LMFDB - Embedded newform 1560.2.bg.f.841.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,2,Mod(601,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1560.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1560.bg (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.2
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1560.841
Dual form			1560.2.bg.f.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-0.219224 - 0.379706i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-0.219224 - 0.379706i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.28078 + 3.95042i) q^{11} +(3.34233 + 1.35234i) q^{13} +(0.500000 - 0.866025i) q^{15} +(1.00000 + 1.73205i) q^{17} +(2.56155 + 4.43674i) q^{19} -0.438447 q^{21} +(-2.28078 + 3.95042i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(1.84233 - 3.19101i) q^{29} +4.12311 q^{31} +(2.28078 + 3.95042i) q^{33} +(-0.219224 - 0.379706i) q^{35} +(-2.28078 + 3.95042i) q^{37} +(2.84233 - 2.21837i) q^{39} +(1.00000 - 1.73205i) q^{41} +(3.06155 + 5.30277i) q^{43} +(-0.500000 - 0.866025i) q^{45} +6.56155 q^{47} +(3.40388 - 5.89570i) q^{49} +2.00000 q^{51} +1.12311 q^{53} +(-2.28078 + 3.95042i) q^{55} +5.12311 q^{57} +(1.84233 + 3.19101i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(-0.219224 + 0.379706i) q^{63} +(3.34233 + 1.35234i) q^{65} +(1.21922 - 2.11176i) q^{67} +(2.28078 + 3.95042i) q^{69} +4.43845 q^{73} +(0.500000 - 0.866025i) q^{75} +2.00000 q^{77} -0.753789 q^{79} +(-0.500000 + 0.866025i) q^{81} -11.3693 q^{83} +(1.00000 + 1.73205i) q^{85} +(-1.84233 - 3.19101i) q^{87} +(-1.00000 + 1.73205i) q^{89} +(-0.219224 - 1.56557i) q^{91} +(2.06155 - 3.57071i) q^{93} +(2.56155 + 4.43674i) q^{95} +(-4.21922 - 7.30791i) q^{97} +4.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 2 q^{15} + 4 q^{17} + 2 q^{19} - 10 q^{21} - 5 q^{23} + 4 q^{25} - 4 q^{27} - 5 q^{29} + 5 q^{33} - 5 q^{35} - 5 q^{37} - q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 18 q^{47} - 7 q^{49} + 8 q^{51} - 12 q^{53} - 5 q^{55} + 4 q^{57} - 5 q^{59} - 9 q^{61} - 5 q^{63} + q^{65} + 9 q^{67} + 5 q^{69} + 26 q^{73} + 2 q^{75} + 8 q^{77} - 36 q^{79} - 2 q^{81} + 4 q^{83} + 4 q^{85} + 5 q^{87} - 4 q^{89} - 5 q^{91} + 2 q^{95} - 21 q^{97} + 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9 - 5 * q^11 + q^13 + 2 * q^15 + 4 * q^17 + 2 * q^19 - 10 * q^21 - 5 * q^23 + 4 * q^25 - 4 * q^27 - 5 * q^29 + 5 * q^33 - 5 * q^35 - 5 * q^37 - q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 18 * q^47 - 7 * q^49 + 8 * q^51 - 12 * q^53 - 5 * q^55 + 4 * q^57 - 5 * q^59 - 9 * q^61 - 5 * q^63 + q^65 + 9 * q^67 + 5 * q^69 + 26 * q^73 + 2 * q^75 + 8 * q^77 - 36 * q^79 - 2 * q^81 + 4 * q^83 + 4 * q^85 + 5 * q^87 - 4 * q^89 - 5 * q^91 + 2 * q^95 - 21 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$.

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.219224	−	0.379706i	−0.0828587	−	0.143516i	0.821618	−	0.570038i	$-0.193072\pi$
$7$	−0.219224	−	0.379706i	−0.0828587	−	0.143516i	−0.904477	+	0.426523i	$0.859738\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.28078	+	3.95042i	−0.687680	+	1.19110i	0.284907	+	0.958555i	$0.408037\pi$
$11$	−2.28078	+	3.95042i	−0.687680	+	1.19110i	−0.972587	+	0.232541i	$0.925296\pi$
$12$		0			0
$13$	3.34233	+	1.35234i	0.926995	+	0.375073i
$13$	3.34233	+	1.35234i	0.926995	+	0.375073i
$14$		0			0
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	2.56155	+	4.43674i	0.587661	+	1.01786i	0.994538	+	0.104375i	$0.0332843\pi$
$19$	2.56155	+	4.43674i	0.587661	+	1.01786i	−0.406877	+	0.913483i	$0.633382\pi$
$20$		0			0
$21$	−0.438447			−0.0956770
$22$		0			0
$23$	−2.28078	+	3.95042i	−0.475575	+	0.823720i	−0.999609	−	0.0279778i	$-0.991093\pi$
$23$	−2.28078	+	3.95042i	−0.475575	+	0.823720i	0.524034	+	0.851697i	$0.324427\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	1.84233	−	3.19101i	0.342112	−	0.592555i	−0.642713	−	0.766107i	$-0.722191\pi$
$29$	1.84233	−	3.19101i	0.342112	−	0.592555i	0.984825	+	0.173552i	$0.0555245\pi$
$30$		0			0
$31$	4.12311			0.740532			0.370266	−	0.928926i	$-0.379267\pi$
$31$	4.12311			0.740532			0.370266	+	0.928926i	$0.379267\pi$
$32$		0			0
$33$	2.28078	+	3.95042i	0.397032	+	0.687680i
$34$		0			0
$35$	−0.219224	−	0.379706i	−0.0370556	−	0.0641821i
$36$		0			0
$37$	−2.28078	+	3.95042i	−0.374957	+	0.649445i	−0.990321	−	0.138798i	$-0.955676\pi$
$37$	−2.28078	+	3.95042i	−0.374957	+	0.649445i	0.615363	+	0.788244i	$0.289009\pi$
$38$		0			0
$39$	2.84233	−	2.21837i	0.455137	−	0.355223i
$40$		0			0
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	3.06155	+	5.30277i	0.466882	+	0.808664i	0.999284	−	0.0378277i	$-0.0120438\pi$
$43$	3.06155	+	5.30277i	0.466882	+	0.808664i	−0.532402	+	0.846492i	$0.678710\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	6.56155			0.957101			0.478550	−	0.878060i	$-0.341162\pi$
$47$	6.56155			0.957101			0.478550	+	0.878060i	$0.341162\pi$
$48$		0			0
$49$	3.40388	−	5.89570i	0.486269	−	0.842242i
$50$		0			0
$51$	2.00000			0.280056
$52$		0			0
$53$	1.12311			0.154270			0.0771352	−	0.997021i	$-0.475423\pi$
$53$	1.12311			0.154270			0.0771352	+	0.997021i	$0.475423\pi$
$54$		0			0
$55$	−2.28078	+	3.95042i	−0.307540	+	0.532675i
$56$		0			0
$57$	5.12311			0.678572
$58$		0			0
$59$	1.84233	+	3.19101i	0.239851	+	0.415434i	0.960671	−	0.277688i	$-0.0895681\pi$
$59$	1.84233	+	3.19101i	0.239851	+	0.415434i	−0.720820	+	0.693122i	$0.756235\pi$
$60$		0			0
$61$	−5.34233	−	9.25319i	−0.684015	−	1.18475i	−0.973745	−	0.227641i	$-0.926899\pi$
$61$	−5.34233	−	9.25319i	−0.684015	−	1.18475i	0.289730	−	0.957108i	$-0.406434\pi$
$62$		0			0
$63$	−0.219224	+	0.379706i	−0.0276196	+	0.0478385i
$64$		0			0
$65$	3.34233	+	1.35234i	0.414565	+	0.167738i
$66$		0			0
$67$	1.21922	−	2.11176i	0.148952	−	0.257992i	−0.781888	−	0.623418i	$-0.785743\pi$
$67$	1.21922	−	2.11176i	0.148952	−	0.257992i	0.930840	+	0.365426i	$0.119077\pi$
$68$		0			0
$69$	2.28078	+	3.95042i	0.274573	+	0.475575i
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$		0			0
$73$	4.43845			0.519481			0.259740	−	0.965678i	$-0.416363\pi$
$73$	4.43845			0.519481			0.259740	+	0.965678i	$0.416363\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	2.00000			0.227921
$78$		0			0
$79$	−0.753789			−0.0848079			−0.0424039	−	0.999101i	$-0.513502\pi$
$79$	−0.753789			−0.0848079			−0.0424039	+	0.999101i	$0.513502\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−11.3693			−1.24794			−0.623972	−	0.781446i	$-0.714482\pi$
$83$	−11.3693			−1.24794			−0.623972	+	0.781446i	$0.714482\pi$
$84$		0			0
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$		0			0
$87$	−1.84233	−	3.19101i	−0.197518	−	0.342112i
$88$		0			0
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	−0.219224	−	1.56557i	−0.0229809	−	0.164116i
$92$		0			0
$93$	2.06155	−	3.57071i	0.213773	−	0.370266i
$94$		0			0
$95$	2.56155	+	4.43674i	0.262810	+	0.455200i
$96$		0			0
$97$	−4.21922	−	7.30791i	−0.428397	−	0.742006i	0.568334	−	0.822798i	$-0.307588\pi$
$97$	−4.21922	−	7.30791i	−0.428397	−	0.742006i	−0.996731	+	0.0807924i	$0.974255\pi$
$98$		0			0
$99$	4.56155			0.458453
$100$		0			0
$101$	−4.12311	+	7.14143i	−0.410264	+	0.710599i	−0.994918	−	0.100684i	$-0.967897\pi$
$101$	−4.12311	+	7.14143i	−0.410264	+	0.710599i	0.584654	+	0.811283i	$0.301230\pi$
$102$		0			0
$103$	−3.56155			−0.350930			−0.175465	−	0.984486i	$-0.556143\pi$
$103$	−3.56155			−0.350930			−0.175465	+	0.984486i	$0.556143\pi$
$104$		0			0
$105$	−0.438447			−0.0427881
$106$		0			0
$107$	1.43845	−	2.49146i	0.139060	−	0.240859i	−0.788081	−	0.615571i	$-0.788925\pi$
$107$	1.43845	−	2.49146i	0.139060	−	0.240859i	0.927141	+	0.374713i	$0.122259\pi$
$108$		0			0
$109$	17.8078			1.70567			0.852837	−	0.522177i	$-0.174880\pi$
$109$	17.8078			1.70567			0.852837	+	0.522177i	$0.174880\pi$
$110$		0			0
$111$	2.28078	+	3.95042i	0.216482	+	0.374957i
$112$		0			0
$113$	−3.15767	−	5.46925i	−0.297049	−	0.514503i	0.678411	−	0.734683i	$-0.262669\pi$
$113$	−3.15767	−	5.46925i	−0.297049	−	0.514503i	−0.975459	+	0.220179i	$0.929336\pi$
$114$		0			0
$115$	−2.28078	+	3.95042i	−0.212683	+	0.368379i
$116$		0			0
$117$	−0.500000	−	3.57071i	−0.0462250	−	0.330113i
$118$		0			0
$119$	0.438447	−	0.759413i	0.0401924	−	0.0696153i
$120$		0			0
$121$	−4.90388	−	8.49377i	−0.445807	−	0.772161i
$122$		0			0
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.34233	+	2.32498i	−0.119112	+	0.206309i	−0.919416	−	0.393286i	$-0.871338\pi$
$127$	−1.34233	+	2.32498i	−0.119112	+	0.206309i	0.800304	+	0.599595i	$0.204672\pi$
$128$		0			0
$129$	6.12311			0.539109
$130$		0			0
$131$	−2.56155			−0.223804			−0.111902	−	0.993719i	$-0.535694\pi$
$131$	−2.56155			−0.223804			−0.111902	+	0.993719i	$0.535694\pi$
$132$		0			0
$133$	1.12311	−	1.94528i	0.0973856	−	0.168677i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	2.28078	+	3.95042i	0.194860	+	0.337507i	0.946855	−	0.321662i	$-0.104241\pi$
$137$	2.28078	+	3.95042i	0.194860	+	0.337507i	−0.751995	+	0.659169i	$0.770908\pi$
$138$		0			0
$139$	8.90388	+	15.4220i	0.755217	+	1.30807i	0.945266	+	0.326300i	$0.105802\pi$
$139$	8.90388	+	15.4220i	0.755217	+	1.30807i	−0.190049	+	0.981775i	$0.560865\pi$
$140$		0			0
$141$	3.28078	−	5.68247i	0.276291	−	0.478550i
$142$		0			0
$143$	−12.9654	+	10.1192i	−1.08422	+	0.846211i
$144$		0			0
$145$	1.84233	−	3.19101i	0.152997	−	0.264999i
$146$		0			0
$147$	−3.40388	−	5.89570i	−0.280747	−	0.486269i
$148$		0			0
$149$	6.96543	+	12.0645i	0.570631	+	0.988361i	0.996501	+	0.0835772i	$0.0266345\pi$
$149$	6.96543	+	12.0645i	0.570631	+	0.988361i	−0.425871	+	0.904784i	$0.640032\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$		0			0
$155$	4.12311			0.331176
$156$		0			0
$157$	11.2462			0.897545			0.448773	−	0.893646i	$-0.351861\pi$
$157$	11.2462			0.897545			0.448773	+	0.893646i	$0.351861\pi$
$158$		0			0
$159$	0.561553	−	0.972638i	0.0445340	−	0.0771352i
$160$		0			0
$161$	2.00000			0.157622
$162$		0			0
$163$	−10.0616	−	17.4271i	−0.788082	−	1.36500i	−0.927141	−	0.374713i	$-0.877741\pi$
$163$	−10.0616	−	17.4271i	−0.788082	−	1.36500i	0.139059	−	0.990284i	$-0.455592\pi$
$164$		0			0
$165$	2.28078	+	3.95042i	0.177558	+	0.307540i
$166$		0			0
$167$	−10.7192	+	18.5662i	−0.829478	+	1.43670i	0.0689695	+	0.997619i	$0.478029\pi$
$167$	−10.7192	+	18.5662i	−0.829478	+	1.43670i	−0.898448	+	0.439080i	$0.855304\pi$
$168$		0			0
$169$	9.34233	+	9.03996i	0.718641	+	0.695382i
$170$		0			0
$171$	2.56155	−	4.43674i	0.195887	−	0.339286i
$172$		0			0
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	−0.219224	−	0.379706i	−0.0165717	−	0.0287031i
$176$		0			0
$177$	3.68466			0.276956
$178$		0			0
$179$	−5.40388	+	9.35980i	−0.403905	+	0.699584i	−0.994193	−	0.107608i	$-0.965681\pi$
$179$	−5.40388	+	9.35980i	−0.403905	+	0.699584i	0.590288	+	0.807193i	$0.299014\pi$
$180$		0			0
$181$	−3.12311			−0.232139			−0.116069	−	0.993241i	$-0.537029\pi$
$181$	−3.12311			−0.232139			−0.116069	+	0.993241i	$0.537029\pi$
$182$		0			0
$183$	−10.6847			−0.789833
$184$		0			0
$185$	−2.28078	+	3.95042i	−0.167686	+	0.290441i
$186$		0			0
$187$	−9.12311			−0.667148
$188$		0			0
$189$	0.219224	+	0.379706i	0.0159462	+	0.0276196i
$190$		0			0
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	−0.959558	−	0.281511i	$-0.909164\pi$
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	0.235983	−	0.971757i	$-0.424169\pi$
$192$		0			0
$193$	9.02699	−	15.6352i	0.649777	−	1.12545i	−0.333399	−	0.942786i	$-0.608196\pi$
$193$	9.02699	−	15.6352i	0.649777	−	1.12545i	0.983176	−	0.182661i	$-0.0584710\pi$
$194$		0			0
$195$	2.84233	−	2.21837i	0.203543	−	0.158861i
$196$		0			0
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$		0			0
$199$	−6.78078	−	11.7446i	−0.480676	−	0.832556i	0.519078	−	0.854727i	$-0.326276\pi$
$199$	−6.78078	−	11.7446i	−0.480676	−	0.832556i	−0.999754	+	0.0221709i	$0.992942\pi$
$200$		0			0
$201$	−1.21922	−	2.11176i	−0.0859974	−	0.148952i
$202$		0			0
$203$	−1.61553			−0.113388
$204$		0			0
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$		0			0
$207$	4.56155			0.317050
$208$		0			0
$209$	−23.3693			−1.61649
$210$		0			0
$211$	7.02699	−	12.1711i	0.483758	−	0.837893i	−0.516068	−	0.856547i	$-0.672605\pi$
$211$	7.02699	−	12.1711i	0.483758	−	0.837893i	0.999826	+	0.0186544i	$0.00593824\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.06155	+	5.30277i	0.208796	+	0.361646i
$216$		0			0
$217$	−0.903882	−	1.56557i	−0.0613595	−	0.106278i
$218$		0			0
$219$	2.21922	−	3.84381i	0.149961	−	0.259740i
$220$		0			0
$221$	1.00000	+	7.14143i	0.0672673	+	0.480384i
$222$		0			0
$223$	−8.80776	+	15.2555i	−0.589812	+	1.02158i	0.404445	+	0.914562i	$0.367465\pi$
$223$	−8.80776	+	15.2555i	−0.589812	+	1.02158i	−0.994257	+	0.107021i	$0.965869\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$		0			0
$227$	−12.6847	−	21.9705i	−0.841910	−	1.45823i	−0.888278	−	0.459307i	$-0.848098\pi$
$227$	−12.6847	−	21.9705i	−0.841910	−	1.45823i	0.0463672	−	0.998924i	$-0.485236\pi$
$228$		0			0
$229$	20.7386			1.37045			0.685224	−	0.728333i	$-0.259704\pi$
$229$	20.7386			1.37045			0.685224	+	0.728333i	$0.259704\pi$
$230$		0			0
$231$	1.00000	−	1.73205i	0.0657952	−	0.113961i
$232$		0			0
$233$	−21.0540			−1.37929			−0.689646	−	0.724147i	$-0.742234\pi$
$233$	−21.0540			−1.37929			−0.689646	+	0.724147i	$0.742234\pi$
$234$		0			0
$235$	6.56155			0.428029
$236$		0			0
$237$	−0.376894	+	0.652800i	−0.0244819	+	0.0424039i
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	0.0345652	+	0.0598686i	0.00222654	+	0.00385648i	0.867137	−	0.498071i	$-0.165958\pi$
$241$	0.0345652	+	0.0598686i	0.00222654	+	0.00385648i	−0.864910	+	0.501927i	$0.832625\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	3.40388	−	5.89570i	0.217466	−	0.376662i
$246$		0			0
$247$	2.56155	+	18.2931i	0.162988	+	1.16397i
$248$		0			0
$249$	−5.68466	+	9.84612i	−0.360251	+	0.623972i
$250$		0			0
$251$	−5.28078	−	9.14657i	−0.333320	−	0.577327i	0.649841	−	0.760070i	$-0.274835\pi$
$251$	−5.28078	−	9.14657i	−0.333320	−	0.577327i	−0.983161	+	0.182744i	$0.941502\pi$
$252$		0			0
$253$	−10.4039	−	18.0201i	−0.654086	−	1.13291i
$254$		0			0
$255$	2.00000			0.125245
$256$		0			0
$257$	−8.28078	+	14.3427i	−0.516541	+	0.894675i	0.483275	+	0.875469i	$0.339447\pi$
$257$	−8.28078	+	14.3427i	−0.516541	+	0.894675i	−0.999816	+	0.0192060i	$0.993886\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$		0			0
$261$	−3.68466			−0.228075
$262$		0			0
$263$	−1.96543	+	3.40423i	−0.121194	+	0.209914i	−0.920239	−	0.391357i	$-0.872006\pi$
$263$	−1.96543	+	3.40423i	−0.121194	+	0.209914i	0.799045	+	0.601271i	$0.205339\pi$
$264$		0			0
$265$	1.12311			0.0689918
$266$		0			0
$267$	1.00000	+	1.73205i	0.0611990	+	0.106000i
$268$		0			0
$269$	4.12311	+	7.14143i	0.251390	+	0.435421i	0.963909	−	0.266233i	$-0.0857789\pi$
$269$	4.12311	+	7.14143i	0.251390	+	0.435421i	−0.712519	+	0.701653i	$0.752446\pi$
$270$		0			0
$271$	−12.8693	+	22.2903i	−0.781755	+	1.35404i	0.149163	+	0.988813i	$0.452342\pi$
$271$	−12.8693	+	22.2903i	−0.781755	+	1.35404i	−0.930918	+	0.365227i	$0.880991\pi$
$272$		0			0
$273$	−1.46543	−	0.592932i	−0.0886922	−	0.0358859i
$274$		0			0
$275$	−2.28078	+	3.95042i	−0.137536	+	0.238219i
$276$		0			0
$277$	−5.71922	−	9.90599i	−0.343635	−	0.595193i	0.641470	−	0.767148i	$-0.278325\pi$
$277$	−5.71922	−	9.90599i	−0.343635	−	0.595193i	−0.985105	+	0.171955i	$0.944992\pi$
$278$		0			0
$279$	−2.06155	−	3.57071i	−0.123422	−	0.213773i
$280$		0			0
$281$	−31.8617			−1.90071			−0.950356	−	0.311165i	$-0.899281\pi$
$281$	−31.8617			−1.90071			−0.950356	+	0.311165i	$0.899281\pi$
$282$		0			0
$283$	−1.50000	+	2.59808i	−0.0891657	+	0.154440i	−0.907159	−	0.420789i	$-0.861753\pi$
$283$	−1.50000	+	2.59808i	−0.0891657	+	0.154440i	0.817993	+	0.575228i	$0.195087\pi$
$284$		0			0
$285$	5.12311			0.303467
$286$		0			0
$287$	−0.876894			−0.0517614
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−8.43845			−0.494671
$292$		0			0
$293$	6.56155	+	11.3649i	0.383330	+	0.663947i	0.991536	−	0.129832i	$-0.0414439\pi$
$293$	6.56155	+	11.3649i	0.383330	+	0.663947i	−0.608206	+	0.793779i	$0.708111\pi$
$294$		0			0
$295$	1.84233	+	3.19101i	0.107265	+	0.185788i
$296$		0			0
$297$	2.28078	−	3.95042i	0.132344	−	0.229227i
$298$		0			0
$299$	−12.9654	+	10.1192i	−0.749810	+	0.585209i
$300$		0			0
$301$	1.34233	−	2.32498i	0.0773706	−	0.134010i
$302$		0			0
$303$	4.12311	+	7.14143i	0.236866	+	0.410264i
$304$		0			0
$305$	−5.34233	−	9.25319i	−0.305901	−	0.529836i
$306$		0			0
$307$	−14.9309			−0.852150			−0.426075	−	0.904688i	$-0.640104\pi$
$307$	−14.9309			−0.852150			−0.426075	+	0.904688i	$0.640104\pi$
$308$		0			0
$309$	−1.78078	+	3.08440i	−0.101305	+	0.175465i
$310$		0			0
$311$	−5.36932			−0.304466			−0.152233	−	0.988345i	$-0.548646\pi$
$311$	−5.36932			−0.304466			−0.152233	+	0.988345i	$0.548646\pi$
$312$		0			0
$313$	−14.0540			−0.794378			−0.397189	−	0.917737i	$-0.630014\pi$
$313$	−14.0540			−0.794378			−0.397189	+	0.917737i	$0.630014\pi$
$314$		0			0
$315$	−0.219224	+	0.379706i	−0.0123519	+	0.0213940i
$316$		0			0
$317$	1.75379			0.0985026			0.0492513	−	0.998786i	$-0.484316\pi$
$317$	1.75379			0.0985026			0.0492513	+	0.998786i	$0.484316\pi$
$318$		0			0
$319$	8.40388	+	14.5560i	0.470527	+	0.814977i
$320$		0			0
$321$	−1.43845	−	2.49146i	−0.0802863	−	0.139060i
$322$		0			0
$323$	−5.12311	+	8.87348i	−0.285057	+	0.493734i
$324$		0			0
$325$	3.34233	+	1.35234i	0.185399	+	0.0750146i
$326$		0			0
$327$	8.90388	−	15.4220i	0.492386	−	0.852837i
$328$		0			0
$329$	−1.43845	−	2.49146i	−0.0793042	−	0.137359i
$330$		0			0
$331$	−4.78078	−	8.28055i	−0.262775	−	0.455140i	0.704203	−	0.709999i	$-0.251304\pi$
$331$	−4.78078	−	8.28055i	−0.262775	−	0.455140i	−0.966978	+	0.254859i	$0.917971\pi$
$332$		0			0
$333$	4.56155			0.249972
$334$		0			0
$335$	1.21922	−	2.11176i	0.0666133	−	0.115378i
$336$		0			0
$337$	−21.8078			−1.18794			−0.593972	−	0.804485i	$-0.702441\pi$
$337$	−21.8078			−1.18794			−0.593972	+	0.804485i	$0.702441\pi$
$338$		0			0
$339$	−6.31534			−0.343002
$340$		0			0
$341$	−9.40388	+	16.2880i	−0.509249	+	0.882045i
$342$		0			0
$343$	−6.05398			−0.326884
$344$		0			0
$345$	2.28078	+	3.95042i	0.122793	+	0.212683i
$346$		0			0
$347$	−5.68466	−	9.84612i	−0.305168	−	0.528567i	0.672130	−	0.740433i	$-0.265379\pi$
$347$	−5.68466	−	9.84612i	−0.305168	−	0.528567i	−0.977299	+	0.211866i	$0.932046\pi$
$348$		0			0
$349$	10.3423	−	17.9134i	0.553612	−	0.958884i	−0.444398	−	0.895830i	$-0.646582\pi$
$349$	10.3423	−	17.9134i	0.553612	−	0.958884i	0.998010	−	0.0630549i	$-0.0200843\pi$
$350$		0			0
$351$	−3.34233	−	1.35234i	−0.178400	−	0.0721828i
$352$		0			0
$353$	5.87689	−	10.1791i	0.312796	−	0.541778i	−0.666171	−	0.745799i	$-0.732068\pi$
$353$	5.87689	−	10.1791i	0.312796	−	0.541778i	0.978966	+	0.204021i	$0.0654012\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.438447	−	0.759413i	−0.0232051	−	0.0401924i
$358$		0			0
$359$	16.8769			0.890728			0.445364	−	0.895349i	$-0.353074\pi$
$359$	16.8769			0.890728			0.445364	+	0.895349i	$0.353074\pi$
$360$		0			0
$361$	−3.62311	+	6.27540i	−0.190690	+	0.330284i
$362$		0			0
$363$	−9.80776			−0.514774
$364$		0			0
$365$	4.43845			0.232319
$366$		0			0
$367$	−10.5885	+	18.3399i	−0.552717	+	0.957334i	0.445360	+	0.895352i	$0.353076\pi$
$367$	−10.5885	+	18.3399i	−0.552717	+	0.957334i	−0.998077	+	0.0619828i	$0.980258\pi$
$368$		0			0
$369$	−2.00000			−0.104116
$370$		0			0
$371$	−0.246211	−	0.426450i	−0.0127827	−	0.0221402i
$372$		0			0
$373$	−3.62311	−	6.27540i	−0.187597	−	0.324928i	0.756851	−	0.653587i	$-0.226737\pi$
$373$	−3.62311	−	6.27540i	−0.187597	−	0.324928i	−0.944449	+	0.328659i	$0.893403\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	10.4730	−	8.17394i	0.539388	−	0.420979i
$378$		0			0
$379$	11.5885	−	20.0719i	0.595263	−	1.03103i	−0.398246	−	0.917279i	$-0.630381\pi$
$379$	11.5885	−	20.0719i	0.595263	−	1.03103i	0.993510	−	0.113748i	$-0.0362856\pi$
$380$		0			0
$381$	1.34233	+	2.32498i	0.0687696	+	0.119112i
$382$		0			0
$383$	−8.52699	−	14.7692i	−0.435709	−	0.754670i	0.561644	−	0.827379i	$-0.310169\pi$
$383$	−8.52699	−	14.7692i	−0.435709	−	0.754670i	−0.997353	+	0.0727090i	$0.976836\pi$
$384$		0			0
$385$	2.00000			0.101929
$386$		0			0
$387$	3.06155	−	5.30277i	0.155627	−	0.269555i
$388$		0			0
$389$	29.3002			1.48558			0.742789	−	0.669525i	$-0.233502\pi$
$389$	29.3002			1.48558			0.742789	+	0.669525i	$0.233502\pi$
$390$		0			0
$391$	−9.12311			−0.461375
$392$		0			0
$393$	−1.28078	+	2.21837i	−0.0646066	+	0.111902i
$394$		0			0
$395$	−0.753789			−0.0379272
$396$		0			0
$397$	6.06155	+	10.4989i	0.304221	+	0.526926i	0.977087	−	0.212838i	$-0.0682707\pi$
$397$	6.06155	+	10.4989i	0.304221	+	0.526926i	−0.672867	+	0.739764i	$0.734937\pi$
$398$		0			0
$399$	−1.12311	−	1.94528i	−0.0562256	−	0.0973856i
$400$		0			0
$401$	2.87689	−	4.98293i	0.143665	−	0.248836i	−0.785209	−	0.619231i	$-0.787444\pi$
$401$	2.87689	−	4.98293i	0.143665	−	0.248836i	0.928874	+	0.370395i	$0.120778\pi$
$402$		0			0
$403$	13.7808	+	5.57586i	0.686469	+	0.277753i
$404$		0			0
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$		0			0
$407$	−10.4039	−	18.0201i	−0.515701	−	0.893221i
$408$		0			0
$409$	−16.9039	−	29.2784i	−0.835843	−	1.44772i	−0.893342	−	0.449377i	$-0.851646\pi$
$409$	−16.9039	−	29.2784i	−0.835843	−	1.44772i	0.0574989	−	0.998346i	$-0.481687\pi$
$410$		0			0
$411$	4.56155			0.225005
$412$		0			0
$413$	0.807764	−	1.39909i	0.0397475	−	0.0688446i
$414$		0			0
$415$	−11.3693			−0.558098
$416$		0			0
$417$	17.8078			0.872050
$418$		0			0
$419$	−7.56155	+	13.0970i	−0.369406	+	0.639830i	−0.989473	−	0.144719i	$-0.953772\pi$
$419$	−7.56155	+	13.0970i	−0.369406	+	0.639830i	0.620067	+	0.784549i	$0.287106\pi$
$420$		0			0
$421$	−35.8078			−1.74516			−0.872582	−	0.488468i	$-0.837556\pi$
$421$	−35.8078			−1.74516			−0.872582	+	0.488468i	$0.837556\pi$
$422$		0			0
$423$	−3.28078	−	5.68247i	−0.159517	−	0.276291i
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	−2.34233	+	4.05703i	−0.113353	+	0.196334i
$428$		0			0
$429$	2.28078	+	16.2880i	0.110117	+	0.786392i
$430$		0			0
$431$	6.24621	−	10.8188i	0.300869	−	0.521121i	−0.675464	−	0.737393i	$-0.736057\pi$
$431$	6.24621	−	10.8188i	0.300869	−	0.521121i	0.976333	+	0.216272i	$0.0693898\pi$
$432$		0			0
$433$	−15.7116	−	27.2134i	−0.755054	−	1.30779i	−0.945348	−	0.326064i	$-0.894278\pi$
$433$	−15.7116	−	27.2134i	−0.755054	−	1.30779i	0.190294	−	0.981727i	$-0.439056\pi$
$434$		0			0
$435$	−1.84233	−	3.19101i	−0.0883329	−	0.152997i
$436$		0			0
$437$	−23.3693			−1.11791
$438$		0			0
$439$	14.1501	−	24.5087i	0.675347	−	1.16974i	−0.301020	−	0.953618i	$-0.597327\pi$
$439$	14.1501	−	24.5087i	0.675347	−	1.16974i	0.976367	−	0.216118i	$-0.0693395\pi$
$440$		0			0
$441$	−6.80776			−0.324179
$442$		0			0
$443$	−29.3693			−1.39538			−0.697689	−	0.716401i	$-0.745788\pi$
$443$	−29.3693			−1.39538			−0.697689	+	0.716401i	$0.745788\pi$
$444$		0			0
$445$	−1.00000	+	1.73205i	−0.0474045	+	0.0821071i
$446$		0			0
$447$	13.9309			0.658908
$448$		0			0
$449$	10.6847	+	18.5064i	0.504240	+	0.873370i	0.999988	+	0.00490311i	$0.00156071\pi$
$449$	10.6847	+	18.5064i	0.504240	+	0.873370i	−0.495748	+	0.868467i	$0.665106\pi$
$450$		0			0
$451$	4.56155	+	7.90084i	0.214795	+	0.372036i
$452$		0			0
$453$	8.00000	−	13.8564i	0.375873	−	0.651031i
$454$		0			0
$455$	−0.219224	−	1.56557i	−0.0102774	−	0.0733950i
$456$		0			0
$457$	−2.46543	+	4.27026i	−0.115328	+	0.199754i	−0.917911	−	0.396787i	$-0.870125\pi$
$457$	−2.46543	+	4.27026i	−0.115328	+	0.199754i	0.802583	+	0.596541i	$0.203459\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	13.4039	+	23.2162i	0.624281	+	1.08129i	0.988679	+	0.150043i	$0.0479413\pi$
$461$	13.4039	+	23.2162i	0.624281	+	1.08129i	−0.364398	+	0.931243i	$0.618725\pi$
$462$		0			0
$463$	1.80776			0.0840139			0.0420070	−	0.999117i	$-0.486625\pi$
$463$	1.80776			0.0840139			0.0420070	+	0.999117i	$0.486625\pi$
$464$		0			0
$465$	2.06155	−	3.57071i	0.0956022	−	0.165588i
$466$		0			0
$467$	21.6155			1.00025			0.500124	−	0.865954i	$-0.333288\pi$
$467$	21.6155			1.00025			0.500124	+	0.865954i	$0.333288\pi$
$468$		0			0
$469$	−1.06913			−0.0493679
$470$		0			0
$471$	5.62311	−	9.73950i	0.259099	−	0.448773i
$472$		0			0
$473$	−27.9309			−1.28426
$474$		0			0
$475$	2.56155	+	4.43674i	0.117532	+	0.203572i
$476$		0			0
$477$	−0.561553	−	0.972638i	−0.0257117	−	0.0445340i
$478$		0			0
$479$	10.9309	−	18.9328i	0.499444	−	0.865063i	−0.500556	−	0.865704i	$-0.666871\pi$
$479$	10.9309	−	18.9328i	0.499444	−	0.865063i	1.00000		0.000641682i	$0.000204254\pi$
$480$		0			0
$481$	−12.9654	+	10.1192i	−0.591173	+	0.461396i
$482$		0			0
$483$	1.00000	−	1.73205i	0.0455016	−	0.0788110i
$484$		0			0
$485$	−4.21922	−	7.30791i	−0.191585	−	0.331835i
$486$		0			0
$487$	−13.6847	−	23.7025i	−0.620111	−	1.07406i	−0.989465	−	0.144775i	$-0.953754\pi$
$487$	−13.6847	−	23.7025i	−0.620111	−	1.07406i	0.369354	−	0.929289i	$-0.379579\pi$
$488$		0			0
$489$	−20.1231			−0.909998
$490$		0			0
$491$	2.24621	−	3.89055i	0.101370	−	0.175578i	−0.810879	−	0.585213i	$-0.801011\pi$
$491$	2.24621	−	3.89055i	0.101370	−	0.175578i	0.912249	+	0.409635i	$0.134344\pi$
$492$		0			0
$493$	7.36932			0.331897
$494$		0			0
$495$	4.56155			0.205027
$496$		0			0
$497$		0			0
$498$		0			0
$499$	16.4924			0.738302			0.369151	−	0.929369i	$-0.379648\pi$
$499$	16.4924			0.738302			0.369151	+	0.929369i	$0.379648\pi$
$500$		0			0
$501$	10.7192	+	18.5662i	0.478900	+	0.829478i
$502$		0			0
$503$	−16.6847	−	28.8987i	−0.743932	−	1.28853i	−0.950692	−	0.310137i	$-0.899625\pi$
$503$	−16.6847	−	28.8987i	−0.743932	−	1.28853i	0.206760	−	0.978392i	$-0.433708\pi$
$504$		0			0
$505$	−4.12311	+	7.14143i	−0.183476	+	0.317789i
$506$		0			0
$507$	12.5000	−	3.57071i	0.555144	−	0.158581i
$508$		0			0
$509$	9.15767	−	15.8616i	0.405907	−	0.703051i	−0.588520	−	0.808483i	$-0.700289\pi$
$509$	9.15767	−	15.8616i	0.405907	−	0.703051i	0.994427	+	0.105432i	$0.0336225\pi$
$510$		0			0
$511$	−0.973012	−	1.68531i	−0.0430435	−	0.0745536i
$512$		0			0
$513$	−2.56155	−	4.43674i	−0.113095	−	0.195887i
$514$		0			0
$515$	−3.56155			−0.156941
$516$		0			0
$517$	−14.9654	+	25.9209i	−0.658179	+	1.14000i
$518$		0			0
$519$	4.00000			0.175581
$520$		0			0
$521$	−24.7386			−1.08382			−0.541910	−	0.840437i	$-0.682298\pi$
$521$	−24.7386			−1.08382			−0.541910	+	0.840437i	$0.682298\pi$
$522$		0			0
$523$	−11.2808	+	19.5389i	−0.493274	+	0.854375i	−0.999970	−	0.00774928i	$-0.997533\pi$
$523$	−11.2808	+	19.5389i	−0.493274	+	0.854375i	0.506696	+	0.862125i	$0.330867\pi$
$524$		0			0
$525$	−0.438447			−0.0191354
$526$		0			0
$527$	4.12311	+	7.14143i	0.179605	+	0.311086i
$528$		0			0
$529$	1.09612	+	1.89853i	0.0476573	+	0.0825449i
$530$		0			0
$531$	1.84233	−	3.19101i	0.0799503	−	0.138478i
$532$		0			0
$533$	5.68466	−	4.43674i	0.246230	−	0.192177i
$534$		0			0
$535$	1.43845	−	2.49146i	0.0621895	−	0.107715i
$536$		0			0
$537$	5.40388	+	9.35980i	0.233195	+	0.403905i
$538$		0			0
$539$	15.5270	+	26.8935i	0.668795	+	1.15839i
$540$		0			0
$541$	5.94602			0.255640			0.127820	−	0.991797i	$-0.459202\pi$
$541$	5.94602			0.255640			0.127820	+	0.991797i	$0.459202\pi$
$542$		0			0
$543$	−1.56155	+	2.70469i	−0.0670126	+	0.116069i
$544$		0			0
$545$	17.8078			0.762801
$546$		0			0
$547$	28.6847			1.22647			0.613234	−	0.789902i	$-0.289868\pi$
$547$	28.6847			1.22647			0.613234	+	0.789902i	$0.289868\pi$
$548$		0			0
$549$	−5.34233	+	9.25319i	−0.228005	+	0.394916i
$550$		0			0
$551$	18.8769			0.804183
$552$		0			0
$553$	0.165248	+	0.286218i	0.00702707	+	0.0121712i
$554$		0			0
$555$	2.28078	+	3.95042i	0.0968136	+	0.167686i
$556$		0			0
$557$	−17.6847	+	30.6307i	−0.749323	+	1.29787i	0.198825	+	0.980035i	$0.436288\pi$
$557$	−17.6847	+	30.6307i	−0.749323	+	1.29787i	−0.948148	+	0.317830i	$0.897046\pi$
$558$		0			0
$559$	3.06155	+	21.8639i	0.129490	+	0.924743i
$560$		0			0
$561$	−4.56155	+	7.90084i	−0.192589	+	0.333574i
$562$		0			0
$563$	−9.80776	−	16.9875i	−0.413348	−	0.715940i	0.581905	−	0.813256i	$-0.302307\pi$
$563$	−9.80776	−	16.9875i	−0.413348	−	0.715940i	−0.995253	+	0.0973167i	$0.968974\pi$
$564$		0			0
$565$	−3.15767	−	5.46925i	−0.132844	−	0.230093i
$566$		0			0
$567$	0.438447			0.0184131
$568$		0			0
$569$	−18.5616	+	32.1496i	−0.778141	+	1.34778i	0.154871	+	0.987935i	$0.450504\pi$
$569$	−18.5616	+	32.1496i	−0.778141	+	1.34778i	−0.933012	+	0.359845i	$0.882830\pi$
$570$		0			0
$571$	39.2311			1.64177			0.820884	−	0.571095i	$-0.193481\pi$
$571$	39.2311			1.64177			0.820884	+	0.571095i	$0.193481\pi$
$572$		0			0
$573$	−20.0000			−0.835512
$574$		0			0
$575$	−2.28078	+	3.95042i	−0.0951150	+	0.164744i
$576$		0			0
$577$	−38.9848			−1.62296			−0.811480	−	0.584380i	$-0.801338\pi$
$577$	−38.9848			−1.62296			−0.811480	+	0.584380i	$0.801338\pi$
$578$		0			0
$579$	−9.02699	−	15.6352i	−0.375149	−	0.649777i
$580$		0			0
$581$	2.49242	+	4.31700i	0.103403	+	0.179099i
$582$		0			0
$583$	−2.56155	+	4.43674i	−0.106089	+	0.183751i
$584$		0			0
$585$	−0.500000	−	3.57071i	−0.0206725	−	0.147631i
$586$		0			0
$587$	8.31534	−	14.4026i	0.343211	−	0.594459i	−0.641816	−	0.766859i	$-0.721819\pi$
$587$	8.31534	−	14.4026i	0.343211	−	0.594459i	0.985027	+	0.172400i	$0.0551521\pi$
$588$		0			0
$589$	10.5616	+	18.2931i	0.435181	+	0.753756i
$590$		0			0
$591$	−4.00000	−	6.92820i	−0.164538	−	0.284988i
$592$		0			0
$593$	43.3002			1.77813			0.889063	−	0.457785i	$-0.151357\pi$
$593$	43.3002			1.77813			0.889063	+	0.457785i	$0.151357\pi$
$594$		0			0
$595$	0.438447	−	0.759413i	0.0179746	−	0.0311329i
$596$		0			0
$597$	−13.5616			−0.555037
$598$		0			0
$599$	3.36932			0.137667			0.0688333	−	0.997628i	$-0.478072\pi$
$599$	3.36932			0.137667			0.0688333	+	0.997628i	$0.478072\pi$
$600$		0			0
$601$	10.0346	−	17.3804i	0.409318	−	0.708960i	−0.585495	−	0.810676i	$-0.699100\pi$
$601$	10.0346	−	17.3804i	0.409318	−	0.708960i	0.994814	+	0.101716i	$0.0324332\pi$
$602$		0			0
$603$	−2.43845			−0.0993012
$604$		0			0
$605$	−4.90388	−	8.49377i	−0.199371	−	0.345321i
$606$		0			0
$607$	15.6847	+	27.1666i	0.636621	+	1.10266i	0.986169	+	0.165741i	$0.0530016\pi$
$607$	15.6847	+	27.1666i	0.636621	+	1.10266i	−0.349549	+	0.936918i	$0.613665\pi$
$608$		0			0
$609$	−0.807764	+	1.39909i	−0.0327323	+	0.0566939i
$610$		0			0
$611$	21.9309	+	8.87348i	0.887228	+	0.358983i
$612$		0			0
$613$	20.3078	−	35.1741i	0.820223	−	1.42067i	−0.0852933	−	0.996356i	$-0.527183\pi$
$613$	20.3078	−	35.1741i	0.820223	−	1.42067i	0.905516	−	0.424312i	$-0.139484\pi$
$614$		0			0
$615$	−1.00000	−	1.73205i	−0.0403239	−	0.0698430i
$616$		0			0
$617$	−7.71922	−	13.3701i	−0.310764	−	0.538259i	0.667764	−	0.744373i	$-0.267252\pi$
$617$	−7.71922	−	13.3701i	−0.310764	−	0.538259i	−0.978528	+	0.206114i	$0.933918\pi$
$618$		0			0
$619$	33.4233			1.34340			0.671698	−	0.740825i	$-0.265565\pi$
$619$	33.4233			1.34340			0.671698	+	0.740825i	$0.265565\pi$
$620$		0			0
$621$	2.28078	−	3.95042i	0.0915244	−	0.158525i
$622$		0			0
$623$	0.876894			0.0351320
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−11.6847	+	20.2384i	−0.466640	+	0.808245i
$628$		0			0
$629$	−9.12311			−0.363762
$630$		0			0
$631$	−1.21922	−	2.11176i	−0.0485365	−	0.0840677i	0.840736	−	0.541445i	$-0.182122\pi$
$631$	−1.21922	−	2.11176i	−0.0485365	−	0.0840677i	−0.889273	+	0.457377i	$0.848789\pi$
$632$		0			0
$633$	−7.02699	−	12.1711i	−0.279298	−	0.483758i
$634$		0			0
$635$	−1.34233	+	2.32498i	−0.0532687	+	0.0922641i
$636$		0			0
$637$	19.3499	−	15.1021i	0.766671	−	0.598369i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	−0.977490	−	0.210981i	$-0.932334\pi$
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	0.306031	−	0.952022i	$-0.400999\pi$
$642$		0			0
$643$	−1.41146	−	2.44472i	−0.0556625	−	0.0964103i	0.836851	−	0.547430i	$-0.184394\pi$
$643$	−1.41146	−	2.44472i	−0.0556625	−	0.0964103i	−0.892514	+	0.451020i	$0.851060\pi$
$644$		0			0
$645$	6.12311			0.241097
$646$		0			0
$647$	18.0540	−	31.2704i	0.709775	−	1.22937i	−0.255165	−	0.966897i	$-0.582130\pi$
$647$	18.0540	−	31.2704i	0.709775	−	1.22937i	0.964940	−	0.262469i	$-0.0845367\pi$
$648$		0			0
$649$	−16.8078			−0.659762
$650$		0			0
$651$	−1.80776			−0.0708519
$652$		0			0
$653$	3.87689	−	6.71498i	0.151715	−	0.262777i	−0.780143	−	0.625601i	$-0.784854\pi$
$653$	3.87689	−	6.71498i	0.151715	−	0.262777i	0.931858	+	0.362823i	$0.118187\pi$
$654$		0			0
$655$	−2.56155			−0.100088
$656$		0			0
$657$	−2.21922	−	3.84381i	−0.0865802	−	0.149961i
$658$		0			0
$659$	16.0885	+	27.8662i	0.626721	+	1.08551i	0.988205	+	0.153134i	$0.0489366\pi$
$659$	16.0885	+	27.8662i	0.626721	+	1.08551i	−0.361485	+	0.932378i	$0.617730\pi$
$660$		0			0
$661$	5.21922	−	9.03996i	0.203004	−	0.351614i	−0.746491	−	0.665396i	$-0.768263\pi$
$661$	5.21922	−	9.03996i	0.203004	−	0.351614i	0.949495	+	0.313782i	$0.101596\pi$
$662$		0			0
$663$	6.68466	+	2.70469i	0.259611	+	0.105041i
$664$		0			0
$665$	1.12311	−	1.94528i	0.0435522	−	0.0754346i
$666$		0			0
$667$	8.40388	+	14.5560i	0.325400	+	0.563609i
$668$		0			0
$669$	8.80776	+	15.2555i	0.340528	+	0.589812i
$670$		0			0
$671$	48.7386			1.88153
$672$		0			0
$673$	−16.3423	+	28.3057i	−0.629950	+	1.09111i	0.357611	+	0.933871i	$0.383592\pi$
$673$	−16.3423	+	28.3057i	−0.629950	+	1.09111i	−0.987561	+	0.157235i	$0.949742\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	10.2462			0.393794			0.196897	−	0.980424i	$-0.436914\pi$
$677$	10.2462			0.393794			0.196897	+	0.980424i	$0.436914\pi$
$678$		0			0
$679$	−1.84991	+	3.20413i	−0.0709929	+	0.122963i
$680$		0			0
$681$	−25.3693			−0.972154
$682$		0			0
$683$	−13.1231	−	22.7299i	−0.502142	−	0.869735i	−0.999997	−	0.00247477i	$-0.999212\pi$
$683$	−13.1231	−	22.7299i	−0.502142	−	0.869735i	0.497855	−	0.867260i	$-0.334121\pi$
$684$		0			0
$685$	2.28078	+	3.95042i	0.0871440	+	0.150938i
$686$		0			0
$687$	10.3693	−	17.9602i	0.395614	−	0.685224i
$688$		0			0
$689$	3.75379	+	1.51883i	0.143008	+	0.0578626i
$690$		0			0
$691$	11.1501	−	19.3125i	0.424170	−	0.734683i	−0.572173	−	0.820133i	$-0.693899\pi$
$691$	11.1501	−	19.3125i	0.424170	−	0.734683i	0.996342	+	0.0854498i	$0.0272327\pi$
$692$		0			0
$693$	−1.00000	−	1.73205i	−0.0379869	−	0.0657952i
$694$		0			0
$695$	8.90388	+	15.4220i	0.337743	+	0.584989i
$696$		0			0
$697$	4.00000			0.151511
$698$		0			0
$699$	−10.5270	+	18.2333i	−0.398167	+	0.689646i
$700$		0			0
$701$	−35.6847			−1.34779			−0.673895	−	0.738827i	$-0.735380\pi$
$701$	−35.6847			−1.34779			−0.673895	+	0.738827i	$0.735380\pi$
$702$		0			0
$703$	−23.3693			−0.881390
$704$		0			0
$705$	3.28078	−	5.68247i	0.123561	−	0.214014i
$706$		0			0
$707$	3.61553			0.135976
$708$		0			0
$709$	21.9039	+	37.9386i	0.822618	+	1.42482i	0.903727	+	0.428110i	$0.140820\pi$
$709$	21.9039	+	37.9386i	0.822618	+	1.42482i	−0.0811090	+	0.996705i	$0.525846\pi$
$710$		0			0
$711$	0.376894	+	0.652800i	0.0141346	+	0.0244819i
$712$		0			0
$713$	−9.40388	+	16.2880i	−0.352178	+	0.609990i
$714$		0			0
$715$	−12.9654	+	10.1192i	−0.484880	+	0.378437i
$716$		0			0
$717$	2.00000	−	3.46410i	0.0746914	−	0.129369i
$718$		0			0
$719$	−9.75379	−	16.8941i	−0.363755	−	0.630042i	0.624821	−	0.780768i	$-0.285172\pi$
$719$	−9.75379	−	16.8941i	−0.363755	−	0.630042i	−0.988576	+	0.150726i	$0.951839\pi$
$720$		0			0
$721$	0.780776	+	1.35234i	0.0290776	+	0.0503639i
$722$		0			0
$723$	0.0691303			0.00257098
$724$		0			0
$725$	1.84233	−	3.19101i	0.0684224	−	0.118511i
$726$		0			0
$727$	−24.6847			−0.915503			−0.457752	−	0.889080i	$-0.651345\pi$
$727$	−24.6847			−0.915503			−0.457752	+	0.889080i	$0.651345\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.12311	+	10.6055i	−0.226471	+	0.392260i
$732$		0			0
$733$	17.4233			0.643544			0.321772	−	0.946817i	$-0.395722\pi$
$733$	17.4233			0.643544			0.321772	+	0.946817i	$0.395722\pi$
$734$		0			0
$735$	−3.40388	−	5.89570i	−0.125554	−	0.217466i
$736$		0			0
$737$	5.56155	+	9.63289i	0.204862	+	0.354832i
$738$		0			0
$739$	24.2462	−	41.9957i	0.891911	−	1.54484i	0.0543300	−	0.998523i	$-0.482698\pi$
$739$	24.2462	−	41.9957i	0.891911	−	1.54484i	0.837581	−	0.546313i	$-0.183969\pi$
$740$		0			0
$741$	17.1231	+	6.92820i	0.629033	+	0.254514i
$742$		0			0
$743$	12.4039	−	21.4842i	0.455054	−	0.788177i	−0.543637	−	0.839320i	$-0.682953\pi$
$743$	12.4039	−	21.4842i	0.455054	−	0.788177i	0.998691	+	0.0511433i	$0.0162865\pi$
$744$		0			0
$745$	6.96543	+	12.0645i	0.255194	+	0.442009i
$746$		0			0
$747$	5.68466	+	9.84612i	0.207991	+	0.360251i
$748$		0			0
$749$	−1.26137			−0.0460893
$750$		0			0
$751$	−11.5270	+	19.9653i	−0.420626	+	0.728545i	−0.996001	−	0.0893445i	$-0.971523\pi$
$751$	−11.5270	+	19.9653i	−0.420626	+	0.728545i	0.575375	+	0.817890i	$0.304856\pi$
$752$		0			0
$753$	−10.5616			−0.384884
$754$		0			0
$755$	16.0000			0.582300
$756$		0			0
$757$	−17.4924	+	30.2978i	−0.635773	+	1.10119i	0.350578	+	0.936534i	$0.385985\pi$
$757$	−17.4924	+	30.2978i	−0.635773	+	1.10119i	−0.986351	+	0.164657i	$0.947348\pi$
$758$		0			0
$759$	−20.8078			−0.755274
$760$		0			0
$761$	10.8769	+	18.8393i	0.394287	+	0.682925i	0.993010	−	0.118031i	$-0.0376582\pi$
$761$	10.8769	+	18.8393i	0.394287	+	0.682925i	−0.598723	+	0.800956i	$0.704325\pi$
$762$		0			0
$763$	−3.90388	−	6.76172i	−0.141330	−	0.244791i
$764$		0			0
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$		0			0
$767$	1.84233	+	13.1569i	0.0665227	+	0.475067i
$768$		0			0
$769$	0.596118	−	1.03251i	0.0214966	−	0.0372331i	−0.855077	−	0.518501i	$-0.826490\pi$
$769$	0.596118	−	1.03251i	0.0214966	−	0.0372331i	0.876574	+	0.481268i	$0.159824\pi$
$770$		0			0
$771$	8.28078	+	14.3427i	0.298225	+	0.516541i
$772$		0			0
$773$	18.4384	+	31.9363i	0.663185	+	1.14867i	0.979774	+	0.200107i	$0.0641290\pi$
$773$	18.4384	+	31.9363i	0.663185	+	1.14867i	−0.316589	+	0.948563i	$0.602538\pi$
$774$		0			0
$775$	4.12311			0.148106
$776$		0			0
$777$	1.00000	−	1.73205i	0.0358748	−	0.0621370i
$778$		0			0
$779$	10.2462			0.367109
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.84233	+	3.19101i	−0.0658395	+	0.114037i
$784$		0			0
$785$	11.2462			0.401394
$786$		0			0
$787$	−11.8153	−	20.4648i	−0.421171	−	0.729490i	0.574883	−	0.818236i	$-0.305048\pi$
$787$	−11.8153	−	20.4648i	−0.421171	−	0.729490i	−0.996054	+	0.0887454i	$0.971714\pi$
$788$		0			0
$789$	1.96543	+	3.40423i	0.0699713	+	0.121194i
$790$		0			0
$791$	−1.38447	+	2.39798i	−0.0492262	+	0.0852622i
$792$		0			0
$793$	−5.34233	−	38.1519i	−0.189712	−	1.35481i
$794$		0			0
$795$	0.561553	−	0.972638i	0.0199162	−	0.0344959i
$796$		0			0
$797$	−13.3153	−	23.0628i	−0.471654	−	0.816928i	0.527820	−	0.849356i	$-0.323009\pi$
$797$	−13.3153	−	23.0628i	−0.471654	−	0.816928i	−0.999474	+	0.0324280i	$0.989676\pi$
$798$		0			0
$799$	6.56155	+	11.3649i	0.232131	+	0.402063i
$800$		0			0
$801$	2.00000			0.0706665
$802$		0			0
$803$	−10.1231	+	17.5337i	−0.357237	+	0.618752i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$	8.24621			0.290280
$808$		0			0
$809$	21.4384	−	37.1325i	0.753736	−	1.30551i	−0.192265	−	0.981343i	$-0.561583\pi$
$809$	21.4384	−	37.1325i	0.753736	−	1.30551i	0.946000	−	0.324165i	$-0.105083\pi$
$810$		0			0
$811$	−16.1922			−0.568586			−0.284293	−	0.958737i	$-0.591759\pi$
$811$	−16.1922			−0.568586			−0.284293	+	0.958737i	$0.591759\pi$
$812$		0			0
$813$	12.8693	+	22.2903i	0.451347	+	0.781755i
$814$		0			0
$815$	−10.0616	−	17.4271i	−0.352441	−	0.610445i
$816$		0			0
$817$	−15.6847	+	27.1666i	−0.548737	+	0.950440i
$818$		0			0
$819$	−1.24621	+	0.972638i	−0.0435461	+	0.0339867i
$820$		0			0
$821$	−2.84233	+	4.92306i	−0.0991980	+	0.171816i	−0.911353	−	0.411626i	$-0.864961\pi$
$821$	−2.84233	+	4.92306i	−0.0991980	+	0.171816i	0.812155	+	0.583442i	$0.198294\pi$
$822$		0			0
$823$	11.9309	+	20.6649i	0.415884	+	0.720332i	0.995521	−	0.0945428i	$-0.0301389\pi$
$823$	11.9309	+	20.6649i	0.415884	+	0.720332i	−0.579637	+	0.814875i	$0.696806\pi$
$824$		0			0
$825$	2.28078	+	3.95042i	0.0794064	+	0.137536i
$826$		0			0
$827$	56.7386			1.97300			0.986498	−	0.163774i	$-0.0523669\pi$
$827$	56.7386			1.97300			0.986498	+	0.163774i	$0.0523669\pi$
$828$		0			0
$829$	−18.6577	+	32.3160i	−0.648008	+	1.12238i	0.335590	+	0.942008i	$0.391064\pi$
$829$	−18.6577	+	32.3160i	−0.648008	+	1.12238i	−0.983598	+	0.180374i	$0.942269\pi$
$830$		0			0
$831$	−11.4384			−0.396795
$832$		0			0
$833$	13.6155			0.471750
$834$		0			0
$835$	−10.7192	+	18.5662i	−0.370954	+	0.642511i
$836$		0			0
$837$	−4.12311			−0.142515
$838$		0			0
$839$	14.1231	+	24.4619i	0.487584	+	0.844520i	0.999898	−	0.0142782i	$-0.00454504\pi$
$839$	14.1231	+	24.4619i	0.487584	+	0.844520i	−0.512314	+	0.858798i	$0.671212\pi$
$840$		0			0
$841$	7.71165	+	13.3570i	0.265919	+	0.460585i
$842$		0			0
$843$	−15.9309	+	27.5931i	−0.548688	+	0.950356i
$844$		0			0
$845$	9.34233	+	9.03996i	0.321386	+	0.310984i
$846$		0			0
$847$	−2.15009	+	3.72407i	−0.0738781	+	0.127961i
$848$		0			0
$849$	1.50000	+	2.59808i	0.0514799	+	0.0891657i
$850$		0			0
$851$	−10.4039	−	18.0201i	−0.356640	−	0.617719i
$852$		0			0
$853$	50.6155			1.73304			0.866521	−	0.499140i	$-0.166351\pi$
$853$	50.6155			1.73304			0.866521	+	0.499140i	$0.166351\pi$
$854$		0			0
$855$	2.56155	−	4.43674i	0.0876033	−	0.151733i
$856$		0			0
$857$	54.4233			1.85906			0.929532	−	0.368741i	$-0.120211\pi$
$857$	54.4233			1.85906			0.929532	+	0.368741i	$0.120211\pi$
$858$		0			0
$859$	1.80776			0.0616801			0.0308401	−	0.999524i	$-0.490182\pi$
$859$	1.80776			0.0616801			0.0308401	+	0.999524i	$0.490182\pi$
$860$		0			0
$861$	−0.438447	+	0.759413i	−0.0149422	+	0.0258807i
$862$		0			0
$863$	55.3002			1.88244			0.941220	−	0.337794i	$-0.109681\pi$
$863$	55.3002			1.88244			0.941220	+	0.337794i	$0.109681\pi$
$864$		0			0
$865$	2.00000	+	3.46410i	0.0680020	+	0.117783i
$866$		0			0
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$		0			0
$869$	1.71922	−	2.97778i	0.0583207	−	0.101014i
$870$		0			0
$871$	6.93087	−	5.40938i	0.234844	−	0.183290i
$872$		0			0
$873$	−4.21922	+	7.30791i	−0.142799	+	0.247335i
$874$		0			0
$875$	−0.219224	−	0.379706i	−0.00741111	−	0.0128364i
$876$		0			0
$877$	7.15767	+	12.3974i	0.241697	+	0.418632i	0.961198	−	0.275860i	$-0.0889625\pi$
$877$	7.15767	+	12.3974i	0.241697	+	0.418632i	−0.719501	+	0.694492i	$0.755629\pi$
$878$		0			0
$879$	13.1231			0.442631
$880$		0			0
$881$	−24.5616	+	42.5419i	−0.827500	+	1.43327i	0.0724940	+	0.997369i	$0.476904\pi$
$881$	−24.5616	+	42.5419i	−0.827500	+	1.43327i	−0.899994	+	0.435903i	$0.856429\pi$
$882$		0			0
$883$	11.8769			0.399689			0.199845	−	0.979828i	$-0.435956\pi$
$883$	11.8769			0.399689			0.199845	+	0.979828i	$0.435956\pi$
$884$		0			0
$885$	3.68466			0.123858
$886$		0			0
$887$	20.8963	−	36.1935i	0.701629	−	1.21526i	−0.266265	−	0.963900i	$-0.585790\pi$
$887$	20.8963	−	36.1935i	0.701629	−	1.21526i	0.967894	−	0.251358i	$-0.0808770\pi$
$888$		0			0
$889$	1.17708			0.0394780
$890$		0			0
$891$	−2.28078	−	3.95042i	−0.0764089	−	0.132344i
$892$		0			0
$893$	16.8078	+	29.1119i	0.562450	+	0.974193i
$894$		0			0
$895$	−5.40388	+	9.35980i	−0.180632	+	0.312864i
$896$		0			0
$897$	2.28078	+	16.2880i	0.0761529	+	0.543841i
$898$		0			0
$899$	7.59612	−	13.1569i	0.253345	−	0.438806i
$900$		0			0
$901$	1.12311	+	1.94528i	0.0374161	+	0.0648065i
$902$		0			0
$903$	−1.34233	−	2.32498i	−0.0446699	−	0.0773706i
$904$		0			0
$905$	−3.12311			−0.103816
$906$		0			0
$907$	−18.7192	+	32.4226i	−0.621562	+	1.07658i	0.367633	+	0.929971i	$0.380168\pi$
$907$	−18.7192	+	32.4226i	−0.621562	+	1.07658i	−0.989195	+	0.146606i	$0.953165\pi$
$908$		0			0
$909$	8.24621			0.273510
$910$		0			0
$911$	37.6155			1.24626			0.623129	−	0.782119i	$-0.285861\pi$
$911$	37.6155			1.24626			0.623129	+	0.782119i	$0.285861\pi$
$912$		0			0
$913$	25.9309	−	44.9136i	0.858187	−	1.48642i
$914$		0			0
$915$	−10.6847			−0.353224
$916$		0			0
$917$	0.561553	+	0.972638i	0.0185441	+	0.0321193i
$918$		0			0
$919$	−16.4924	−	28.5657i	−0.544035	−	0.942296i	−0.998667	−	0.0516167i	$-0.983563\pi$
$919$	−16.4924	−	28.5657i	−0.544035	−	0.942296i	0.454632	−	0.890679i	$-0.349771\pi$
$920$		0			0
$921$	−7.46543	+	12.9305i	−0.245994	+	0.426075i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−2.28078	+	3.95042i	−0.0749915	+	0.129889i
$926$		0			0
$927$	1.78078	+	3.08440i	0.0584884	+	0.101305i
$928$		0			0
$929$	−15.6155	−	27.0469i	−0.512329	−	0.887380i	−0.999898	−	0.0142951i	$-0.995450\pi$
$929$	−15.6155	−	27.0469i	−0.512329	−	0.887380i	0.487569	−	0.873084i	$-0.337884\pi$
$930$		0			0
$931$	34.8769			1.14304
$932$		0			0
$933$	−2.68466	+	4.64996i	−0.0878918	+	0.152233i
$934$		0			0
$935$	−9.12311			−0.298357
$936$		0			0
$937$	−24.2462			−0.792089			−0.396045	−	0.918231i	$-0.629617\pi$
$937$	−24.2462			−0.792089			−0.396045	+	0.918231i	$0.629617\pi$
$938$		0			0
$939$	−7.02699	+	12.1711i	−0.229317	+	0.397189i
$940$		0			0
$941$	56.3542			1.83709			0.918547	−	0.395313i	$-0.129364\pi$
$941$	56.3542			1.83709			0.918547	+	0.395313i	$0.129364\pi$
$942$		0			0
$943$	4.56155	+	7.90084i	0.148545	+	0.257287i
$944$		0			0
$945$	0.219224	+	0.379706i	0.00713134	+	0.0123519i
$946$		0			0
$947$	−15.3153	+	26.5269i	−0.497682	+	0.862010i	−0.999996	−	0.00267484i	$-0.999149\pi$
$947$	−15.3153	+	26.5269i	−0.497682	+	0.862010i	0.502315	+	0.864685i	$0.332482\pi$
$948$		0			0
$949$	14.8348	+	6.00231i	0.481556	+	0.194843i
$950$		0			0
$951$	0.876894	−	1.51883i	0.0284352	−	0.0492513i
$952$		0			0
$953$	−10.5961	−	18.3530i	−0.343242	−	0.594512i	0.641791	−	0.766880i	$-0.278192\pi$
$953$	−10.5961	−	18.3530i	−0.343242	−	0.594512i	−0.985033	+	0.172367i	$0.944858\pi$
$954$		0			0
$955$	−10.0000	−	17.3205i	−0.323592	−	0.560478i
$956$		0			0
$957$	16.8078			0.543318
$958$		0			0
$959$	1.00000	−	1.73205i	0.0322917	−	0.0559308i
$960$		0			0
$961$	−14.0000			−0.451613
$962$		0			0
$963$	−2.87689			−0.0927066
$964$		0			0
$965$	9.02699	−	15.6352i	0.290589	−	0.503315i
$966$		0			0
$967$	10.2462			0.329496			0.164748	−	0.986336i	$-0.447319\pi$
$967$	10.2462			0.329496			0.164748	+	0.986336i	$0.447319\pi$
$968$		0			0
$969$	5.12311	+	8.87348i	0.164578	+	0.285057i
$970$		0			0
$971$	−18.2462	−	31.6034i	−0.585549	−	1.01420i	−0.994807	−	0.101782i	$-0.967546\pi$
$971$	−18.2462	−	31.6034i	−0.585549	−	1.01420i	0.409258	−	0.912419i	$-0.365788\pi$
$972$		0			0
$973$	3.90388	−	6.76172i	0.125153	−	0.216771i
$974$		0			0
$975$	2.84233	−	2.21837i	0.0910274	−	0.0710447i
$976$		0			0
$977$	0.650093	−	1.12599i	0.0207983	−	0.0360238i	−0.855439	−	0.517904i	$-0.826713\pi$
$977$	0.650093	−	1.12599i	0.0207983	−	0.0360238i	0.876237	+	0.481880i	$0.160046\pi$
$978$		0			0
$979$	−4.56155	−	7.90084i	−0.145788	−	0.252512i
$980$		0			0
$981$	−8.90388	−	15.4220i	−0.284279	−	0.492386i
$982$		0			0
$983$	1.19224			0.0380264			0.0190132	−	0.999819i	$-0.493948\pi$
$983$	1.19224			0.0380264			0.0190132	+	0.999819i	$0.493948\pi$
$984$		0			0
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$		0			0
$987$	−2.87689			−0.0915726
$988$		0			0
$989$	−27.9309			−0.888150
$990$		0			0
$991$	−17.8423	+	30.9038i	−0.566780	+	0.981692i	0.430101	+	0.902781i	$0.358478\pi$
$991$	−17.8423	+	30.9038i	−0.566780	+	0.981692i	−0.996882	+	0.0789116i	$0.974856\pi$
$992$		0			0
$993$	−9.56155			−0.303427
$994$		0			0
$995$	−6.78078	−	11.7446i	−0.214965	−	0.372330i
$996$		0			0
$997$	−18.2732	−	31.6501i	−0.578718	−	1.00237i	−0.995627	−	0.0934206i	$-0.970220\pi$
$997$	−18.2732	−	31.6501i	−0.578718	−	1.00237i	0.416909	−	0.908948i	$-0.363113\pi$
$998$		0			0
$999$	2.28078	−	3.95042i	0.0721606	−	0.124986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.bg.f.841.2	yes	4
13.3	even	3	inner	1560.2.bg.f.601.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.bg.f.601.2	✓	4	13.3	even	3	inner
1560.2.bg.f.841.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-0.219224 - 0.379706i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-0.219224 - 0.379706i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.28078 + 3.95042i) q^{11} +(3.34233 + 1.35234i) q^{13} +(0.500000 - 0.866025i) q^{15} +(1.00000 + 1.73205i) q^{17} +(2.56155 + 4.43674i) q^{19} -0.438447 q^{21} +(-2.28078 + 3.95042i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(1.84233 - 3.19101i) q^{29} +4.12311 q^{31} +(2.28078 + 3.95042i) q^{33} +(-0.219224 - 0.379706i) q^{35} +(-2.28078 + 3.95042i) q^{37} +(2.84233 - 2.21837i) q^{39} +(1.00000 - 1.73205i) q^{41} +(3.06155 + 5.30277i) q^{43} +(-0.500000 - 0.866025i) q^{45} +6.56155 q^{47} +(3.40388 - 5.89570i) q^{49} +2.00000 q^{51} +1.12311 q^{53} +(-2.28078 + 3.95042i) q^{55} +5.12311 q^{57} +(1.84233 + 3.19101i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(-0.219224 + 0.379706i) q^{63} +(3.34233 + 1.35234i) q^{65} +(1.21922 - 2.11176i) q^{67} +(2.28078 + 3.95042i) q^{69} +4.43845 q^{73} +(0.500000 - 0.866025i) q^{75} +2.00000 q^{77} -0.753789 q^{79} +(-0.500000 + 0.866025i) q^{81} -11.3693 q^{83} +(1.00000 + 1.73205i) q^{85} +(-1.84233 - 3.19101i) q^{87} +(-1.00000 + 1.73205i) q^{89} +(-0.219224 - 1.56557i) q^{91} +(2.06155 - 3.57071i) q^{93} +(2.56155 + 4.43674i) q^{95} +(-4.21922 - 7.30791i) q^{97} +4.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 2 q^{15} + 4 q^{17} + 2 q^{19} - 10 q^{21} - 5 q^{23} + 4 q^{25} - 4 q^{27} - 5 q^{29} + 5 q^{33} - 5 q^{35} - 5 q^{37} - q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 18 q^{47} - 7 q^{49} + 8 q^{51} - 12 q^{53} - 5 q^{55} + 4 q^{57} - 5 q^{59} - 9 q^{61} - 5 q^{63} + q^{65} + 9 q^{67} + 5 q^{69} + 26 q^{73} + 2 q^{75} + 8 q^{77} - 36 q^{79} - 2 q^{81} + 4 q^{83} + 4 q^{85} + 5 q^{87} - 4 q^{89} - 5 q^{91} + 2 q^{95} - 21 q^{97} + 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9 - 5 * q^11 + q^13 + 2 * q^15 + 4 * q^17 + 2 * q^19 - 10 * q^21 - 5 * q^23 + 4 * q^25 - 4 * q^27 - 5 * q^29 + 5 * q^33 - 5 * q^35 - 5 * q^37 - q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 18 * q^47 - 7 * q^49 + 8 * q^51 - 12 * q^53 - 5 * q^55 + 4 * q^57 - 5 * q^59 - 9 * q^61 - 5 * q^63 + q^65 + 9 * q^67 + 5 * q^69 + 26 * q^73 + 2 * q^75 + 8 * q^77 - 36 * q^79 - 2 * q^81 + 4 * q^83 + 4 * q^85 + 5 * q^87 - 4 * q^89 - 5 * q^91 + 2 * q^95 - 21 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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