862i
$249$		0			0
$250$	1.23596	+	0.687323i	0.0781687	+	0.0434701i
$251$			8.66260i			0.546779i	0.961903	+	0.273389i	$0.0881447\pi$
$251$			8.66260i			0.546779i	−0.961903	+	0.273389i	$0.911855\pi$
$252$		0			0
$253$			0.694887i			0.0436872i
$254$	2.37564	−	4.27191i	0.149061	−	0.268043i
$255$		0			0
$256$	−9.71140	−	12.7157i	−0.606962	−	0.794730i
$257$			22.7615i			1.41982i	0.704291	+	0.709912i	$0.251265\pi$
$257$			22.7615i			1.41982i	−0.704291	+	0.709912i	$0.748735\pi$
$258$		0			0
$259$	2.15179			0.133706
$260$	−3.42778	+	2.12884i	−0.212582	+	0.132025i
$261$		0			0
$262$	11.9962	−	21.5718i	0.741130	−	1.33271i
$263$	−20.7096			−1.27701			−0.638506	−	0.769617i	$-0.720447\pi$
$263$	−20.7096			−1.27701			−0.638506	+	0.769617i	$0.720447\pi$
$264$		0			0
$265$	10.5190			0.646175
$266$	−0.495198	+	0.890473i	−0.0303625	+	0.0545984i
$267$		0			0
$268$	−11.8346	−	19.0556i	−0.722910	−	1.16400i
$269$	−13.2212			−0.806112			−0.403056	−	0.915175i	$-0.632052\pi$
$269$	−13.2212			−0.806112			−0.403056	+	0.915175i	$0.632052\pi$
$270$		0			0
$271$		−	4.05018i		−	0.246031i	−0.992405	−	0.123016i	$-0.960743\pi$
$271$		−	4.05018i		−	0.246031i	0.992405	−	0.123016i	$-0.0392565\pi$
$272$	−2.51533	−	1.24397i	−0.152514	−	0.0754266i
$273$		0			0
$274$	−6.29587	+	11.3213i	−0.380347	+	0.683947i
$275$			0.482221i			0.0290790i
$276$		0			0
$277$		−	4.33623i		−	0.260539i	−0.991479	−	0.130269i	$-0.958416\pi$
$277$		−	4.33623i		−	0.260539i	0.991479	−	0.130269i	$-0.0415842\pi$
$278$	−11.0980	−	6.17166i	−0.665612	−	0.370151i
$279$		0			0
$280$	−2.59971	+	0.125502i	−0.155362	+	0.00750016i
$281$			24.2605i			1.44726i	0.690188	+	0.723630i	$0.257528\pi$
$281$			24.2605i			1.44726i	−0.690188	+	0.723630i	$0.742472\pi$
$282$		0			0
$283$	−27.0761			−1.60951			−0.804754	−	0.593609i	$-0.797703\pi$
$283$	−27.0761			−1.60951			−0.804754	+	0.593609i	$0.797703\pi$
$284$	5.88274	+	9.47218i	0.349076	+	0.562070i
$285$		0			0
$286$	−1.20245	−	0.668693i	−0.0711026	−	0.0395406i
$287$	6.78038			0.400233
$288$		0			0
$289$	16.5079			0.971050
$290$	2.65119	+	1.47434i	0.155683	+	0.0865764i
$291$		0			0
$292$	1.07587	+	1.73233i	0.0629607	+	0.101377i
$293$	20.2078			1.18055			0.590275	−	0.807202i	$-0.299019\pi$
$293$	20.2078			1.18055			0.590275	+	0.807202i	$0.299019\pi$
$294$		0			0
$295$		−	10.8042i		−	0.629046i
$296$	6.60623	−	0.318917i	0.383979	−	0.0185367i
$297$		0			0
$298$	6.52107	+	3.62641i	0.377756	+	0.210072i
$299$			2.90728i			0.168132i
$300$		0			0
$301$		−	6.50566i		−	0.374980i
$302$	−11.6043	+	20.8671i	−0.667755	+	1.20077i
$303$		0			0
$304$	−1.38834	+	2.80725i	−0.0796266	+	0.161007i
$305$			8.65852i			0.495786i
$306$		0			0
$307$	−9.07799			−0.518108			−0.259054	−	0.965863i	$-0.583411\pi$
$307$	−9.07799			−0.518108			−0.259054	+	0.965863i	$0.583411\pi$
$308$	−0.468226	−	0.753921i	−0.0266797	−	0.0429586i
$309$		0			0
$310$	−4.53059	+	8.14697i	−0.257320	+	0.462717i
$311$	15.9031			0.901782			0.450891	−	0.892579i	$-0.351106\pi$
$311$	15.9031			0.901782			0.450891	+	0.892579i	$0.351106\pi$
$312$		0			0
$313$	−22.2979			−1.26035			−0.630176	−	0.776452i	$-0.717017\pi$
$313$	−22.2979			−1.26035			−0.630176	+	0.776452i	$0.717017\pi$
$314$	9.80413	−	17.6299i	0.553279	−	0.994915i
$315$		0			0
$316$	−3.17140	+	1.96961i	−0.178405	+	0.110799i
$317$	−24.9636			−1.40210			−0.701048	−	0.713114i	$-0.747284\pi$
$317$	−24.9636			−1.40210			−0.701048	+	0.713114i	$0.747284\pi$
$318$		0			0
$319$			1.03439i			0.0579146i
$320$	−7.96280	+	0.770608i	−0.445134	+	0.0430783i
$321$		0			0
$322$	−0.911410	+	1.63891i	−0.0507909	+	0.0913330i
$323$			0.549262i			0.0305618i
$324$		0			0
$325$			2.01753i			0.111912i
$326$	−3.32070	−	1.84666i	−0.183916	−	0.102277i
$327$		0			0
$328$	20.8165	−	1.00492i	1.14940	−	0.0554876i
$329$			0.270821i			0.0149308i
$330$		0			0
$331$	−1.81036			−0.0995065			−0.0497532	−	0.998762i	$-0.515843\pi$
$331$	−1.81036			−0.0995065			−0.0497532	+	0.998762i	$0.515843\pi$
$332$	2.98863	−	1.85610i	0.164022	−	0.101867i
$333$		0			0
$334$	9.00399	+	5.00718i	0.492676	+	0.273981i
$335$	−11.2157			−0.612781
$336$		0			0
$337$	27.1410			1.47847			0.739233	−	0.673449i	$-0.235188\pi$
$337$	27.1410			1.47847			0.739233	+	0.673449i	$0.235188\pi$
$338$	11.0366	+	6.13751i	0.600311	+	0.333837i
$339$		0			0
$340$	−1.19190	+	0.740238i	−0.0646401	+	0.0401450i
$341$	−3.17863			−0.172132
$342$		0			0
$343$			12.1037i			0.653537i
$344$	−0.964206	−	19.9731i	−0.0519865	−	1.07688i
$345$		0			0
$346$	−7.49690	−	4.16907i	−0.403036	−	0.224131i
$347$			29.1993i			1.56750i	0.621075	+	0.783751i	$0.286696\pi$
$347$			29.1993i			1.56750i	−0.621075	+	0.783751i	$0.713304\pi$
$348$		0			0
$349$		−	4.81219i		−	0.257591i	−0.991671	−	0.128795i	$-0.958889\pi$
$349$		−	4.81219i		−	0.257591i	0.991671	−	0.128795i	$-0.0411110\pi$
$350$	−0.632479	+	1.13733i	−0.0338074	+	0.0607931i
$351$		0			0
$352$	−1.54925	−	2.24522i	−0.0825751	−	0.119671i
$353$			2.68613i			0.142968i	0.997442	+	0.0714841i	$0.0227735\pi$
$353$			2.68613i			0.142968i	−0.997442	+	0.0714841i	$0.977226\pi$
$354$		0			0
$355$	5.57514			0.295898
$356$	20.2439	−	12.5726i	1.07293	−	0.666346i
$357$		0			0
$358$	12.5072	−	22.4906i	0.661024	−	1.18866i
$359$	1.20997			0.0638600			0.0319300	−	0.999490i	$-0.489835\pi$
$359$	1.20997			0.0638600			0.0319300	+	0.999490i	$0.489835\pi$
$360$		0			0
$361$	−18.3870			−0.967736
$362$	3.85427	−	6.93081i	0.202576	−	0.364275i
$363$		0			0
$364$	−1.95897	−	3.15427i	−0.102678	−	0.165329i
$365$	1.01962			0.0533692
$366$		0			0
$367$			2.67794i			0.139787i	0.997554	+	0.0698936i	$0.0222660\pi$
$367$			2.67794i			0.139787i	−0.997554	+	0.0698936i	$0.977734\pi$
$368$	−2.55523	+	5.16673i	−0.133200	+	0.269334i
$369$		0			0
$370$	1.60722	−	2.89013i	0.0835553	−	0.150251i
$371$			9.67962i			0.502541i
$372$		0			0
$373$			17.6359i			0.913155i	0.889684	+	0.456577i	$0.150925\pi$
$373$			17.6359i			0.913155i	−0.889684	+	0.456577i	$0.849075\pi$
$374$	−0.418116	−	0.232517i	−0.0216203	−	0.0120232i
$375$		0			0
$376$	0.0401384	+	0.831450i	0.00206998	+	0.0428787i
$377$			4.32769i			0.222888i
$378$		0			0
$379$	26.4128			1.35673			0.678367	−	0.734723i	$-0.262688\pi$
$379$	26.4128			1.35673			0.678367	+	0.734723i	$0.262688\pi$
$380$	0.826146	+	1.33023i	0.0423804	+	0.0682394i
$381$		0			0
$382$	10.1498	+	5.64436i	0.519308	+	0.288791i
$383$	−31.4773			−1.60841			−0.804207	−	0.594349i	$-0.797410\pi$
$383$	−31.4773			−1.60841			−0.804207	+	0.594349i	$0.797410\pi$
$384$		0			0
$385$	−0.443743			−0.0226152
$386$	17.6366	+	9.80781i	0.897677	+	0.499204i
$387$		0			0
$388$	4.15547	+	6.69098i	0.210962	+	0.339683i
$389$	12.9035			0.654233			0.327116	−	0.944984i	$-0.393923\pi$
$389$	12.9035			0.654233			0.327116	+	0.944984i	$0.393923\pi$
$390$		0			0
$391$			1.01092i			0.0511242i
$392$	0.839202	+	17.3837i	0.0423861	+	0.878009i
$393$		0			0
$394$	4.92500	+	2.73883i	0.248118	+	0.137980i
$395$			1.86662i			0.0939200i
$396$		0			0
$397$			29.0747i			1.45922i	0.683866	+	0.729608i	$0.260297\pi$
$397$			29.0747i			1.45922i	−0.683866	+	0.729608i	$0.739703\pi$
$398$	19.0450	−	34.2471i	0.954640	−	1.71665i
$399$		0			0
$400$	−1.77322	+	3.58548i	−0.0886609	+	0.179274i
$401$		−	4.03847i		−	0.201672i	−0.994903	−	0.100836i	$-0.967848\pi$
$401$		−	4.03847i		−	0.201672i	0.994903	−	0.100836i	$-0.0321517\pi$
$402$		0			0
$403$	−13.2988			−0.662461
$404$	−8.55761	−	13.7792i	−0.425757	−	0.685539i
$405$		0			0
$406$	−1.35670	+	2.43964i	−0.0673318	+	0.121077i
$407$	1.12761			0.0558937
$408$		0			0
$409$	23.4511			1.15958			0.579792	−	0.814764i	$-0.303134\pi$
$409$	23.4511			1.15958			0.579792	+	0.814764i	$0.303134\pi$
$410$	5.06442	−	9.10693i	0.250114	−	0.449759i
$411$		0			0
$412$	−23.9441	+	14.8706i	−1.17964	+	0.732622i
$413$	9.94211			0.489219
$414$		0			0
$415$		−	1.75905i		−	0.0863484i
$416$	−6.48176	−	9.39361i	−0.317795	−	0.460560i
$417$		0			0
$418$	−0.259502	+	0.466640i	−0.0126926	+	0.0228241i
$419$			10.7206i			0.523734i	0.965104	+	0.261867i	$0.0843381\pi$
$419$			10.7206i			0.523734i	−0.965104	+	0.261867i	$0.915662\pi$
$420$		0			0
$421$			14.6900i			0.715945i	0.933732	+	0.357972i	$0.116532\pi$
$421$			14.6900i			0.715945i	−0.933732	+	0.357972i	$0.883468\pi$
$422$	−21.6821	−	12.0576i	−1.05547	−	0.586952i
$423$		0			0
$424$	1.43462	+	29.7175i	0.0696713	+	1.44321i
$425$			0.701532i			0.0340293i
$426$		0			0
$427$	−7.96763			−0.385581
$428$	3.80134	−	2.36084i	0.183745	−	0.114115i
$429$		0			0
$430$	−8.73794	−	4.85922i	−0.421381	−	0.234333i
$431$	11.1052			0.534921			0.267460	−	0.963569i	$-0.413816\pi$
$431$	11.1052			0.534921			0.267460	+	0.963569i	$0.413816\pi$
$432$		0			0
$433$	−13.1055			−0.629812			−0.314906	−	0.949123i	$-0.601973\pi$
$433$	−13.1055			−0.629812			−0.314906	+	0.949123i	$0.601973\pi$
$434$	−7.49690	−	4.16907i	−0.359862	−	0.200122i
$435$		0			0
$436$	25.0571	−	15.5618i	1.20002	−	0.745275i
$437$	1.12824			0.0539709
$438$		0			0
$439$		−	11.5099i		−	0.549338i	−0.961539	−	0.274669i	$-0.911432\pi$
$439$		−	11.5099i		−	0.549338i	0.961539	−	0.274669i	$-0.0885682\pi$
$440$	−1.36234	+	0.0657674i	−0.0649471	+	0.00313534i
$441$		0			0
$442$	−1.74932	−	0.972809i	−0.0832067	−	0.0462718i
$443$			14.5661i			0.692055i	0.938224	+	0.346028i	$0.112470\pi$
$443$			14.5661i			0.692055i	−0.938224	+	0.346028i	$0.887530\pi$
$444$		0			0
$445$		−	11.9152i		−	0.564834i
$446$	−0.279163	+	0.501995i	−0.0132187	+	0.0237702i
$447$		0			0
$448$	−0.709118	−	7.32742i	−0.0335027	−	0.346188i
$449$		−	12.5436i		−	0.591967i	−0.955193	−	0.295984i	$-0.904353\pi$
$449$		−	12.5436i		−	0.591967i	0.955193	−	0.295984i	$-0.0956474\pi$
$450$		0			0
$451$	3.55317			0.167312
$452$	29.4558	−	18.2936i	1.38548	−	0.860460i
$453$		0			0
$454$	−12.0979	+	21.7547i	−0.567783	+	1.02100i
$455$	−1.85654			−0.0870360
$456$		0			0
$457$	5.52282			0.258347			0.129173	−	0.991622i	$-0.458768\pi$
$457$	5.52282			0.258347			0.129173	+	0.991622i	$0.458768\pi$
$458$	17.3339	−	31.1701i	0.809961	−	1.45648i
$459$		0			0
$460$	1.52052	+	2.44828i	0.0708945	+	0.114152i
$461$	−37.7632			−1.75881			−0.879405	−	0.476075i	$-0.842059\pi$
$461$	−37.7632			−1.75881			−0.879405	+	0.476075i	$0.842059\pi$
$462$		0			0
$463$			34.1260i			1.58597i	0.609241	+	0.792985i	$0.291474\pi$
$463$			34.1260i			1.58597i	−0.609241	+	0.792985i	$0.708526\pi$
$464$	−3.80364	+	7.69104i	−0.176579	+	0.357048i
$465$		0			0
$466$	8.90767	−	16.0179i	0.412640	−	0.742016i
$467$		−	12.9667i		−	0.600026i	−0.953935	−	0.300013i	$-0.903009\pi$
$467$		−	12.9667i		−	0.600026i	0.953935	−	0.300013i	$-0.0969910\pi$
$468$		0			0
$469$		−	10.3208i		−	0.476570i
$470$	0.363747	+	0.202282i	0.0167784	+	0.00933058i
$471$		0			0
$472$	30.5234	−	1.47352i	1.40495	−	0.0678245i
$473$		−	3.40920i		−	0.156755i
$474$		0			0
$475$	0.782948			0.0359241
$476$	−0.681171	−	1.09680i	−0.0312214	−	0.0502716i
$477$		0			0
$478$	14.9768	+	8.32870i	0.685023	+	0.380946i
$479$	−36.0652			−1.64786			−0.823931	−	0.566690i	$-0.808224\pi$
$479$	−36.0652			−1.64786			−0.823931	+	0.566690i	$0.808224\pi$
$480$		0			0
$481$	4.71773			0.215110
$482$	8.06705	+	4.48614i	0.367444	+	0.204338i
$483$		0			0
$484$	11.3615	+	18.2939i	0.516434	+	0.831543i
$485$	3.93818			0.178824
$486$		0			0
$487$			40.1129i			1.81769i	0.417135	+	0.908845i	$0.363034\pi$
$487$			40.1129i			1.81769i	−0.417135	+	0.908845i	$0.636966\pi$
$488$	−24.4615	+	1.18089i	−1.10732	+	0.0534562i
$489$		0			0
$490$	7.60511	+	4.22925i	0.343564	+	0.191058i
$491$		−	38.8605i		−	1.75375i	−0.480720	−	0.876874i	$-0.659625\pi$
$491$		−	38.8605i		−	1.75375i	0.480720	−	0.876874i	$-0.340375\pi$
$492$		0			0
$493$			1.50482i			0.0677737i
$494$	−1.08571	+	1.95234i	−0.0488483	+	0.0878398i
$495$		0			0
$496$	−23.6342	−	11.6884i	−1.06121	−	0.524825i
$497$			5.13028i			0.230124i
$498$		0			0
$499$	−10.1400			−0.453928			−0.226964	−	0.973903i	$-0.572880\pi$
$499$	−10.1400			−0.453928			−0.226964	+	0.973903i	$0.572880\pi$
$500$	1.05517	+	1.69900i	0.0471888	+	0.0759817i
$501$		0			0
$502$	−5.95401	+	10.7066i	−0.265740	+	0.477859i
$503$	−29.8213			−1.32967			−0.664834	−	0.746991i	$-0.731498\pi$
$503$	−29.8213			−1.32967			−0.664834	+	0.746991i	$0.731498\pi$
$504$		0			0
$505$	−8.11015			−0.360897
$506$	−0.477612	+	0.858849i	−0.0212324	+	0.0381805i
$507$		0			0
$508$	5.87236	−	3.64706i	0.260544	−	0.161812i
$509$	−31.1769			−1.38189			−0.690945	−	0.722907i	$-0.742805\pi$
$509$	−31.1769			−1.38189			−0.690945	+	0.722907i	$0.742805\pi$
$510$		0			0
$511$			0.938258i			0.0415061i
$512$	−3.26307	−	22.3909i	−0.144209	−	0.989547i
$513$		0			0
$514$	−15.6445	+	28.1322i	−0.690050	+	1.24086i
$515$			14.0930i			0.621013i
$516$		0			0
$517$			0.141920i			0.00624162i
$518$	2.65951	+	1.47897i	0.116852	+	0.0649823i
$519$		0			0
$520$	−5.69979	+	0.275159i	−0.249952	+	0.0120665i
$521$			30.7989i			1.34932i	0.738127	+	0.674662i	$0.235711\pi$
$521$			30.7989i			1.34932i	−0.738127	+	0.674662i	$0.764289\pi$
$522$		0			0
$523$	26.0367			1.13851			0.569253	−	0.822162i	$-0.307233\pi$
$523$	26.0367			1.13851			0.569253	+	0.822162i	$0.307233\pi$
$524$	29.6536	−	18.4165i	1.29543	−	0.804530i
$525$		0			0
$526$	−25.5962	−	14.2342i	−1.11605	−	0.620641i
$527$	−4.62424			−0.201435
$528$		0			0
$529$	−20.9235			−0.909717
$530$	13.0010	+	7.22993i	0.564726	+	0.314048i
$531$		0			0
$532$	−1.22409	+	0.760224i	−0.0530709	+	0.0329599i
$533$	14.8658			0.643909
$534$		0			0
$535$		−	2.23739i		−	0.0967310i
$536$	−1.52965	−	31.6860i	−0.0660708	−	1.36863i
$537$		0			0
$538$	−16.3408	−	9.08725i	−0.704504	−	0.391779i
$539$			2.96721i			0.127807i
$540$		0			0
$541$			17.2351i			0.740994i	0.928834	+	0.370497i	$0.120813\pi$
$541$			17.2351i			0.740994i	−0.928834	+	0.370497i	$0.879187\pi$
$542$	2.78378	−	5.00585i	0.119574	−	0.215020i
$543$		0			0
$544$	−2.25383	−	3.26633i	−0.0966321	−	0.140043i
$545$		−	14.7481i		−	0.631739i
$546$		0			0
$547$	33.1887			1.41905			0.709523	−	0.704682i	$-0.248910\pi$
$547$	33.1887			1.41905			0.709523	+	0.704682i	$0.248910\pi$
$548$	−15.5628	+	9.66537i	−0.664811	+	0.412884i
$549$		0			0
$550$	−0.331442	+	0.596004i	−0.0141327	+	0.0254137i
$551$	1.67946			0.0715475
$552$		0			0
$553$	−1.71768			−0.0730431
$554$	2.98039	−	5.35939i	0.126625	−	0.227699i
$555$		0			0
$556$	−9.47469	−	15.2558i	−0.401816	−	0.646990i
$557$	−19.8024			−0.839053			−0.419526	−	0.907743i	$-0.637804\pi$
$557$	−19.8024			−0.839053			−0.419526	+	0.907743i	$0.637804\pi$
$558$		0			0
$559$		−	14.2635i		−	0.603280i
$560$	−3.29939	−	1.63173i	−0.139424	−	0.0689530i
$561$		0			0
$562$	−16.6748	+	29.9849i	−0.703384	+	1.26484i
$563$			23.6881i			0.998333i	0.866506	+	0.499166i	$0.166360\pi$
$563$			23.6881i			0.998333i	−0.866506	+	0.499166i	$0.833640\pi$
$564$		0			0
$565$		−	17.3371i		−	0.729377i
$566$	−33.4649	−	18.6100i	−1.40663	−	0.782238i
$567$		0			0
$568$	0.760361	+	15.7505i	0.0319040	+	0.660878i
$569$		−	1.15817i		−	0.0485531i	−0.999705	−	0.0242765i	$-0.992272\pi$
$569$		−	1.15817i		−	0.0485531i	0.999705	−	0.0242765i	$-0.00772822\pi$
$570$		0			0
$571$	−26.1823			−1.09570			−0.547848	−	0.836578i	$-0.684553\pi$
$571$	−26.1823			−1.09570			−0.547848	+	0.836578i	$0.684553\pi$
$572$	−1.02657	−	1.65295i	−0.0429231	−	0.0691133i
$573$		0			0
$574$	8.38025	+	4.66032i	0.349785	+	0.194518i
$575$	1.44101			0.0600944
$576$		0			0
$577$	−35.9581			−1.49696			−0.748479	−	0.663159i	$-0.769215\pi$
$577$	−35.9581			−1.49696			−0.748479	+	0.663159i	$0.769215\pi$
$578$	20.4030	+	11.3462i	0.848652	+	0.471941i
$579$		0			0
$580$	2.26340	+	3.64444i	0.0939825	+	0.151327i
$581$	1.61869			0.0671545
$582$		0			0
$583$			5.07247i			0.210080i
$584$	0.139060	+	2.88056i	0.00575433	+	0.119198i
$585$		0			0
$586$	24.9759	+	13.8893i	1.03174	+	0.573760i
$587$		−	7.68401i		−	0.317153i	−0.987347	−	0.158577i	$-0.949310\pi$
$587$		−	7.68401i		−	0.317153i	0.987347	−	0.158577i	$-0.0506905\pi$
$588$		0			0
$589$			5.16091i			0.212651i
$590$	7.42599	−	13.3535i	0.305723	−	0.549756i
$591$		0			0
$592$	8.38420	+	4.14645i	0.344589	+	0.170418i
$593$		−	14.3657i		−	0.589930i	−0.955508	−	0.294965i	$-0.904692\pi$
$593$		−	14.3657i		−	0.589930i	0.955508	−	0.294965i	$-0.0953080\pi$
$594$		0			0
$595$	−0.645554			−0.0264651
$596$	5.56724	+	8.96417i	0.228043	+	0.367187i
$597$		0			0
$598$	−1.99824	+	3.59327i	−0.0817142	+	0.146940i
$599$	17.9780			0.734562			0.367281	−	0.930110i	$-0.380289\pi$
$599$	17.9780			0.734562			0.367281	+	0.930110i	$0.380289\pi$
$600$		0			0
$601$	−21.2552			−0.867018			−0.433509	−	0.901149i	$-0.642725\pi$
$601$	−21.2552			−0.867018			−0.433509	+	0.901149i	$0.642725\pi$
$602$	4.47149	−	8.04070i	0.182244	−	0.327715i
$603$		0			0
$604$	−28.6849	+	17.8149i	−1.16717	+	0.724878i
$605$	10.7675			0.437760
$606$		0			0
$607$		−	0.428639i		−	0.0173979i	−0.999962	−	0.00869897i	$-0.997231\pi$
$607$		−	0.428639i		−	0.0173979i	0.999962	−	0.00869897i	$-0.00276900\pi$
$608$	−3.64541	+	2.51540i	−0.147841	+	0.102013i
$609$		0			0
$610$	−5.95121	+	10.7016i	−0.240957	+	0.433293i
$611$			0.593766i			0.0240212i
$612$		0			0
$613$			40.6593i			1.64221i	0.570774	+	0.821107i	$0.306643\pi$
$613$			40.6593i			1.64221i	−0.570774	+	0.821107i	$0.693357\pi$
$614$	−11.2200	−	6.23951i	−0.452802	−	0.251806i
$615$		0			0
$616$	−0.0605195	−	1.25364i	−0.00243840	−	0.0505104i
$617$			16.8640i			0.678920i	0.940621	+	0.339460i	$0.110244\pi$
$617$			16.8640i			0.678920i	−0.940621	+	0.339460i	$0.889756\pi$
$618$		0			0
$619$	16.2055			0.651353			0.325677	−	0.945481i	$-0.394408\pi$
$619$	16.2055			0.651353			0.325677	+	0.945481i	$0.394408\pi$
$620$	−11.1992	+	6.95532i	−0.449771	+	0.279332i
$621$		0			0
$622$	19.6555	+	10.9306i	0.788114	+	0.438276i
$623$	10.9644			0.439280
$624$		0			0
$625$	1.00000			0.0400000
$626$	−27.5592	−	15.3259i	−1.10149	−	0.612545i
$627$		0			0
$628$	24.2349	−	15.0512i	0.967079	−	0.600609i
$629$	1.64044			0.0654088
$630$		0			0
$631$		−	10.7163i		−	0.426609i	−0.976986	−	0.213304i	$-0.931577\pi$
$631$		−	10.7163i		−	0.426609i	0.976986	−	0.213304i	$-0.0684226\pi$
$632$	−5.27347	+	0.254578i	−0.209767	+	0.0101266i
$633$		0			0
$634$	−30.8539	−	17.1581i	−1.22537	−	0.681434i
$635$		−	3.45636i		−	0.137161i
$636$		0			0
$637$			12.4143i			0.491872i
$638$	−0.710959	+	1.27846i	−0.0281471	+	0.0506147i
$639$		0			0
$640$	−10.3713	−	4.52058i	−0.409963	−	0.178692i
$641$			25.7665i			1.01772i	0.860851	+	0.508858i	$0.169932\pi$
$641$			25.7665i			1.01772i	−0.860851	+	0.508858i	$0.830068\pi$
$642$		0			0
$643$	−9.51281			−0.375149			−0.187574	−	0.982250i	$-0.560063\pi$
$643$	−9.51281			−0.375149			−0.187574	+	0.982250i	$0.560063\pi$
$644$	−2.25293	+	1.39919i	−0.0887777	+	0.0551358i
$645$		0			0
$646$	−0.377521	+	0.678864i	−0.0148534	+	0.0267096i
$647$	0.478556			0.0188140			0.00940699	−	0.999956i	$-0.497006\pi$
$647$	0.478556			0.0188140			0.00940699	+	0.999956i	$0.497006\pi$
$648$		0			0
$649$	5.21002			0.204511
$650$	−1.38669	+	2.49357i	−0.0543906	+	0.0978060i
$651$		0			0
$652$	−2.83498	−	4.56478i	−0.111026	−	0.178771i
$653$	35.1846			1.37688			0.688439	−	0.725294i	$-0.258296\pi$
$653$	35.1846			1.37688			0.688439	+	0.725294i	$0.258296\pi$
$654$		0			0
$655$		−	17.4536i		−	0.681967i
$656$	26.4190	+	13.0657i	1.03149	+	0.510128i
$657$		0			0
$658$	−0.186141	+	0.334722i	−0.00725654	+	0.0130488i
$659$			11.6312i			0.453088i	0.974001	+	0.226544i	$0.0727427\pi$
$659$			11.6312i			0.453088i	−0.974001	+	0.226544i	$0.927257\pi$
$660$		0			0
$661$		−	25.6802i		−	0.998843i	−0.866359	−	0.499421i	$-0.833546\pi$
$661$		−	25.6802i		−	0.998843i	0.866359	−	0.499421i	$-0.166454\pi$
$662$	−2.23753	−	1.24430i	−0.0869640	−	0.0483612i
$663$		0			0
$664$	4.96956	−	0.239907i	0.192856	−	0.00931018i
$665$			0.720473i			0.0279388i
$666$		0			0
$667$	3.09104			0.119686
$668$	7.68698	+	12.3773i	0.297418	+	0.478892i
$669$		0			0
$670$	−13.8622	−	7.70884i	−0.535542	−	0.297818i
$671$	−4.17533			−0.161187
$672$		0			0
$673$	−1.60255			−0.0617738			−0.0308869	−	0.999523i	$-0.509833\pi$
$673$	−1.60255			−0.0617738			−0.0308869	+	0.999523i	$0.509833\pi$
$674$	33.5451	+	18.6547i	1.29211	+	0.718551i
$675$		0			0
$676$	9.42226	+	15.1714i	0.362395	+	0.583515i
$677$	7.62519			0.293060			0.146530	−	0.989206i	$-0.453190\pi$
$677$	7.62519			0.293060			0.146530	+	0.989206i	$0.453190\pi$
$678$		0			0
$679$			3.62394i			0.139074i
$680$	−1.98192	+	0.0956778i	−0.0760033	+	0.00366908i
$681$		0			0
$682$	−3.92864	−	2.18474i	−0.150436	−	0.0836582i
$683$			28.3435i			1.08453i	0.840207	+	0.542266i	$0.182434\pi$
$683$			28.3435i			1.08453i	−0.840207	+	0.542266i	$0.817566\pi$
$684$		0			0
$685$			9.15998i			0.349985i
$686$	−8.31914	+	14.9596i	−0.317626	+	0.571161i
$687$		0			0
$688$	12.5363	−	25.3486i	0.477940	−	0.966406i
$689$			21.2223i			0.808505i
$690$		0			0
$691$	19.3466			0.735979			0.367990	−	0.929830i	$-0.380046\pi$
$691$	19.3466			0.735979			0.367990	+	0.929830i	$0.380046\pi$
$692$	−6.40033	−	10.3056i	−0.243304	−	0.391759i
$693$		0			0
$694$	−20.0694	+	36.0891i	−0.761823	+	1.36992i
$695$	−8.97927			−0.340603
$696$		0			0
$697$	5.16912			0.195794
$698$	3.30753	−	5.94766i	0.125192	−	0.225122i
$699$		0			0
$700$	−1.56343	+	0.970977i	−0.0590922	+	0.0366995i
$701$	−49.8239			−1.88182			−0.940912	−	0.338650i	$-0.890030\pi$
$701$	−49.8239			−1.88182			−0.940912	+	0.338650i	$0.890030\pi$
$702$		0			0
$703$		−	1.83082i		−	0.0690509i
$704$	−0.371604	−	3.83983i	−0.0140053	−	0.144719i
$705$		0			0
$706$	−1.84624	+	3.31993i	−0.0694841	+	0.124947i
$707$		−	7.46301i		−	0.280675i
$708$		0			0
$709$			2.93005i			0.110040i	0.998485	+	0.0550202i	$0.0175223\pi$
$709$			2.93005i			0.110040i	−0.998485	+	0.0550202i	$0.982478\pi$
$710$	6.89063	+	3.83192i	0.258601	+	0.143810i
$711$		0			0
$712$	33.6620	−	1.62504i	1.26154	−	0.0609010i
$713$			9.49863i			0.355726i
$714$		0			0
$715$	−0.972894			−0.0363842
$716$	30.9166	−	19.2009i	1.15541	−	0.717571i
$717$		0			0
$718$	1.49547	+	0.831643i	0.0558106	+	0.0310367i
$719$	42.4103			1.58164			0.790818	−	0.612051i	$-0.209655\pi$
$719$	42.4103			1.58164			0.790818	+	0.612051i	$0.209655\pi$
$720$		0			0
$721$	−12.9685			−0.482972
$722$	−22.7255	−	12.6378i	−0.845756	−	0.470330i
$723$		0			0
$724$	9.52741	−	5.91704i	0.354083	−	0.219905i
$725$	2.14505			0.0796651
$726$		0			0
$727$		−	33.8955i		−	1.25712i	−0.777763	−	0.628558i	$-0.783645\pi$
$727$		−	33.8955i		−	1.25712i	0.777763	−	0.628558i	$-0.216355\pi$
$728$	−0.253203	−	5.24498i	−0.00938432	−	0.194392i
$729$		0			0
$730$	1.26020	+	0.700807i	0.0466422	+	0.0259380i
$731$		−	4.95967i		−	0.183440i
$732$		0			0
$733$			4.65523i			0.171945i	0.996298	+	0.0859724i	$0.0273997\pi$
$733$			4.65523i			0.171945i	−0.996298	+	0.0859724i	$0.972600\pi$
$734$	−1.84061	+	3.30981i	−0.0679381	+	0.122167i
$735$		0			0
$736$	−6.70936	+	4.62958i	−0.247310	+	0.170649i
$737$		−	5.40847i		−	0.199223i
$738$		0			0
$739$	42.8311			1.57557			0.787783	−	0.615953i	$-0.211229\pi$
$739$	42.8311			1.57557			0.787783	+	0.615953i	$0.211229\pi$
$740$	3.97290	−	2.46739i	0.146047	−	0.0907031i
$741$		0			0
$742$	−6.65303	+	11.9636i	−0.244240	+	0.439197i
$743$	−22.1930			−0.814182			−0.407091	−	0.913388i	$-0.633457\pi$
$743$	−22.1930			−0.814182			−0.407091	+	0.913388i	$0.633457\pi$
$744$		0			0
$745$	5.27614			0.193303
$746$	−12.1216	+	21.7973i	−0.443803	+	0.798054i
$747$		0			0
$748$	−0.356958	−	0.574761i	−0.0130517	−	0.0210154i
$749$	2.05886			0.0752293
$750$		0			0
$751$		−	0.0193272i		−	0.000705259i	−1.00000		0.000352629i	$-0.999888\pi$
$751$		−	0.0193272i		−	0.000705259i	1.00000		0.000352629i	$-0.000112245\pi$
$752$	−0.521865	+	1.05522i	−0.0190305	+	0.0384800i
$753$		0			0
$754$	−2.97452	+	5.34884i	−0.108326	+	0.194793i
$755$			16.8834i			0.614450i
$756$		0			0
$757$			47.2539i			1.71747i	0.512417	+	0.858736i	$0.328750\pi$
$757$			47.2539i			1.71747i	−0.512417	+	0.858736i	$0.671250\pi$
$758$	32.6451	+	18.1541i	1.18572	+	0.659388i
$759$		0			0
$760$	0.106782	+	2.21193i	0.00387338	+	0.0802353i
$761$		−	40.7068i		−	1.47562i	−0.675007	−	0.737811i	$-0.735860\pi$
$761$		−	40.7068i		−	1.47562i	0.675007	−	0.737811i	$-0.264140\pi$
$762$		0			0
$763$	13.5713			0.491314
$764$	8.66519	+	13.9524i	0.313495	+	0.504779i
$765$		0			0
$766$	−38.9045	−	21.6351i	−1.40568	−	0.781707i
$767$	21.7978			0.787073
$768$		0			0
$769$	1.80744			0.0651780			0.0325890	−	0.999469i	$-0.489625\pi$
$769$	1.80744			0.0651780			0.0325890	+	0.999469i	$0.489625\pi$
$770$	−0.548447	−	0.304995i	−0.0197647	−	0.0109913i
$771$		0			0
$772$	15.0569	+	24.2440i	0.541909	+	0.872562i
$773$	39.1312			1.40745			0.703726	−	0.710471i	$-0.251518\pi$
$773$	39.1312			1.40745			0.703726	+	0.710471i	$0.251518\pi$
$774$		0			0
$775$			6.59164i			0.236779i
$776$	0.537106	+	11.1259i	0.0192810	+	0.399397i
$777$		0			0
$778$	15.9481	+	8.86887i	0.571769	+	0.317964i
$779$		−	5.76902i		−	0.206696i
$780$		0			0
$781$			2.68845i			0.0962004i
$782$	−0.694826	+	1.24945i	−0.0248469	+	0.0446801i
$783$		0			0
$784$	−10.9110	+	22.0623i	−0.389678	+	0.787938i
$785$		−	14.2642i		−	0.509112i
$786$		0			0
$787$	4.89070			0.174335			0.0871673	−	0.996194i	$-0.472219\pi$
$787$	4.89070			0.174335			0.0871673	+	0.996194i	$0.472219\pi$
$788$	4.20463	+	6.77014i	0.149784	+	0.241176i
$789$		0			0
$790$	−1.28297	+	2.30706i	−0.0456461	+	0.0820816i
$791$	15.9537			0.567248
$792$		0			0
$793$	−17.4688			−0.620335
$794$	−19.9837	+	35.9350i	−0.709195	+	1.27529i
$795$		0			0
$796$	47.0776	−	29.2378i	1.66862	−	1.03631i
$797$	−31.9556			−1.13193			−0.565963	−	0.824430i	$-0.691496\pi$
$797$	−31.9556			−1.13193			−0.565963	+	0.824430i	$0.691496\pi$
$798$		0			0
$799$			0.206464i			0.00730416i
$800$	−4.65601	+	3.21273i	−0.164615	+	0.113587i
$801$		0			0
$802$	2.77574	−	4.99137i	0.0980147	−	0.176252i
$803$			0.491681i			0.0173511i
$804$		0			0
$805$			1.32603i			0.0467364i
$806$	−16.4367	−	9.14058i	−0.578959	−	0.321963i
$807$		0			0
$808$	−1.10610	−	22.9123i	−0.0389123	−	0.806051i
$809$			37.3798i			1.31420i	0.753801	+	0.657102i	$0.228218\pi$
$809$			37.3798i			1.31420i	−0.753801	+	0.657102i	$0.771782\pi$
$810$		0			0
$811$	17.2532			0.605842			0.302921	−	0.953016i	$-0.402038\pi$
$811$	17.2532			0.605842			0.302921	+	0.953016i	$0.402038\pi$
$812$	−3.35364	+	2.08279i	−0.117690	+	0.0730918i
$813$		0			0
$814$	1.39368	+	0.775035i	0.0488485	+	0.0271650i
$815$	−2.68674			−0.0941125
$816$		0			0
$817$	−5.53527			−0.193655
$818$	28.9846	+	16.1185i	1.01342	+	0.563571i
$819$		0			0
$820$	12.5188	−	7.77487i	0.437176	−	0.271510i
$821$	5.86159			0.204571			0.102285	−	0.994755i	$-0.467384\pi$
$821$	5.86159			0.204571			0.102285	+	0.994755i	$0.467384\pi$
$822$		0			0
$823$		−	2.27164i		−	0.0791843i	−0.999216	−	0.0395921i	$-0.987394\pi$
$823$		−	2.27164i		−	0.0791843i	0.999216	−	0.0395921i	$-0.0126059\pi$
$824$	−39.8147	+	1.92207i	−1.38701	+	0.0669584i
$825$		0			0
$826$	12.2880	+	6.83344i	0.427554	+	0.237766i
$827$		−	43.9531i		−	1.52840i	−0.644981	−	0.764199i	$-0.723135\pi$
$827$		−	43.9531i		−	1.52840i	0.644981	−	0.764199i	$-0.276865\pi$
$828$		0			0
$829$		−	19.7872i		−	0.687239i	−0.939109	−	0.343620i	$-0.888347\pi$
$829$		−	19.7872i		−	0.687239i	0.939109	−	0.343620i	$-0.111653\pi$
$830$	1.20904	−	2.17411i	0.0419663	−	0.0754644i
$831$		0			0
$832$	−1.55472	−	16.0652i	−0.0539003	−	0.556959i
$833$			4.31668i			0.149564i
$834$		0			0
$835$	7.28504			0.252109
$836$	−0.641465	+	0.398385i	−0.0221855	+	0.0137784i
$837$		0			0
$838$	−7.36849	+	13.2501i	−0.254540	+	0.457719i
$839$	−17.6073			−0.607872			−0.303936	−	0.952692i	$-0.598301\pi$
$839$	−17.6073			−0.607872			−0.303936	+	0.952692i	$0.598301\pi$
$840$		0			0
$841$	−24.3988			−0.841337
$842$	−10.0968	+	18.1561i	−0.347957	+	0.625702i
$843$		0			0
$844$	−18.5107	−	29.8052i	−0.637163	−	1.02594i
$845$	8.92959			0.307187
$846$		0			0
$847$			9.90829i			0.340453i
$848$	−18.6524	+	37.7156i	−0.640526	+	1.29516i
$849$		0			0
$850$	−0.482179	+	0.867062i	−0.0165386	+	0.0297400i
$851$		−	3.36963i		−	0.115509i
$852$		0			0
$853$			31.9062i			1.09245i	0.837640	+	0.546223i	$0.183935\pi$
$853$			31.9062i			1.09245i	−0.837640	+	0.546223i	$0.816065\pi$
$854$	−9.84764	−	5.47634i	−0.336979	−	0.187396i
$855$		0			0
$856$	6.32095	−	0.305145i	0.216045	−	0.0104296i
$857$		−	16.0007i		−	0.546574i	−0.961933	−	0.273287i	$-0.911889\pi$
$857$		−	16.0007i		−	0.546574i	0.961933	−	0.273287i	$-0.0881108\pi$
$858$		0			0
$859$	5.29765			0.180754			0.0903768	−	0.995908i	$-0.471193\pi$
$859$	5.29765			0.180754			0.0903768	+	0.995908i	$0.471193\pi$
$860$	−7.45985	−	12.0116i	−0.254379	−	0.409591i
$861$		0			0
$862$	13.7256	+	7.63289i	0.467496	+	0.259977i
$863$	−30.1157			−1.02515			−0.512576	−	0.858642i	$-0.671309\pi$
$863$	−30.1157			−1.02515			−0.512576	+	0.858642i	$0.671309\pi$
$864$		0			0
$865$	−6.06567			−0.206239
$866$	−16.1979	−	9.00774i	−0.550426	−	0.306095i
$867$		0			0
$868$	−6.40033	−	10.3056i	−0.217241	−	0.349794i
$869$	−0.900125			−0.0305347
$870$		0			0
$871$		−	22.6280i		−	0.766722i
$872$	41.6654	−	2.01141i	1.41097	−	0.0681149i
$873$		0			0
$874$	1.39445	+	0.775464i	0.0471680	+	0.0262304i
$875$			0.920206i			0.0311087i
$876$		0			0
$877$		−	27.0663i		−	0.913963i	−0.889476	−	0.456981i	$-0.848931\pi$
$877$		−	27.0663i		−	0.913963i	0.889476	−	0.456981i	$-0.151069\pi$
$878$	7.91102	−	14.2257i	0.266984	−	0.480095i
$879$		0			0
$880$	−1.72900	−	0.855083i	−0.0582845	−	0.0288249i
$881$			26.2189i			0.883338i	0.897178	+	0.441669i	$0.145613\pi$
$881$			26.2189i			0.883338i	−0.897178	+	0.441669i	$0.854387\pi$
$882$		0			0
$883$	1.87380			0.0630584			0.0315292	−	0.999503i	$-0.489962\pi$
$883$	1.87380			0.0630584			0.0315292	+	0.999503i	$0.489962\pi$
$884$	−1.49345	−	2.40470i	−0.0502301	−	0.0808787i
$885$		0			0
$886$	−10.0116	+	18.0030i	−0.336346	+	0.604824i
$887$	20.9667			0.703992			0.351996	−	0.936001i	$-0.385503\pi$
$887$	20.9667			0.703992			0.351996	+	0.936001i	$0.385503\pi$
$888$		0			0
$889$	3.18056			0.106673
$890$	8.18958	−	14.7266i	0.274515	−	0.493638i
$891$		0			0
$892$	−0.690066	+	0.428569i	−0.0231051	+	0.0143495i
$893$	0.230425			0.00771087
$894$		0			0
$895$		−	18.1969i		−	0.608256i
$896$	4.15987	−	9.54376i	0.138971	−	0.318835i
$897$		0			0
$898$	8.62148	−	15.5033i	0.287703	−	0.517352i
$899$			14.1394i			0.471575i
$900$		0			0
$901$			7.37938i			0.245843i
$902$	4.39156	+	2.44217i	0.146223	+	0.0813155i
$903$		0			0
$904$	48.9797	−	2.36450i	1.62904	−	0.0786423i
$905$		−	5.60765i		−	0.186405i
$906$		0			0
$907$	7.98889			0.265267			0.132633	−	0.991165i	$-0.457657\pi$
$907$	7.98889			0.265267			0.132633	+	0.991165i	$0.457657\pi$
$908$	−29.9050	+	18.5726i	−0.992432	+	0.616354i
$909$		0			0
$910$	−2.29460	−	1.27604i	−0.0760653	−	0.0423004i
$911$	55.3654			1.83434			0.917169	−	0.398497i	$-0.130468\pi$
$911$	55.3654			1.83434			0.917169	+	0.398497i	$0.130468\pi$
$912$		0			0
$913$	0.848251			0.0280730
$914$	6.82597	+	3.79597i	0.225783	+	0.125559i
$915$		0			0
$916$	42.8479	−	26.6109i	1.41573	−	0.879249i
$917$	16.0609			0.530377
$918$		0			0
$919$		−	39.2576i		−	1.29499i	−0.762070	−	0.647495i	$-0.775817\pi$
$919$		−	39.2576i		−	1.29499i	0.762070	−	0.647495i	$-0.224183\pi$
$920$	0.196531	+	4.07106i	0.00647945	+	0.134219i
$921$		0			0
$922$	−46.6737	−	25.9556i	−1.53712	−	0.854801i
$923$			11.2480i			0.370232i
$924$		0			0
$925$		−	2.33837i		−	0.0768853i
$926$	−23.4556	+	42.1783i	−0.770799	+	1.38606i
$927$		0			0
$928$	−9.98736	+	6.89146i	−0.327851	+	0.226223i
$929$		−	42.8360i		−	1.40540i	−0.711485	−	0.702701i	$-0.751977\pi$
$929$		−	42.8360i		−	1.40540i	0.711485	−	0.702701i	$-0.248023\pi$
$930$		0			0
$931$	4.81765			0.157892
$932$	22.0190	−	13.6750i	0.721255	−	0.447939i
$933$		0			0
$934$	8.91229	−	16.0262i	0.291619	−	0.524394i
$935$	−0.338293			−0.0110634
$936$		0			0
$937$	−30.5942			−0.999469			−0.499734	−	0.866179i	$-0.666569\pi$
$937$	−30.5942			−0.999469			−0.499734	+	0.866179i	$0.666569\pi$
$938$	7.09372	−	12.7560i	0.231618	−	0.416500i
$939$		0			0
$940$	0.310542	+	0.500023i	0.0101288	+	0.0163090i
$941$	−46.8808			−1.52827			−0.764136	−	0.645055i	$-0.776834\pi$
$941$	−46.8808			−1.52827			−0.764136	+	0.645055i	$0.776834\pi$
$942$		0			0
$943$		−	10.6179i		−	0.345765i
$944$	38.7384	+	19.1582i	1.26083	+	0.623547i
$945$		0			0
$946$	2.34322	−	4.21362i	0.0761847	−	0.136997i
$947$		−	53.5877i		−	1.74137i	−0.491844	−	0.870684i	$-0.663677\pi$
$947$		−	53.5877i		−	1.74137i	0.491844	−	0.870684i	$-0.336323\pi$
$948$		0			0
$949$			2.05711i			0.0667765i
$950$	0.967689	+	0.538138i	0.0313960	+	0.0174595i
$951$		0			0
$952$	−0.0880433	−	1.82378i	−0.00285350	−	0.0591090i
$953$		−	23.4773i		−	0.760503i	−0.924883	−	0.380252i	$-0.875837\pi$
$953$		−	23.4773i		−	0.760503i	0.924883	−	0.380252i	$-0.124163\pi$
$954$		0			0
$955$	8.21210			0.265737
$956$	12.7862	+	20.5878i	0.413534	+	0.665857i
$957$		0			0
$958$	−44.5750	−	24.7885i	−1.44015	−	0.800879i
$959$	−8.42907			−0.272189
$960$		0			0
$961$	−12.4497			−0.401603
$962$	5.83091	+	3.24261i	0.187996	+	0.104546i
$963$		0			0
$964$	6.88709	+	11.0893i	0.221818	+	0.357164i
$965$	14.2696			0.459354
$966$		0			0
$967$			0.755493i			0.0242950i	0.999926	+	0.0121475i	$0.00386677\pi$
$967$			0.755493i			0.0242950i	−0.999926	+	0.0121475i	$0.996133\pi$
$968$	1.46851	+	30.4196i	0.0471998	+	0.977722i
$969$		0			0
$970$	4.86742	+	2.70680i	0.156283	+	0.0869102i
$971$			0.229783i			0.00737407i	0.999993	+	0.00368704i	$0.00117362\pi$
$971$			0.229783i			0.00737407i	−0.999993	+	0.00368704i	$0.998826\pi$
$972$		0			0
$973$		−	8.26278i		−	0.264893i
$974$	−27.5705	+	49.5778i	−0.883417	+	1.58857i
$975$		0			0
$976$	−31.0450	−	15.3534i	−0.993726	−	0.491452i
$977$		−	12.4218i		−	0.397410i	−0.980059	−	0.198705i	$-0.936326\pi$
$977$		−	12.4218i		−	0.397410i	0.980059	−	0.198705i	$-0.0636735\pi$
$978$		0			0
$979$	5.74575			0.183635
$980$	6.49272	+	10.4543i	0.207402	+	0.333951i
$981$		0			0
$982$	26.7097	−	48.0298i	0.852341	−	1.53269i
$983$	23.7013			0.755956			0.377978	−	0.925815i	$-0.376620\pi$
$983$	23.7013			0.755956			0.377978	+	0.925815i	$0.376620\pi$
$984$		0			0
$985$	3.98477			0.126965
$986$	−1.03430	+	1.85989i	−0.0329387	+	0.0592310i
$987$		0			0
$988$	−2.68377	+	1.66677i	−0.0853822	+	0.0530270i
$989$	−10.1876			−0.323948
$990$		0			0
$991$			4.03872i			0.128294i	0.997940	+	0.0641471i	$0.0204327\pi$
$991$			4.03872i			0.128294i	−0.997940	+	0.0641471i	$0.979567\pi$
$992$	−21.1771	−	30.6907i	−0.672375	−	0.974431i
$993$		0			0
$994$	−3.52616	+	6.34080i	−0.111843	+	0.201118i
$995$		−	27.7090i		−	0.878433i
$996$		0			0
$997$		−	49.3776i		−	1.56380i	−0.623401	−	0.781902i	$-0.714250\pi$
$997$		−	49.3776i		−	1.56380i	0.623401	−	0.781902i	$-0.285750\pi$
$998$	−12.5326	−	6.96945i	−0.396712	−	0.220614i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.b.a.971.14	yes	16
3.2	odd	2		1080.2.b.d.971.3	yes	16
4.3	odd	2		4320.2.b.d.431.7		16
8.3	odd	2		1080.2.b.d.971.4	yes	16
8.5	even	2		4320.2.b.b.431.10		16
12.11	even	2		4320.2.b.b.431.7		16
24.5	odd	2		4320.2.b.d.431.10		16
24.11	even	2	inner	1080.2.b.a.971.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.b.a.971.13	✓	16	24.11	even	2	inner
1080.2.b.a.971.14	yes	16	1.1	even	1	trivial
1080.2.b.d.971.3	yes	16	3.2	odd	2
1080.2.b.d.971.4	yes	16	8.3	odd	2
4320.2.b.b.431.7		16	12.11	even	2
4320.2.b.b.431.10		16	8.5	even	2
4320.2.b.d.431.7		16	4.3	odd	2
4320.2.b.d.431.10		16	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23596 + 0.687323i) q^{2} +(1.05517 + 1.69900i) q^{4} +1.00000 q^{5} +0.920206i q^{7} +(0.136384 + 2.82514i) q^{8} +(1.23596 + 0.687323i) q^{10} +0.482221i q^{11} +2.01753i q^{13} +(-0.632479 + 1.13733i) q^{14} +(-1.77322 + 3.58548i) q^{16} +0.701532i q^{17} +0.782948 q^{19} +(1.05517 + 1.69900i) q^{20} +(-0.331442 + 0.596004i) q^{22} +1.44101 q^{23} +1.00000 q^{25} +(-1.38669 + 2.49357i) q^{26} +(-1.56343 + 0.970977i) q^{28} +2.14505 q^{29} +6.59164i q^{31} +(-4.65601 + 3.21273i) q^{32} +(-0.482179 + 0.867062i) q^{34} +0.920206i q^{35} -2.33837i q^{37} +(0.967689 + 0.538138i) q^{38} +(0.136384 + 2.82514i) q^{40} -7.36833i q^{41} -7.06978 q^{43} +(-0.819295 + 0.508827i) q^{44} +(1.78103 + 0.990441i) q^{46} +0.294304 q^{47} +6.15322 q^{49} +(1.23596 + 0.687323i) q^{50} +(-3.42778 + 2.12884i) q^{52} +10.5190 q^{53} +0.482221i q^{55} +(-2.59971 + 0.125502i) q^{56} +(2.65119 + 1.47434i) q^{58} -10.8042i q^{59} +8.65852i q^{61} +(-4.53059 + 8.14697i) q^{62} +(-7.96280 + 0.770608i) q^{64} +2.01753i q^{65} -11.2157 q^{67} +(-1.19190 + 0.740238i) q^{68} +(-0.632479 + 1.13733i) q^{70} +5.57514 q^{71} +1.01962 q^{73} +(1.60722 - 2.89013i) q^{74} +(0.826146 + 1.33023i) q^{76} -0.443743 q^{77} +1.86662i q^{79} +(-1.77322 + 3.58548i) q^{80} +(5.06442 - 9.10693i) q^{82} -1.75905i q^{83} +0.701532i q^{85} +(-8.73794 - 4.85922i) q^{86} +(-1.36234 + 0.0657674i) q^{88} -11.9152i q^{89} -1.85654 q^{91} +(1.52052 + 2.44828i) q^{92} +(0.363747 + 0.202282i) q^{94} +0.782948 q^{95} +3.93818 q^{97} +(7.60511 + 4.22925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} + 16 q^{5} + 4 q^{8} - 2 q^{10} - 6 q^{14} + 10 q^{16} - 8 q^{19} + 2 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{25} + 16 q^{26} + 20 q^{28} + 8 q^{32} + 18 q^{34} + 14 q^{38} + 4 q^{40}+ \cdots + 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 + 16 * q^5 + 4 * q^8 - 2 * q^10 - 6 * q^14 + 10 * q^16 - 8 * q^19 + 2 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^25 + 16 * q^26 + 20 * q^28 + 8 * q^32 + 18 * q^34 + 14 * q^38 + 4 * q^40 - 6 * q^44 + 2 * q^46 + 16 * q^47 - 8 * q^49 - 2 * q^50 - 20 * q^52 - 32 * q^53 - 12 * q^56 - 16 * q^58 - 16 * q^62 + 14 * q^64 + 32 * q^67 + 8 * q^68 - 6 * q^70 - 24 * q^71 + 8 * q^73 - 34 * q^74 + 36 * q^76 + 10 * q^80 - 8 * q^82 + 34 * q^86 + 16 * q^88 + 48 * q^91 + 32 * q^92 + 10 * q^94 - 8 * q^95 - 8 * q^97 + 32 * q^98

Introduction

L-functions

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Database

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