LMFDB - Embedded newform 1232.2.q.j.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$0.356769 - 0.617942i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.j.177.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.745432 - 1.29113i) q^{3} +(0.143231 + 0.248083i) q^{5} +(-2.63409 - 0.248083i) q^{7} +(0.388663 + 0.673184i) q^{9} +(0.500000 - 0.866025i) q^{11} -3.49086 q^{13} +0.427076 q^{15} +(-0.888663 + 1.53921i) q^{17} +(-3.31574 - 5.74303i) q^{19} +(-2.28384 + 3.21602i) q^{21} +(-4.30660 - 7.45925i) q^{23} +(2.45897 - 4.25906i) q^{25} +5.63148 q^{27} -3.69527 q^{29} +(-0.929693 + 1.61028i) q^{31} +(-0.745432 - 1.29113i) q^{33} +(-0.315739 - 0.689008i) q^{35} +(-3.71354 - 6.43204i) q^{37} +(-2.60220 + 4.50714i) q^{39} -2.63671 q^{41} -10.8997 q^{43} +(-0.111337 + 0.192842i) q^{45} +(3.80660 + 6.59323i) q^{47} +(6.87691 + 1.30695i) q^{49} +(1.32488 + 2.29475i) q^{51} +(3.74543 - 6.48728i) q^{53} +0.286462 q^{55} -9.88663 q^{57} +(-1.18164 + 2.04667i) q^{59} +(-0.777326 - 1.34637i) q^{61} +(-0.856769 - 1.86965i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(-3.06379 + 5.30664i) q^{67} -12.8411 q^{69} -12.3137 q^{71} +(4.22716 - 7.32165i) q^{73} +(-3.66599 - 6.34968i) q^{75} +(-1.53189 + 2.15715i) q^{77} +(5.19788 + 9.00300i) q^{79} +(3.03189 - 5.25139i) q^{81} +16.1861 q^{83} -0.509136 q^{85} +(-2.75457 + 4.77105i) q^{87} +(5.07031 + 8.78203i) q^{89} +(9.19527 + 0.866025i) q^{91} +(1.38605 + 2.40070i) q^{93} +(0.949833 - 1.64516i) q^{95} +3.04551 q^{97} +0.777326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 2 q^{5} - 2 q^{7} - 4 q^{9} + 3 q^{11} - 6 q^{13} - 2 q^{15} + q^{17} - 9 q^{19} - 8 q^{21} + 5 q^{25} + 12 q^{27} + 10 q^{29} - 9 q^{31} + 3 q^{33} + 9 q^{35} - 20 q^{37} - 7 q^{39} - 10 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 2 * q^5 - 2 * q^7 - 4 * q^9 + 3 * q^11 - 6 * q^13 - 2 * q^15 + q^17 - 9 * q^19 - 8 * q^21 + 5 * q^25 + 12 * q^27 + 10 * q^29 - 9 * q^31 + 3 * q^33 + 9 * q^35 - 20 * q^37 - 7 * q^39 - 10 * q^41 - 16 * q^43 - 7 * q^45 - 3 * q^47 + 12 * q^49 + 12 * q^51 + 15 * q^53 + 4 * q^55 + 4 * q^57 - 10 * q^59 + 8 * q^61 - 4 * q^63 - 3 * q^65 - 8 * q^67 - 54 * q^69 - 6 * q^71 - 12 * q^73 - 3 * q^75 - 4 * q^77 + 7 * q^79 + 13 * q^81 + 50 * q^83 - 18 * q^85 - 24 * q^87 + 27 * q^89 + 23 * q^91 - 6 * q^93 - 19 * q^95 - 22 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.745432	−	1.29113i	0.430375	−	0.745432i	−0.566530	−	0.824041i	$-0.691715\pi$
$3$	0.745432	−	1.29113i	0.430375	−	0.745432i	0.996906	+	0.0786091i	$0.0250479\pi$
$4$		0			0
$5$	0.143231	+	0.248083i	0.0640549	+	0.110946i	0.896274	−	0.443500i	$-0.146263\pi$
$5$	0.143231	+	0.248083i	0.0640549	+	0.110946i	−0.832219	+	0.554446i	$0.812930\pi$
$6$		0			0
$7$	−2.63409	−	0.248083i	−0.995594	−	0.0937667i
$7$	−2.63409	−	0.248083i	−0.995594	−	0.0937667i
$8$		0			0
$9$	0.388663	+	0.673184i	0.129554	+	0.224395i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−3.49086			−0.968191			−0.484096	−	0.875015i	$-0.660851\pi$
$13$	−3.49086			−0.968191			−0.484096	+	0.875015i	$0.660851\pi$
$14$		0			0
$15$	0.427076			0.110271
$16$		0			0
$17$	−0.888663	+	1.53921i	−0.215532	+	0.373313i	−0.953437	−	0.301592i	$-0.902482\pi$
$17$	−0.888663	+	1.53921i	−0.215532	+	0.373313i	0.737905	+	0.674905i	$0.235815\pi$
$18$		0			0
$19$	−3.31574	−	5.74303i	−0.760683	−	1.31754i	−0.942499	−	0.334208i	$-0.891531\pi$
$19$	−3.31574	−	5.74303i	−0.760683	−	1.31754i	0.181817	−	0.983332i	$-0.441802\pi$
$20$		0			0
$21$	−2.28384	+	3.21602i	−0.498376	+	0.701793i
$22$		0			0
$23$	−4.30660	−	7.45925i	−0.897989	−	1.55536i	−0.830062	−	0.557672i	$-0.811695\pi$
$23$	−4.30660	−	7.45925i	−0.897989	−	1.55536i	−0.0679270	−	0.997690i	$-0.521639\pi$
$24$		0			0
$25$	2.45897	−	4.25906i	0.491794	−	0.851812i
$26$		0			0
$27$	5.63148			1.08378
$28$		0			0
$29$	−3.69527			−0.686194			−0.343097	−	0.939300i	$-0.611476\pi$
$29$	−3.69527			−0.686194			−0.343097	+	0.939300i	$0.611476\pi$
$30$		0			0
$31$	−0.929693	+	1.61028i	−0.166978	+	0.289214i	−0.937356	−	0.348373i	$-0.886734\pi$
$31$	−0.929693	+	1.61028i	−0.166978	+	0.289214i	0.770378	+	0.637587i	$0.220067\pi$
$32$		0			0
$33$	−0.745432	−	1.29113i	−0.129763	−	0.224756i
$34$		0			0
$35$	−0.315739	−	0.689008i	−0.0533696	−	0.116464i
$36$		0			0
$37$	−3.71354	−	6.43204i	−0.610502	−	1.05742i	−0.991156	−	0.132703i	$-0.957634\pi$
$37$	−3.71354	−	6.43204i	−0.610502	−	1.05742i	0.380654	−	0.924718i	$-0.375699\pi$
$38$		0			0
$39$	−2.60220	+	4.50714i	−0.416686	+	0.721721i
$40$		0			0
$41$	−2.63671			−0.411785			−0.205893	−	0.978575i	$-0.566010\pi$
$41$	−2.63671			−0.411785			−0.205893	+	0.978575i	$0.566010\pi$
$42$		0			0
$43$	−10.8997			−1.66218			−0.831092	−	0.556135i	$-0.812284\pi$
$43$	−10.8997			−1.66218			−0.831092	+	0.556135i	$0.812284\pi$
$44$		0			0
$45$	−0.111337	+	0.192842i	−0.0165972	+	0.0287471i
$46$		0			0
$47$	3.80660	+	6.59323i	0.555250	+	0.961721i	0.997884	+	0.0650189i	$0.0207108\pi$
$47$	3.80660	+	6.59323i	0.555250	+	0.961721i	−0.442634	+	0.896702i	$0.645956\pi$
$48$		0			0
$49$	6.87691	+	1.30695i	0.982416	+	0.186707i
$50$		0			0
$51$	1.32488	+	2.29475i	0.185520	+	0.321329i
$52$		0			0
$53$	3.74543	−	6.48728i	0.514475	−	0.891096i	−0.485384	−	0.874301i	$-0.661320\pi$
$53$	3.74543	−	6.48728i	0.514475	−	0.891096i	0.999859	−	0.0167953i	$-0.00534636\pi$
$54$		0			0
$55$	0.286462			0.0386265
$56$		0			0
$57$	−9.88663			−1.30952
$58$		0			0
$59$	−1.18164	+	2.04667i	−0.153837	+	0.266453i	−0.932635	−	0.360821i	$-0.882496\pi$
$59$	−1.18164	+	2.04667i	−0.153837	+	0.266453i	0.778798	+	0.627275i	$0.215830\pi$
$60$		0			0
$61$	−0.777326	−	1.34637i	−0.0995264	−	0.172385i	0.811962	−	0.583710i	$-0.198399\pi$
$61$	−0.777326	−	1.34637i	−0.0995264	−	0.172385i	−0.911489	+	0.411325i	$0.865066\pi$
$62$		0			0
$63$	−0.856769	−	1.86965i	−0.107943	−	0.235554i
$64$		0			0
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	−3.06379	+	5.30664i	−0.374301	+	0.648309i	−0.990222	−	0.139499i	$-0.955451\pi$
$67$	−3.06379	+	5.30664i	−0.374301	+	0.648309i	0.615921	+	0.787808i	$0.288784\pi$
$68$		0			0
$69$	−12.8411			−1.54589
$70$		0			0
$71$	−12.3137			−1.46137			−0.730684	−	0.682716i	$-0.760799\pi$
$71$	−12.3137			−1.46137			−0.730684	+	0.682716i	$0.760799\pi$
$72$		0			0
$73$	4.22716	−	7.32165i	0.494752	−	0.856935i	−0.505230	−	0.862985i	$-0.668592\pi$
$73$	4.22716	−	7.32165i	0.494752	−	0.856935i	0.999982	+	0.00604983i	$0.00192573\pi$
$74$		0			0
$75$	−3.66599	−	6.34968i	−0.423312	−	0.733198i
$76$		0			0
$77$	−1.53189	+	2.15715i	−0.174576	+	0.245830i
$78$		0			0
$79$	5.19788	+	9.00300i	0.584807	+	1.01292i	0.994899	+	0.100872i	$0.0321633\pi$
$79$	5.19788	+	9.00300i	0.584807	+	1.01292i	−0.410092	+	0.912044i	$0.634503\pi$
$80$		0			0
$81$	3.03189	−	5.25139i	0.336877	−	0.583488i
$82$		0			0
$83$	16.1861			1.77666			0.888329	−	0.459207i	$-0.151866\pi$
$83$	16.1861			1.77666			0.888329	+	0.459207i	$0.151866\pi$
$84$		0			0
$85$	−0.509136			−0.0552236
$86$		0			0
$87$	−2.75457	+	4.77105i	−0.295321	+	0.511510i
$88$		0			0
$89$	5.07031	+	8.78203i	0.537451	+	0.930893i	0.999040	+	0.0437993i	$0.0139462\pi$
$89$	5.07031	+	8.78203i	0.537451	+	0.930893i	−0.461589	+	0.887094i	$0.652720\pi$
$90$		0			0
$91$	9.19527	+	0.866025i	0.963926	+	0.0907841i
$92$		0			0
$93$	1.38605	+	2.40070i	0.143726	+	0.248941i
$94$		0			0
$95$	0.949833	−	1.64516i	0.0974508	−	0.168790i
$96$		0			0
$97$	3.04551			0.309225			0.154613	−	0.987975i	$-0.450587\pi$
$97$	3.04551			0.309225			0.154613	+	0.987975i	$0.450587\pi$
$98$		0			0
$99$	0.777326			0.0781242
$100$		0			0
$101$	−2.18426	+	3.78325i	−0.217342	+	0.376448i	−0.953995	−	0.299824i	$-0.903072\pi$
$101$	−2.18426	+	3.78325i	−0.217342	+	0.376448i	0.736652	+	0.676272i	$0.236405\pi$
$102$		0			0
$103$	−2.61134	−	4.52297i	−0.257303	−	0.445661i	0.708216	−	0.705996i	$-0.249500\pi$
$103$	−2.61134	−	4.52297i	−0.257303	−	0.445661i	−0.965518	+	0.260335i	$0.916167\pi$
$104$		0			0
$105$	−1.12496	−	0.105950i	−0.109785	−	0.0103397i
$106$		0			0
$107$	5.26557	+	9.12024i	0.509042	+	0.881687i	0.999945	+	0.0104725i	$0.00333357\pi$
$107$	5.26557	+	9.12024i	0.509042	+	0.881687i	−0.490903	+	0.871214i	$0.663333\pi$
$108$		0			0
$109$	−1.77471	+	3.07389i	−0.169986	+	0.294425i	−0.938415	−	0.345511i	$-0.887706\pi$
$109$	−1.77471	+	3.07389i	−0.169986	+	0.294425i	0.768429	+	0.639936i	$0.221039\pi$
$110$		0			0
$111$	−11.0728			−1.05098
$112$		0			0
$113$	−6.31370			−0.593943			−0.296972	−	0.954886i	$-0.595977\pi$
$113$	−6.31370			−0.593943			−0.296972	+	0.954886i	$0.595977\pi$
$114$		0			0
$115$	1.23368	−	2.13679i	0.115041	−	0.199257i
$116$		0			0
$117$	−1.35677	−	2.34999i	−0.125433	−	0.217257i
$118$		0			0
$119$	2.72267	−	3.83396i	0.249587	−	0.351459i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−1.96549	+	3.40433i	−0.177222	+	0.306958i
$124$		0			0
$125$	2.84111			0.254117
$126$		0			0
$127$	−3.88139			−0.344418			−0.172209	−	0.985060i	$-0.555090\pi$
$127$	−3.88139			−0.344418			−0.172209	+	0.985060i	$0.555090\pi$
$128$		0			0
$129$	−8.12496	+	14.0728i	−0.715363	+	1.23904i
$130$		0			0
$131$	−9.11582	−	15.7891i	−0.796453	−	1.37950i	−0.921912	−	0.387398i	$-0.873374\pi$
$131$	−9.11582	−	15.7891i	−0.796453	−	1.37950i	0.125459	−	0.992099i	$-0.459960\pi$
$132$		0			0
$133$	7.30922	+	15.9503i	0.633790	+	1.38306i
$134$		0			0
$135$	0.806602	+	1.39708i	0.0694213	+	0.120241i
$136$		0			0
$137$	0.690780	−	1.19647i	0.0590174	−	0.102221i	−0.835007	−	0.550239i	$-0.814537\pi$
$137$	0.690780	−	1.19647i	0.0590174	−	0.102221i	0.894025	+	0.448018i	$0.147870\pi$
$138$		0			0
$139$	0.591197			0.0501447			0.0250723	−	0.999686i	$-0.492018\pi$
$139$	0.591197			0.0501447			0.0250723	+	0.999686i	$0.492018\pi$
$140$		0			0
$141$	11.3502			0.955863
$142$		0			0
$143$	−1.74543	+	3.02318i	−0.145960	+	0.252811i
$144$		0			0
$145$	−0.529277	−	0.916734i	−0.0439540	−	0.0761306i
$146$		0			0
$147$	6.81370	−	7.90471i	0.561985	−	0.651970i
$148$		0			0
$149$	−6.39967	−	11.0845i	−0.524281	−	0.908082i	−0.999600	−	0.0282682i	$-0.991001\pi$
$149$	−6.39967	−	11.0845i	−0.524281	−	0.908082i	0.475319	−	0.879813i	$-0.342333\pi$
$150$		0			0
$151$	−2.82749	+	4.89736i	−0.230098	+	0.398542i	−0.957837	−	0.287313i	$-0.907238\pi$
$151$	−2.82749	+	4.89736i	−0.230098	+	0.398542i	0.727739	+	0.685854i	$0.240571\pi$
$152$		0			0
$153$	−1.38156			−0.111693
$154$		0			0
$155$	−0.532644			−0.0427830
$156$		0			0
$157$	9.82674	−	17.0204i	0.784259	−	1.35838i	−0.145181	−	0.989405i	$-0.546376\pi$
$157$	9.82674	−	17.0204i	0.784259	−	1.35838i	0.929440	−	0.368972i	$-0.120290\pi$
$158$		0			0
$159$	−5.58393	−	9.67165i	−0.442834	−	0.767011i
$160$		0			0
$161$	9.49348	+	20.7168i	0.748191	+	1.63271i
$162$		0			0
$163$	−4.50000	−	7.79423i	−0.352467	−	0.610491i	0.634214	−	0.773158i	$-0.281324\pi$
$163$	−4.50000	−	7.79423i	−0.352467	−	0.610491i	−0.986681	+	0.162667i	$0.947991\pi$
$164$		0			0
$165$	0.213538	−	0.369859i	0.0166239	−	0.0287934i
$166$		0			0
$167$	14.8046			1.14561			0.572806	−	0.819691i	$-0.305855\pi$
$167$	14.8046			1.14561			0.572806	+	0.819691i	$0.305855\pi$
$168$		0			0
$169$	−0.813871			−0.0626055
$170$		0			0
$171$	2.57741	−	4.46420i	0.197099	−	0.341386i
$172$		0			0
$173$	−7.59958	−	13.1629i	−0.577786	−	1.00075i	−0.995733	−	0.0922828i	$-0.970584\pi$
$173$	−7.59958	−	13.1629i	−0.577786	−	1.00075i	0.417947	−	0.908471i	$-0.362750\pi$
$174$		0			0
$175$	−7.53376	+	10.6087i	−0.569499	+	0.801945i
$176$		0			0
$177$	1.76167	+	3.05130i	0.132415	+	0.229350i
$178$		0			0
$179$	9.22716	−	15.9819i	0.689670	−	1.19454i	−0.282274	−	0.959334i	$-0.591089\pi$
$179$	9.22716	−	15.9819i	0.689670	−	1.19454i	0.971945	−	0.235210i	$-0.0755778\pi$
$180$		0			0
$181$	19.0272			1.41428			0.707142	−	0.707072i	$-0.249984\pi$
$181$	19.0272			1.41428			0.707142	+	0.707072i	$0.249984\pi$
$182$		0			0
$183$	−2.31777			−0.171335
$184$		0			0
$185$	1.06379	−	1.84253i	0.0782112	−	0.135466i
$186$		0			0
$187$	0.888663	+	1.53921i	0.0649855	+	0.112558i
$188$		0			0
$189$	−14.8338	−	1.39708i	−1.07900	−	0.101622i
$190$		0			0
$191$	−5.13148	−	8.88798i	−0.371301	−	0.643112i	0.618465	−	0.785812i	$-0.287755\pi$
$191$	−5.13148	−	8.88798i	−0.371301	−	0.643112i	−0.989766	+	0.142701i	$0.954421\pi$
$192$		0			0
$193$	−6.86777	+	11.8953i	−0.494353	+	0.856245i	−0.999979	−	0.00650824i	$-0.997928\pi$
$193$	−6.86777	+	11.8953i	−0.494353	+	0.856245i	0.505626	+	0.862753i	$0.331262\pi$
$194$		0			0
$195$	−1.49086			−0.106763
$196$		0			0
$197$	4.05075			0.288604			0.144302	−	0.989534i	$-0.453906\pi$
$197$	4.05075			0.288604			0.144302	+	0.989534i	$0.453906\pi$
$198$		0			0
$199$	−12.8931	+	22.3316i	−0.913971	+	1.58304i	−0.105570	+	0.994412i	$0.533667\pi$
$199$	−12.8931	+	22.3316i	−0.913971	+	1.58304i	−0.808401	+	0.588632i	$0.799667\pi$
$200$		0			0
$201$	4.56769	+	7.91147i	0.322180	+	0.558032i
$202$		0			0
$203$	9.73368	+	0.916734i	0.683170	+	0.0643421i
$204$		0			0
$205$	−0.377659	−	0.654125i	−0.0263768	−	0.0456860i
$206$		0			0
$207$	3.34763	−	5.79827i	0.232677	−	0.403008i
$208$		0			0
$209$	−6.63148			−0.458709
$210$		0			0
$211$	11.8359			0.814816			0.407408	−	0.913246i	$-0.366433\pi$
$211$	11.8359			0.814816			0.407408	+	0.913246i	$0.366433\pi$
$212$		0			0
$213$	−9.17903	+	15.8985i	−0.628937	+	1.08935i
$214$		0			0
$215$	−1.56117	−	2.70403i	−0.106471	−	0.184413i
$216$		0			0
$217$	2.84838	−	4.01098i	0.193361	−	0.272283i
$218$		0			0
$219$	−6.30212	−	10.9156i	−0.425858	−	0.737607i
$220$		0			0
$221$	3.10220	−	5.37317i	0.208677	−	0.361438i
$222$		0			0
$223$	17.7005			1.18531			0.592657	−	0.805455i	$-0.298079\pi$
$223$	17.7005			1.18531			0.592657	+	0.805455i	$0.298079\pi$
$224$		0			0
$225$	3.82284			0.254856
$226$		0			0
$227$	11.8568	−	20.5365i	0.786961	−	1.36306i	−0.140859	−	0.990030i	$-0.544986\pi$
$227$	11.8568	−	20.5365i	0.786961	−	1.36306i	0.927820	−	0.373027i	$-0.121680\pi$
$228$		0			0
$229$	9.39967	+	16.2807i	0.621147	+	1.07586i	0.989272	+	0.146083i	$0.0466665\pi$
$229$	9.39967	+	16.2807i	0.621147	+	1.07586i	−0.368125	+	0.929776i	$0.620000\pi$
$230$		0			0
$231$	1.64323	+	3.58588i	0.108117	+	0.235933i
$232$		0			0
$233$	−9.99086	−	17.3047i	−0.654523	−	1.13367i	−0.982013	−	0.188813i	$-0.939536\pi$
$233$	−9.99086	−	17.3047i	−0.654523	−	1.13367i	0.327490	−	0.944855i	$-0.393797\pi$
$234$		0			0
$235$	−1.09045	+	1.88871i	−0.0711329	+	0.123206i
$236$		0			0
$237$	15.4987			1.00675
$238$		0			0
$239$	−15.4946			−1.00226			−0.501131	−	0.865371i	$-0.667083\pi$
$239$	−15.4946			−1.00226			−0.501131	+	0.865371i	$0.667083\pi$
$240$		0			0
$241$	2.12309	−	3.67730i	0.136760	−	0.236876i	−0.789508	−	0.613740i	$-0.789664\pi$
$241$	2.12309	−	3.67730i	0.136760	−	0.236876i	0.926269	+	0.376864i	$0.122998\pi$
$242$		0			0
$243$	3.92708	+	6.80189i	0.251922	+	0.436342i
$244$		0			0
$245$	0.660754	+	1.89324i	0.0422140	+	0.120955i
$246$		0			0
$247$	11.5748	+	20.0481i	0.736486	+	1.27563i
$248$		0			0
$249$	12.0657	−	20.8983i	0.764630	−	1.32438i
$250$		0			0
$251$	3.77733			0.238423			0.119211	−	0.992869i	$-0.461963\pi$
$251$	3.77733			0.238423			0.119211	+	0.992869i	$0.461963\pi$
$252$		0			0
$253$	−8.61320			−0.541508
$254$		0			0
$255$	−0.379526	+	0.657359i	−0.0237669	+	0.0411654i
$256$		0			0
$257$	−9.17961	−	15.8996i	−0.572608	−	0.991787i	−0.996297	−	0.0859788i	$-0.972598\pi$
$257$	−9.17961	−	15.8996i	−0.572608	−	0.991787i	0.423689	−	0.905808i	$-0.360735\pi$
$258$		0			0
$259$	8.18613	+	17.8639i	0.508661	+	1.11001i
$260$		0			0
$261$	−1.43621	−	2.48759i	−0.0888993	−	0.153978i
$262$		0			0
$263$	0.248049	−	0.429634i	0.0152954	−	0.0264923i	−0.858276	−	0.513188i	$-0.828464\pi$
$263$	0.248049	−	0.429634i	0.0152954	−	0.0264923i	0.873572	+	0.486695i	$0.161798\pi$
$264$		0			0
$265$	2.14585			0.131818
$266$		0			0
$267$	15.1183			0.925223
$268$		0			0
$269$	−4.91142	+	8.50683i	−0.299455	+	0.518671i	−0.976011	−	0.217720i	$-0.930138\pi$
$269$	−4.91142	+	8.50683i	−0.299455	+	0.518671i	0.676557	+	0.736391i	$0.263471\pi$
$270$		0			0
$271$	5.74992	+	9.95915i	0.349283	+	0.604975i	0.986122	−	0.166021i	$-0.0530920\pi$
$271$	5.74992	+	9.95915i	0.349283	+	0.604975i	−0.636840	+	0.770996i	$0.719759\pi$
$272$		0			0
$273$	7.97259	−	11.2267i	0.482523	−	0.679470i
$274$		0			0
$275$	−2.45897	−	4.25906i	−0.148281	−	0.256831i
$276$		0			0
$277$	1.09958	−	1.90453i	0.0660676	−	0.114432i	−0.831099	−	0.556124i	$-0.812288\pi$
$277$	1.09958	−	1.90453i	0.0660676	−	0.114432i	0.897167	+	0.441691i	$0.145621\pi$
$278$		0			0
$279$	−1.44535			−0.0865308
$280$		0			0
$281$	16.6222			0.991596			0.495798	−	0.868438i	$-0.334876\pi$
$281$	16.6222			0.991596			0.495798	+	0.868438i	$0.334876\pi$
$282$		0			0
$283$	−7.52928	+	13.0411i	−0.447569	+	0.775212i	−0.998227	−	0.0595185i	$-0.981043\pi$
$283$	−7.52928	+	13.0411i	−0.447569	+	0.775212i	0.550658	+	0.834731i	$0.314377\pi$
$284$		0			0
$285$	−1.41607	−	2.45271i	−0.0838809	−	0.145286i
$286$		0			0
$287$	6.94535	+	0.654125i	0.409971	+	0.0386117i
$288$		0			0
$289$	6.92056	+	11.9868i	0.407092	+	0.705103i
$290$		0			0
$291$	2.27022	−	3.93214i	0.133083	−	0.230506i
$292$		0			0
$293$	26.3905			1.54175			0.770876	−	0.636986i	$-0.219819\pi$
$293$	26.3905			1.54175			0.770876	+	0.636986i	$0.219819\pi$
$294$		0			0
$295$	−0.676992			−0.0394160
$296$		0			0
$297$	2.81574	−	4.87700i	0.163386	−	0.282992i
$298$		0			0
$299$	15.0338	+	26.0392i	0.869425	+	1.50589i
$300$		0			0
$301$	28.7108	+	2.70403i	1.65486	+	0.155858i
$302$		0			0
$303$	3.25644	+	5.64031i	0.187077	+	0.324027i
$304$		0			0
$305$	0.222674	−	0.385683i	0.0127503	−	0.0220842i
$306$		0			0
$307$	19.2316			1.09761			0.548804	−	0.835951i	$-0.315083\pi$
$307$	19.2316			1.09761			0.548804	+	0.835951i	$0.315083\pi$
$308$		0			0
$309$	−7.78630			−0.442947
$310$		0			0
$311$	−12.8385	+	22.2369i	−0.728004	+	1.26094i	0.229721	+	0.973257i	$0.426219\pi$
$311$	−12.8385	+	22.2369i	−0.728004	+	1.26094i	−0.957725	+	0.287684i	$0.907115\pi$
$312$		0			0
$313$	0.684261	+	1.18518i	0.0386767	+	0.0669901i	0.884716	−	0.466131i	$-0.154352\pi$
$313$	0.684261	+	1.18518i	0.0386767	+	0.0669901i	−0.846039	+	0.533121i	$0.821019\pi$
$314$		0			0
$315$	0.341113	−	0.480342i	0.0192196	−	0.0270642i
$316$		0			0
$317$	−1.74153	−	3.01642i	−0.0978141	−	0.169419i	0.812966	−	0.582312i	$-0.197852\pi$
$317$	−1.74153	−	3.01642i	−0.0978141	−	0.169419i	−0.910780	+	0.412893i	$0.864518\pi$
$318$		0			0
$319$	−1.84763	+	3.20019i	−0.103448	+	0.179176i
$320$		0			0
$321$	15.7005			0.876316
$322$		0			0
$323$	11.7863			0.655807
$324$		0			0
$325$	−8.58393	+	14.8678i	−0.476151	+	0.824717i
$326$		0			0
$327$	2.64585	+	4.58274i	0.146316	+	0.253426i
$328$		0			0
$329$	−8.39128	−	18.3115i	−0.462626	−	1.00955i
$330$		0			0
$331$	−8.95432	−	15.5093i	−0.492174	−	0.852470i	0.507786	−	0.861484i	$-0.330464\pi$
$331$	−8.95432	−	15.5093i	−0.492174	−	0.852470i	−0.999959	+	0.00901343i	$0.997131\pi$
$332$		0			0
$333$	2.88663	−	4.99979i	0.158186	−	0.273987i
$334$		0			0
$335$	−1.75532			−0.0959033
$336$		0			0
$337$	−34.1496			−1.86025			−0.930123	−	0.367248i	$-0.880300\pi$
$337$	−34.1496			−1.86025			−0.930123	+	0.367248i	$0.880300\pi$
$338$		0			0
$339$	−4.70644	+	8.15179i	−0.255619	+	0.442744i
$340$		0			0
$341$	0.929693	+	1.61028i	0.0503457	+	0.0872013i
$342$		0			0
$343$	−17.7902	−	5.14868i	−0.960580	−	0.278003i
$344$		0			0
$345$	−1.83925	−	3.18567i	−0.0990217	−	0.171511i
$346$		0			0
$347$	3.15237	−	5.46006i	0.169228	−	0.293111i	−0.768921	−	0.639344i	$-0.779206\pi$
$347$	3.15237	−	5.46006i	0.169228	−	0.293111i	0.938149	+	0.346233i	$0.112539\pi$
$348$		0			0
$349$	−10.7628			−0.576119			−0.288059	−	0.957613i	$-0.593010\pi$
$349$	−10.7628			−0.576119			−0.288059	+	0.957613i	$0.593010\pi$
$350$		0			0
$351$	−19.6587			−1.04930
$352$		0			0
$353$	3.93156	−	6.80966i	0.209256	−	0.362442i	−0.742224	−	0.670151i	$-0.766229\pi$
$353$	3.93156	−	6.80966i	0.209256	−	0.362442i	0.951480	+	0.307710i	$0.0995625\pi$
$354$		0			0
$355$	−1.76370	−	3.05483i	−0.0936077	−	0.162133i
$356$		0			0
$357$	−2.92056	−	6.37327i	−0.154572	−	0.337309i
$358$		0			0
$359$	−9.49797	−	16.4510i	−0.501283	−	0.868248i	−0.999999	−	0.00148263i	$-0.999528\pi$
$359$	−9.49797	−	16.4510i	−0.501283	−	0.868248i	0.498715	−	0.866766i	$-0.333805\pi$
$360$		0			0
$361$	−12.4882	+	21.6303i	−0.657276	+	1.13844i
$362$		0			0
$363$	−1.49086			−0.0782500
$364$		0			0
$365$	2.42184			0.126765
$366$		0			0
$367$	9.19788	−	15.9312i	0.480126	−	0.831602i	−0.519615	−	0.854401i	$-0.673924\pi$
$367$	9.19788	−	15.9312i	0.480126	−	0.831602i	0.999740	+	0.0227990i	$0.00725776\pi$
$368$		0			0
$369$	−1.02479	−	1.77499i	−0.0533485	−	0.0924024i
$370$		0			0
$371$	−11.4752	+	16.1589i	−0.595763	+	0.838930i
$372$		0			0
$373$	11.6276	+	20.1396i	0.602053	+	1.04279i	0.992510	+	0.122165i	$0.0389838\pi$
$373$	11.6276	+	20.1396i	0.602053	+	1.04279i	−0.390457	+	0.920621i	$0.627683\pi$
$374$		0			0
$375$	2.11786	−	3.66823i	0.109366	−	0.189427i
$376$		0			0
$377$	12.8997			0.664367
$378$		0			0
$379$	3.53264			0.181460			0.0907299	−	0.995876i	$-0.471080\pi$
$379$	3.53264			0.181460			0.0907299	+	0.995876i	$0.471080\pi$
$380$		0			0
$381$	−2.89331	+	5.01137i	−0.148229	+	0.256740i
$382$		0			0
$383$	12.2818	+	21.2727i	0.627571	+	1.08699i	0.988038	+	0.154213i	$0.0492842\pi$
$383$	12.2818	+	21.2727i	0.627571	+	1.08699i	−0.360466	+	0.932772i	$0.617382\pi$
$384$		0			0
$385$	−0.754568	−	0.0710665i	−0.0384564	−	0.00362188i
$386$		0			0
$387$	−4.23630	−	7.33748i	−0.215343	−	0.372985i
$388$		0			0
$389$	0.661504	−	1.14576i	0.0335396	−	0.0580922i	−0.848768	−	0.528765i	$-0.822655\pi$
$389$	0.661504	−	1.14576i	0.0335396	−	0.0580922i	0.882308	+	0.470673i	$0.155989\pi$
$390$		0			0
$391$	15.3085			0.774183
$392$		0			0
$393$	−27.1809			−1.37109
$394$		0			0
$395$	−1.48900	+	2.57902i	−0.0749195	+	0.129764i
$396$		0			0
$397$	−7.67699	−	13.2969i	−0.385297	−	0.667354i	0.606513	−	0.795073i	$-0.292568\pi$
$397$	−7.67699	−	13.2969i	−0.385297	−	0.667354i	−0.991810	+	0.127719i	$0.959234\pi$
$398$		0			0
$399$	26.0423	+	2.45271i	1.30375	+	0.122789i
$400$		0			0
$401$	7.22716	+	12.5178i	0.360907	+	0.625109i	0.988110	−	0.153746i	$-0.0491338\pi$
$401$	7.22716	+	12.5178i	0.360907	+	0.625109i	−0.627203	+	0.778856i	$0.715800\pi$
$402$		0			0
$403$	3.24543	−	5.62125i	0.161666	−	0.280015i
$404$		0			0
$405$	1.73705			0.0863145
$406$		0			0
$407$	−7.42708			−0.368146
$408$		0			0
$409$	−16.1561	+	27.9832i	−0.798868	+	1.38368i	0.121486	+	0.992593i	$0.461234\pi$
$409$	−16.1561	+	27.9832i	−0.798868	+	1.38368i	−0.920354	+	0.391087i	$0.872099\pi$
$410$		0			0
$411$	−1.02986	−	1.78377i	−0.0507992	−	0.0879868i
$412$		0			0
$413$	3.62031	−	5.09797i	0.178144	−	0.250855i
$414$		0			0
$415$	2.31836	+	4.01551i	0.113804	+	0.197114i
$416$		0			0
$417$	0.440697	−	0.763310i	0.0215810	−	0.0373794i
$418$		0			0
$419$	−15.5259			−0.758490			−0.379245	−	0.925296i	$-0.623816\pi$
$419$	−15.5259			−0.758490			−0.379245	+	0.925296i	$0.623816\pi$
$420$		0			0
$421$	10.9049			0.531472			0.265736	−	0.964046i	$-0.414385\pi$
$421$	10.9049			0.531472			0.265736	+	0.964046i	$0.414385\pi$
$422$		0			0
$423$	−2.95897	+	5.12509i	−0.143870	+	0.249190i
$424$		0			0
$425$	4.37039	+	7.56974i	0.211995	+	0.367186i
$426$		0			0
$427$	1.71354	+	3.73930i	0.0829239	+	0.180957i
$428$		0			0
$429$	2.60220	+	4.50714i	0.125635	+	0.217607i
$430$		0			0
$431$	8.41271	−	14.5712i	0.405226	−	0.701872i	−0.589122	−	0.808044i	$-0.700526\pi$
$431$	8.41271	−	14.5712i	0.405226	−	0.701872i	0.994348	+	0.106173i	$0.0338596\pi$
$432$		0			0
$433$	12.1641			0.584570			0.292285	−	0.956331i	$-0.405584\pi$
$433$	12.1641			0.584570			0.292285	+	0.956331i	$0.405584\pi$
$434$		0			0
$435$	−1.57816			−0.0756669
$436$		0			0
$437$	−28.5591	+	49.4659i	−1.36617	+	2.36627i
$438$		0			0
$439$	3.49273	+	6.04959i	0.166699	+	0.288731i	0.937257	−	0.348638i	$-0.113356\pi$
$439$	3.49273	+	6.04959i	0.166699	+	0.288731i	−0.770558	+	0.637369i	$0.780023\pi$
$440$		0			0
$441$	1.79298	+	5.13739i	0.0853801	+	0.244637i
$442$		0			0
$443$	−19.6796	−	34.0861i	−0.935006	−	1.61948i	−0.774622	−	0.632424i	$-0.782060\pi$
$443$	−19.6796	−	34.0861i	−0.935006	−	1.61948i	−0.160384	−	0.987055i	$-0.551273\pi$
$444$		0			0
$445$	−1.45245	+	2.51572i	−0.0688528	+	0.119256i
$446$		0			0
$447$	−19.0821			−0.902550
$448$		0			0
$449$	13.3723			0.631076			0.315538	−	0.948913i	$-0.397815\pi$
$449$	13.3723			0.631076			0.315538	+	0.948913i	$0.397815\pi$
$450$		0			0
$451$	−1.31836	+	2.28346i	−0.0620790	+	0.107524i
$452$		0			0
$453$	4.21541	+	7.30130i	0.198057	+	0.343045i
$454$		0			0
$455$	1.10220	+	2.40523i	0.0516720	+	0.112759i
$456$		0			0
$457$	−3.44331	−	5.96400i	−0.161071	−	0.278984i	0.774182	−	0.632963i	$-0.218162\pi$
$457$	−3.44331	−	5.96400i	−0.161071	−	0.278984i	−0.935253	+	0.353979i	$0.884828\pi$
$458$		0			0
$459$	−5.00448	+	8.66802i	−0.233589	+	0.404589i
$460$		0			0
$461$	−5.16786			−0.240691			−0.120346	−	0.992732i	$-0.538400\pi$
$461$	−5.16786			−0.240691			−0.120346	+	0.992732i	$0.538400\pi$
$462$		0			0
$463$	18.6039			0.864597			0.432298	−	0.901731i	$-0.357703\pi$
$463$	18.6039			0.864597			0.432298	+	0.901731i	$0.357703\pi$
$464$		0			0
$465$	−0.397049	+	0.687710i	−0.0184127	+	0.0318918i
$466$		0			0
$467$	−7.63858	−	13.2304i	−0.353471	−	0.612230i	0.633384	−	0.773838i	$-0.281665\pi$
$467$	−7.63858	−	13.2304i	−0.353471	−	0.612230i	−0.986855	+	0.161608i	$0.948332\pi$
$468$		0			0
$469$	9.38680	−	13.2181i	0.433442	−	0.610355i
$470$		0			0
$471$	−14.6503	−	25.3751i	−0.675052	−	1.16922i
$472$		0			0
$473$	−5.44983	+	9.43939i	−0.250584	+	0.434024i
$474$		0			0
$475$	−32.6132			−1.49640
$476$		0			0
$477$	5.82284			0.266610
$478$		0			0
$479$	6.46084	−	11.1905i	0.295203	−	0.511307i	−0.679829	−	0.733371i	$-0.737946\pi$
$479$	6.46084	−	11.1905i	0.295203	−	0.511307i	0.975032	+	0.222064i	$0.0712793\pi$
$480$		0			0
$481$	12.9635	+	22.4534i	0.591083	+	1.02379i
$482$		0			0
$483$	33.8247	+	3.18567i	1.53908	+	0.144953i
$484$		0			0
$485$	0.436212	+	0.755542i	0.0198074	+	0.0343074i
$486$		0			0
$487$	7.23239	−	12.5269i	0.327731	−	0.567647i	−0.654330	−	0.756209i	$-0.727049\pi$
$487$	7.23239	−	12.5269i	0.327731	−	0.567647i	0.982061	+	0.188562i	$0.0603827\pi$
$488$		0			0
$489$	−13.4178			−0.606773
$490$		0			0
$491$	40.8799			1.84488			0.922442	−	0.386136i	$-0.126190\pi$
$491$	40.8799			1.84488			0.922442	+	0.386136i	$0.126190\pi$
$492$		0			0
$493$	3.28384	−	5.68779i	0.147897	−	0.256165i
$494$		0			0
$495$	0.111337	+	0.192842i	0.00500423	+	0.00866759i
$496$		0			0
$497$	32.4355	+	3.05483i	1.45493	+	0.137028i
$498$		0			0
$499$	8.84240	+	15.3155i	0.395840	+	0.685615i	0.993208	−	0.116352i	$-0.0371201\pi$
$499$	8.84240	+	15.3155i	0.395840	+	0.685615i	−0.597368	+	0.801967i	$0.703787\pi$
$500$		0			0
$501$	11.0358	−	19.1146i	0.493043	−	0.853976i
$502$		0			0
$503$	−43.8266			−1.95413			−0.977065	−	0.212940i	$-0.931696\pi$
$503$	−43.8266			−1.95413			−0.977065	+	0.212940i	$0.931696\pi$
$504$		0			0
$505$	−1.25142			−0.0556873
$506$		0			0
$507$	−0.606685	+	1.05081i	−0.0269438	+	0.0466681i
$508$		0			0
$509$	−16.3652	−	28.3453i	−0.725373	−	1.25638i	−0.958820	−	0.284013i	$-0.908334\pi$
$509$	−16.3652	−	28.3453i	−0.725373	−	1.25638i	0.233448	−	0.972369i	$-0.424999\pi$
$510$		0			0
$511$	−12.9511	+	18.2372i	−0.572924	+	0.806768i
$512$		0			0
$513$	−18.6725	−	32.3417i	−0.824411	−	1.42792i
$514$		0			0
$515$	0.748049	−	1.29566i	0.0329630	−	0.0570936i
$516$		0			0
$517$	7.61320			0.334828
$518$		0			0
$519$	−22.6599			−0.994659
$520$		0			0
$521$	20.2335	−	35.0455i	0.886446	−	1.53537i	0.0423992	−	0.999101i	$-0.486500\pi$
$521$	20.2335	−	35.0455i	0.886446	−	1.53537i	0.844047	−	0.536269i	$-0.180167\pi$
$522$		0			0
$523$	−17.3430	−	30.0389i	−0.758356	−	1.31351i	−0.943689	−	0.330835i	$-0.892670\pi$
$523$	−17.3430	−	30.0389i	−0.758356	−	1.31351i	0.185333	−	0.982676i	$-0.440664\pi$
$524$		0			0
$525$	8.08131	+	17.6351i	0.352697	+	0.769660i
$526$		0			0
$527$	−1.65237	−	2.86198i	−0.0719783	−	0.124670i
$528$		0			0
$529$	−25.5936	+	44.3295i	−1.11277	+	1.92737i
$530$		0			0
$531$	−1.83704			−0.0797209
$532$		0			0
$533$	9.20440			0.398687
$534$		0			0
$535$	−1.50839	+	2.61260i	−0.0652132	+	0.112953i
$536$		0			0
$537$	−13.7564	−	23.8268i	−0.593634	−	1.02820i
$538$		0			0
$539$	4.57031	−	5.30210i	0.196857	−	0.228378i
$540$		0			0
$541$	2.97521	+	5.15321i	0.127914	+	0.221554i	0.922868	−	0.385116i	$-0.125838\pi$
$541$	2.97521	+	5.15321i	0.127914	+	0.221554i	−0.794954	+	0.606670i	$0.792505\pi$
$542$		0			0
$543$	14.1835	−	24.5666i	0.608673	−	1.05425i
$544$		0			0
$545$	−1.01677			−0.0435538
$546$		0			0
$547$	1.32824			0.0567915			0.0283958	−	0.999597i	$-0.490960\pi$
$547$	1.32824			0.0567915			0.0283958	+	0.999597i	$0.490960\pi$
$548$		0			0
$549$	0.604235	−	1.04657i	0.0257881	−	0.0446664i
$550$		0			0
$551$	12.2525	+	21.2220i	0.521975	+	0.904088i
$552$		0			0
$553$	−11.4582	−	25.0043i	−0.487253	−	1.06329i
$554$		0			0
$555$	−1.58596	−	2.74697i	−0.0673204	−	0.116602i
$556$		0			0
$557$	5.55727	−	9.62547i	0.235469	−	0.407844i	−0.723940	−	0.689863i	$-0.757671\pi$
$557$	5.55727	−	9.62547i	0.235469	−	0.407844i	0.959409	+	0.282019i	$0.0910040\pi$
$558$		0			0
$559$	38.0492			1.60931
$560$		0			0
$561$	2.64975			0.111873
$562$		0			0
$563$	−9.73816	+	16.8670i	−0.410415	+	0.710859i	−0.994935	−	0.100520i	$-0.967949\pi$
$563$	−9.73816	+	16.8670i	−0.410415	+	0.710859i	0.584520	+	0.811379i	$0.301283\pi$
$564$		0			0
$565$	−0.904318	−	1.56633i	−0.0380450	−	0.0658958i
$566$		0			0
$567$	−9.28908	+	13.0805i	−0.390105	+	0.549330i
$568$		0			0
$569$	−14.1112	−	24.4413i	−0.591571	−	1.02463i	−0.994021	−	0.109189i	$-0.965175\pi$
$569$	−14.1112	−	24.4413i	−0.591571	−	1.02463i	0.402450	−	0.915442i	$-0.368159\pi$
$570$		0			0
$571$	11.9655	−	20.7248i	0.500740	−	0.867307i	−0.499260	−	0.866453i	$-0.666395\pi$
$571$	11.9655	−	20.7248i	0.500740	−	0.867307i	1.00000		0.000854835i	$-0.000272102\pi$
$572$		0			0
$573$	−15.3007			−0.639194
$574$		0			0
$575$	−42.3592			−1.76650
$576$		0			0
$577$	−13.6477	+	23.6385i	−0.568162	+	0.984085i	0.428586	+	0.903501i	$0.359012\pi$
$577$	−13.6477	+	23.6385i	−0.568162	+	0.984085i	−0.996748	+	0.0805842i	$0.974321\pi$
$578$		0			0
$579$	10.2389	+	17.7343i	0.425515	+	0.737013i
$580$		0			0
$581$	−42.6358	−	4.01551i	−1.76883	−	0.166591i
$582$		0			0
$583$	−3.74543	−	6.48728i	−0.155120	−	0.268676i
$584$		0			0
$585$	0.388663	−	0.673184i	0.0160692	−	0.0278327i
$586$		0			0
$587$	−15.9179			−0.657004			−0.328502	−	0.944503i	$-0.606544\pi$
$587$	−15.9179			−0.657004			−0.328502	+	0.944503i	$0.606544\pi$
$588$		0			0
$589$	12.3305			0.508068
$590$		0			0
$591$	3.01956	−	5.23003i	0.124208	−	0.215135i
$592$		0			0
$593$	3.21092	+	5.56148i	0.131857	+	0.228383i	0.924392	−	0.381443i	$-0.124573\pi$
$593$	3.21092	+	5.56148i	0.131857	+	0.228383i	−0.792536	+	0.609826i	$0.791239\pi$
$594$		0			0
$595$	1.34111	+	0.126308i	0.0549803	+	0.00517814i
$596$		0			0
$597$	19.2219	+	33.2933i	0.786701	+	1.36261i
$598$		0			0
$599$	−2.11786	+	3.66823i	−0.0865333	+	0.149880i	−0.906044	−	0.423184i	$-0.860912\pi$
$599$	−2.11786	+	3.66823i	−0.0865333	+	0.149880i	0.819510	+	0.573064i	$0.194246\pi$
$600$		0			0
$601$	26.4946			1.08074			0.540369	−	0.841428i	$-0.318285\pi$
$601$	26.4946			1.08074			0.540369	+	0.841428i	$0.318285\pi$
$602$		0			0
$603$	−4.76312			−0.193969
$604$		0			0
$605$	0.143231	−	0.248083i	0.00582317	−	0.0100860i
$606$		0			0
$607$	−15.3131	−	26.5231i	−0.621540	−	1.07654i	−0.989199	−	0.146579i	$-0.953174\pi$
$607$	−15.3131	−	26.5231i	−0.621540	−	1.07654i	0.367659	−	0.929961i	$-0.380160\pi$
$608$		0			0
$609$	8.43941	−	11.8840i	0.341982	−	0.481566i
$610$		0			0
$611$	−13.2883	−	23.0161i	−0.537588	−	0.931130i
$612$		0			0
$613$	−14.1679	+	24.5394i	−0.572234	+	0.991139i	0.424102	+	0.905615i	$0.360590\pi$
$613$	−14.1679	+	24.5394i	−0.572234	+	0.991139i	−0.996336	+	0.0855244i	$0.972743\pi$
$614$		0			0
$615$	−1.12608			−0.0454078
$616$		0			0
$617$	−49.3279			−1.98587			−0.992933	−	0.118673i	$-0.962136\pi$
$617$	−49.3279			−1.98587			−0.992933	+	0.118673i	$0.962136\pi$
$618$		0			0
$619$	−20.0638	+	34.7515i	−0.806432	+	1.39678i	0.108889	+	0.994054i	$0.465271\pi$
$619$	−20.0638	+	34.7515i	−0.806432	+	1.39678i	−0.915320	+	0.402727i	$0.868062\pi$
$620$		0			0
$621$	−24.2525	−	42.0066i	−0.973221	−	1.68567i
$622$		0			0
$623$	−11.1770	−	24.3906i	−0.447797	−	0.977187i
$624$		0			0
$625$	−11.8879	−	20.5905i	−0.475517	−	0.823619i
$626$		0			0
$627$	−4.94331	+	8.56207i	−0.197417	+	0.341936i
$628$		0			0
$629$	13.2003			0.526332
$630$		0			0
$631$	39.2354			1.56194			0.780968	−	0.624571i	$-0.214726\pi$
$631$	39.2354			1.56194			0.780968	+	0.624571i	$0.214726\pi$
$632$		0			0
$633$	8.82284	−	15.2816i	0.350676	−	0.607389i
$634$		0			0
$635$	−0.555936	−	0.962910i	−0.0220616	−	0.0382119i
$636$		0			0
$637$	−24.0064	−	4.56239i	−0.951166	−	0.180768i
$638$		0			0
$639$	−4.78588	−	8.28939i	−0.189326	−	0.327923i
$640$		0			0
$641$	2.48434	−	4.30301i	0.0981257	−	0.169959i	−0.812783	−	0.582566i	$-0.802049\pi$
$641$	2.48434	−	4.30301i	0.0981257	−	0.169959i	0.910909	+	0.412608i	$0.135382\pi$
$642$		0			0
$643$	1.88289			0.0742541			0.0371270	−	0.999311i	$-0.488179\pi$
$643$	1.88289			0.0742541			0.0371270	+	0.999311i	$0.488179\pi$
$644$		0			0
$645$	−4.65498			−0.183290
$646$		0			0
$647$	−7.45955	+	12.9203i	−0.293265	+	0.507950i	−0.974580	−	0.224040i	$-0.928075\pi$
$647$	−7.45955	+	12.9203i	−0.293265	+	0.507950i	0.681315	+	0.731991i	$0.261409\pi$
$648$		0			0
$649$	1.18164	+	2.04667i	0.0463836	+	0.0803387i
$650$		0			0
$651$	−3.05540	−	6.66753i	−0.119751	−	0.261321i
$652$		0			0
$653$	−20.7674	−	35.9703i	−0.812693	−	1.40763i	−0.910973	−	0.412466i	$-0.864667\pi$
$653$	−20.7674	−	35.9703i	−0.812693	−	1.40763i	0.0982802	−	0.995159i	$-0.468666\pi$
$654$		0			0
$655$	2.61134	−	4.52297i	0.102033	−	0.176727i
$656$		0			0
$657$	6.57176			0.256389
$658$		0			0
$659$	−12.4596			−0.485355			−0.242678	−	0.970107i	$-0.578026\pi$
$659$	−12.4596			−0.485355			−0.242678	+	0.970107i	$0.578026\pi$
$660$		0			0
$661$	−2.63409	+	4.56239i	−0.102454	+	0.177456i	−0.912695	−	0.408641i	$-0.866003\pi$
$661$	−2.63409	+	4.56239i	−0.102454	+	0.177456i	0.810241	+	0.586097i	$0.199336\pi$
$662$		0			0
$663$	−4.62496	−	8.01066i	−0.179618	−	0.311108i
$664$		0			0
$665$	−2.91009	+	4.09787i	−0.112848	+	0.158909i
$666$		0			0
$667$	15.9140	+	27.5639i	0.616194	+	1.06728i
$668$		0			0
$669$	13.1945	−	22.8536i	0.510129	−	0.883570i
$670$		0			0
$671$	−1.55465			−0.0600167
$672$		0			0
$673$	−27.8254			−1.07259			−0.536295	−	0.844030i	$-0.680177\pi$
$673$	−27.8254			−1.07259			−0.536295	+	0.844030i	$0.680177\pi$
$674$		0			0
$675$	13.8476	−	23.9848i	0.532996	−	0.923176i
$676$		0			0
$677$	−10.5436	−	18.2621i	−0.405225	−	0.701871i	0.589122	−	0.808044i	$-0.299474\pi$
$677$	−10.5436	−	18.2621i	−0.405225	−	0.701871i	−0.994348	+	0.106173i	$0.966140\pi$
$678$		0			0
$679$	−8.02217	−	0.755542i	−0.307863	−	0.0289950i
$680$		0			0
$681$	−17.6768	−	30.6172i	−0.677377	−	1.17325i
$682$		0			0
$683$	−23.9536	+	41.4888i	−0.916558	+	1.58752i	−0.111953	+	0.993713i	$0.535711\pi$
$683$	−23.9536	+	41.4888i	−0.916558	+	1.58752i	−0.804604	+	0.593811i	$0.797623\pi$
$684$		0			0
$685$	0.395765			0.0151214
$686$		0			0
$687$	28.0272			1.06931
$688$		0			0
$689$	−13.0748	+	22.6462i	−0.498110	+	0.862752i
$690$		0			0
$691$	−2.73705	−	4.74070i	−0.104122	−	0.180345i	0.809257	−	0.587455i	$-0.199870\pi$
$691$	−2.73705	−	4.74070i	−0.104122	−	0.180345i	−0.913379	+	0.407110i	$0.866537\pi$
$692$		0			0
$693$	−2.04755	−	0.192842i	−0.0777800	−	0.00732545i
$694$		0			0
$695$	0.0846777	+	0.146666i	0.00321201	+	0.00556336i
$696$		0			0
$697$	2.34315	−	4.05845i	0.0887531	−	0.153725i
$698$		0			0
$699$	−29.7900			−1.12676
$700$		0			0
$701$	31.1679			1.17719			0.588597	−	0.808427i	$-0.299681\pi$
$701$	31.1679			1.17719			0.588597	+	0.808427i	$0.299681\pi$
$702$		0			0
$703$	−24.6262	+	42.6539i	−0.928796	+	1.60872i
$704$		0			0
$705$	1.62571	+	2.81581i	0.0612277	+	0.106049i
$706$		0			0
$707$	6.69211	−	9.42356i	0.251683	−	0.354410i
$708$		0			0
$709$	−24.1833	−	41.8868i	−0.908225	−	1.57309i	−0.816529	−	0.577304i	$-0.804105\pi$
$709$	−24.1833	−	41.8868i	−0.908225	−	1.57309i	−0.0916953	−	0.995787i	$-0.529229\pi$
$710$		0			0
$711$	−4.04045	+	6.99826i	−0.151529	+	0.262455i
$712$		0			0
$713$	16.0153			0.599777
$714$		0			0
$715$	−1.00000			−0.0373979
$716$		0			0
$717$	−11.5502	+	20.0055i	−0.431349	+	0.747118i
$718$		0			0
$719$	0.893315	+	1.54727i	0.0333150	+	0.0577033i	0.882202	−	0.470871i	$-0.156060\pi$
$719$	0.893315	+	1.54727i	0.0333150	+	0.0577033i	−0.848887	+	0.528574i	$0.822727\pi$
$720$		0			0
$721$	5.75644	+	12.5618i	0.214381	+	0.467824i
$722$		0			0
$723$	−3.16524	−	5.48235i	−0.117716	−	0.203891i
$724$		0			0
$725$	−9.08655	+	15.7384i	−0.337466	+	0.584508i
$726$		0			0
$727$	22.5494			0.836312			0.418156	−	0.908375i	$-0.362677\pi$
$727$	22.5494			0.836312			0.418156	+	0.908375i	$0.362677\pi$
$728$		0			0
$729$	29.9008			1.10744
$730$		0			0
$731$	9.68613	−	16.7769i	0.358254	−	0.620515i
$732$		0			0
$733$	−2.72978	−	4.72811i	−0.100827	−	0.174637i	0.811199	−	0.584770i	$-0.198815\pi$
$733$	−2.72978	−	4.72811i	−0.100827	−	0.174637i	−0.912025	+	0.410134i	$0.865482\pi$
$734$		0			0
$735$	2.93696	+	0.558167i	0.108331	+	0.0205883i
$736$		0			0
$737$	3.06379	+	5.30664i	0.112856	+	0.195472i
$738$		0			0
$739$	−7.45507	+	12.9126i	−0.274239	+	0.474996i	−0.969943	−	0.243333i	$-0.921759\pi$
$739$	−7.45507	+	12.9126i	−0.274239	+	0.474996i	0.695704	+	0.718329i	$0.255093\pi$
$740$		0			0
$741$	34.5129			1.26786
$742$		0			0
$743$	12.7680			0.468413			0.234207	−	0.972187i	$-0.424751\pi$
$743$	12.7680			0.468413			0.234207	+	0.972187i	$0.424751\pi$
$744$		0			0
$745$	1.83326	−	3.17530i	0.0671655	−	0.116334i
$746$		0			0
$747$	6.29095	+	10.8962i	0.230174	+	0.398673i
$748$		0			0
$749$	−11.6074	−	25.3299i	−0.424126	−	0.925533i
$750$		0			0
$751$	−15.7564	−	27.2909i	−0.574961	−	0.995861i	−0.996046	−	0.0888398i	$-0.971684\pi$
$751$	−15.7564	−	27.2909i	−0.574961	−	0.995861i	0.421085	−	0.907021i	$-0.361649\pi$
$752$		0			0
$753$	2.81574	−	4.87700i	0.102611	−	0.177728i
$754$		0			0
$755$	−1.61994			−0.0589556
$756$		0			0
$757$	−19.0936			−0.693969			−0.346984	−	0.937871i	$-0.612794\pi$
$757$	−19.0936			−0.693969			−0.346984	+	0.937871i	$0.612794\pi$
$758$		0			0
$759$	−6.42056	+	11.1207i	−0.233051	+	0.403657i
$760$		0			0
$761$	6.51100	+	11.2774i	0.236024	+	0.408805i	0.959570	−	0.281471i	$-0.0908224\pi$
$761$	6.51100	+	11.2774i	0.236024	+	0.408805i	−0.723546	+	0.690276i	$0.757489\pi$
$762$		0			0
$763$	5.43733	−	7.65663i	0.196845	−	0.277189i
$764$		0			0
$765$	−0.197882	−	0.342742i	−0.00715445	−	0.0123919i
$766$		0			0
$767$	4.12496	−	7.14464i	0.148944	−	0.257978i
$768$		0			0
$769$	−25.5103			−0.919925			−0.459963	−	0.887938i	$-0.652137\pi$
$769$	−25.5103			−0.919925			−0.459963	+	0.887938i	$0.652137\pi$
$770$		0			0
$771$	−27.3711			−0.985746
$772$		0			0
$773$	23.9342	−	41.4552i	0.860853	−	1.49104i	−0.0102547	−	0.999947i	$-0.503264\pi$
$773$	23.9342	−	41.4552i	0.860853	−	1.49104i	0.871107	−	0.491093i	$-0.163402\pi$
$774$		0			0
$775$	4.57217	+	7.91924i	0.164237	+	0.284467i
$776$		0			0
$777$	29.1667	+	2.74697i	1.04635	+	0.0985469i
$778$		0			0
$779$	8.74265	+	15.1427i	0.313238	+	0.542544i
$780$		0			0
$781$	−6.15685	+	10.6640i	−0.220309	+	0.381587i
$782$		0			0
$783$	−20.8098			−0.743682
$784$		0			0
$785$	5.62998			0.200943
$786$		0			0
$787$	−13.7909	+	23.8866i	−0.491594	+	0.851466i	−0.999953	−	0.00967918i	$-0.996919\pi$
$787$	−13.7909	+	23.8866i	−0.491594	+	0.851466i	0.508359	+	0.861145i	$0.330252\pi$
$788$		0			0
$789$	−0.369807	−	0.640525i	−0.0131655	−	0.0228033i
$790$		0			0
$791$	16.6309	+	1.56633i	0.591327	+	0.0556921i
$792$		0			0
$793$	2.71354	+	4.69999i	0.0963606	+	0.166901i
$794$		0			0
$795$	1.59958	−	2.77056i	0.0567314	−	0.0982616i
$796$		0			0
$797$	−26.7773			−0.948502			−0.474251	−	0.880390i	$-0.657281\pi$
$797$	−26.7773			−0.948502			−0.474251	+	0.880390i	$0.657281\pi$
$798$		0			0
$799$	−13.5311			−0.478697
$800$		0			0
$801$	−3.94128	+	6.82650i	−0.139258	+	0.241202i
$802$		0			0
$803$	−4.22716	−	7.32165i	−0.149173	−	0.258376i
$804$		0			0
$805$	−3.77973	+	5.32246i	−0.133218	+	0.187592i
$806$		0			0
$807$	7.32226	+	12.6825i	0.257756	+	0.446446i
$808$		0			0
$809$	−18.5806	+	32.1825i	−0.653258	+	1.13148i	0.329070	+	0.944306i	$0.393265\pi$
$809$	−18.5806	+	32.1825i	−0.653258	+	1.13148i	−0.982328	+	0.187170i	$0.940068\pi$
$810$		0			0
$811$	−15.0414			−0.528177			−0.264088	−	0.964499i	$-0.585071\pi$
$811$	−15.0414			−0.528177			−0.264088	+	0.964499i	$0.585071\pi$
$812$		0			0
$813$	17.1447			0.601290
$814$		0			0
$815$	1.28908	−	2.23275i	0.0451545	−	0.0782099i
$816$		0			0
$817$	36.1404	+	62.5971i	1.26439	+	2.18999i
$818$		0			0
$819$	2.99086	+	6.52670i	0.104509	+	0.228061i
$820$		0			0
$821$	0.106685	+	0.184785i	0.00372335	+	0.00644903i	0.867881	−	0.496772i	$-0.165481\pi$
$821$	0.106685	+	0.184785i	0.00372335	+	0.00644903i	−0.864158	+	0.503221i	$0.832148\pi$
$822$		0			0
$823$	20.2199	−	35.0219i	0.704821	−	1.22079i	−0.261935	−	0.965086i	$-0.584361\pi$
$823$	20.2199	−	35.0219i	0.704821	−	1.22079i	0.966756	−	0.255700i	$-0.0823061\pi$
$824$		0			0
$825$	−7.33198			−0.255267
$826$		0			0
$827$	−50.0713			−1.74115			−0.870574	−	0.492037i	$-0.836252\pi$
$827$	−50.0713			−1.74115			−0.870574	+	0.492037i	$0.836252\pi$
$828$		0			0
$829$	−16.4133	+	28.4286i	−0.570057	+	0.987368i	0.426502	+	0.904486i	$0.359746\pi$
$829$	−16.4133	+	28.4286i	−0.570057	+	0.987368i	−0.996559	+	0.0828813i	$0.973588\pi$
$830$		0			0
$831$	−1.63933	−	2.83940i	−0.0568677	−	0.0984977i
$832$		0			0
$833$	−8.12292	+	9.42356i	−0.281443	+	0.326507i
$834$		0			0
$835$	2.12047	+	3.67277i	0.0733820	+	0.127101i
$836$		0			0
$837$	−5.23555	+	9.06823i	−0.180967	+	0.313444i
$838$		0			0
$839$	36.7758			1.26964			0.634821	−	0.772659i	$-0.281074\pi$
$839$	36.7758			1.26964			0.634821	+	0.772659i	$0.281074\pi$
$840$		0			0
$841$	−15.3450			−0.529138
$842$		0			0
$843$	12.3907	−	21.4613i	0.426758	−	0.739167i
$844$		0			0
$845$	−0.116572	−	0.201908i	−0.00401019	−	0.00694584i
$846$		0			0
$847$	1.10220	+	2.40523i	0.0378721	+	0.0826448i
$848$		0			0
$849$	11.2251	+	19.4425i	0.385245	+	0.667264i
$850$		0			0
$851$	−31.9855	+	55.4004i	−1.09645	+	1.89910i
$852$		0			0
$853$	−21.6613			−0.741668			−0.370834	−	0.928699i	$-0.620928\pi$
$853$	−21.6613			−0.741668			−0.370834	+	0.928699i	$0.620928\pi$
$854$		0			0
$855$	1.47666			0.0505007
$856$		0			0
$857$	2.18426	−	3.78325i	0.0746129	−	0.129233i	−0.826305	−	0.563223i	$-0.809561\pi$
$857$	2.18426	−	3.78325i	0.0746129	−	0.129233i	0.900918	+	0.433990i	$0.142895\pi$
$858$		0			0
$859$	−6.58131	−	11.3992i	−0.224551	−	0.388934i	0.731633	−	0.681698i	$-0.238758\pi$
$859$	−6.58131	−	11.3992i	−0.224551	−	0.388934i	−0.956185	+	0.292764i	$0.905425\pi$
$860$		0			0
$861$	6.02184	−	8.47971i	0.205224	−	0.288988i
$862$		0			0
$863$	−14.8892	−	25.7889i	−0.506836	−	0.877865i	−0.999969	−	0.00791139i	$-0.997482\pi$
$863$	−14.8892	−	25.7889i	−0.506836	−	0.877865i	0.493133	−	0.869954i	$-0.335852\pi$
$864$		0			0
$865$	2.17699	−	3.77066i	0.0740200	−	0.128206i
$866$		0			0
$867$	20.6352			0.700809
$868$		0			0
$869$	10.3958			0.352652
$870$		0			0
$871$	10.6953	−	18.5247i	0.362395	−	0.627687i
$872$		0			0
$873$	1.18368	+	2.05019i	0.0400614	+	0.0693885i
$874$		0			0
$875$	−7.48376	−	0.704833i	−0.252997	−	0.0238277i
$876$		0			0
$877$	−6.62699	−	11.4783i	−0.223778	−	0.387594i	0.732174	−	0.681117i	$-0.238506\pi$
$877$	−6.62699	−	11.4783i	−0.223778	−	0.387594i	−0.955952	+	0.293523i	$0.905172\pi$
$878$		0			0
$879$	19.6723	−	34.0735i	0.663532	−	1.14927i
$880$		0			0
$881$	−46.3890			−1.56289			−0.781443	−	0.623977i	$-0.785516\pi$
$881$	−46.3890			−1.56289			−0.781443	+	0.623977i	$0.785516\pi$
$882$		0			0
$883$	−11.6550			−0.392221			−0.196111	−	0.980582i	$-0.562831\pi$
$883$	−11.6550			−0.392221			−0.196111	+	0.980582i	$0.562831\pi$
$884$		0			0
$885$	−0.504652	+	0.874082i	−0.0169637	+	0.0293820i
$886$		0			0
$887$	13.8599	+	24.0061i	0.465371	+	0.806046i	0.999218	−	0.0395352i	$-0.0125877\pi$
$887$	13.8599	+	24.0061i	0.465371	+	0.806046i	−0.533848	+	0.845581i	$0.679254\pi$
$888$		0			0
$889$	10.2240	+	0.962910i	0.342901	+	0.0322949i
$890$		0			0
$891$	−3.03189	−	5.25139i	−0.101572	−	0.175928i
$892$		0			0
$893$	25.2434	−	43.7228i	0.844738	−	1.46313i
$894$		0			0
$895$	5.28646			0.176707
$896$		0			0
$897$	44.8266			1.49672
$898$		0			0
$899$	3.43546	−	5.95040i	0.114579	−	0.198457i
$900$		0			0
$901$	6.65685	+	11.5300i	0.221772	+	0.384120i
$902$		0			0
$903$	24.8931	−	35.0535i	0.828392	−	1.16651i
$904$		0			0
$905$	2.72529	+	4.72034i	0.0905918	+	0.156910i
$906$		0			0
$907$	1.86329	−	3.22731i	0.0618695	−	0.107161i	−0.833432	−	0.552623i	$-0.813627\pi$
$907$	1.86329	−	3.22731i	0.0618695	−	0.107161i	0.895301	+	0.445462i	$0.146960\pi$
$908$		0			0
$909$	−3.39576			−0.112630
$910$		0			0
$911$	42.4685			1.40704			0.703522	−	0.710673i	$-0.251609\pi$
$911$	42.4685			1.40704			0.703522	+	0.710673i	$0.251609\pi$
$912$		0			0
$913$	8.09306	−	14.0176i	0.267841	−	0.463915i
$914$		0			0
$915$	−0.331977	−	0.575001i	−0.0109748	−	0.0190090i
$916$		0			0
$917$	20.0949	+	43.8514i	0.663593	+	1.44810i
$918$		0			0
$919$	−1.03114	−	1.78599i	−0.0340143	−	0.0589145i	0.848517	−	0.529168i	$-0.177496\pi$
$919$	−1.03114	−	1.78599i	−0.0340143	−	0.0589145i	−0.882531	+	0.470253i	$0.844163\pi$
$920$		0			0
$921$	14.3359	−	24.8305i	0.472383	−	0.818192i
$922$		0			0
$923$	42.9855			1.41488
$924$		0			0
$925$	−36.5259			−1.20096
$926$		0			0
$927$	2.02986	−	3.51582i	0.0666693	−	0.115475i
$928$		0			0
$929$	25.3111	+	43.8401i	0.830430	+	1.43835i	0.897698	+	0.440612i	$0.145238\pi$
$929$	25.3111	+	43.8401i	0.830430	+	1.43835i	−0.0672680	+	0.997735i	$0.521428\pi$
$930$		0			0
$931$	−15.2962	−	43.8278i	−0.501312	−	1.43640i
$932$		0			0
$933$	19.1404	+	33.1522i	0.626630	+	1.08536i
$934$		0			0
$935$	−0.254568	+	0.440925i	−0.00832527	+	0.0144198i
$936$		0			0
$937$	32.5129			1.06215			0.531075	−	0.847325i	$-0.321788\pi$
$937$	32.5129			1.06215			0.531075	+	0.847325i	$0.321788\pi$
$938$		0			0
$939$	2.04028			0.0665820
$940$		0			0
$941$	−13.0996	+	22.6891i	−0.427034	+	0.739645i	−0.996608	−	0.0822953i	$-0.973775\pi$
$941$	−13.0996	+	22.6891i	−0.427034	+	0.739645i	0.569574	+	0.821940i	$0.307108\pi$
$942$		0			0
$943$	11.3553	+	19.6679i	0.369778	+	0.640475i
$944$		0			0
$945$	−1.77808	−	3.88014i	−0.0578408	−	0.126221i
$946$		0			0
$947$	28.1015	+	48.6731i	0.913174	+	1.58166i	0.809552	+	0.587048i	$0.199710\pi$
$947$	28.1015	+	48.6731i	0.913174	+	1.58166i	0.103622	+	0.994617i	$0.466957\pi$
$948$		0			0
$949$	−14.7564	+	25.5589i	−0.479014	+	0.829677i
$950$		0			0
$951$	−5.19277			−0.168387
$952$		0			0
$953$	14.9855			0.485427			0.242713	−	0.970098i	$-0.421963\pi$
$953$	14.9855			0.485427			0.242713	+	0.970098i	$0.421963\pi$
$954$		0			0
$955$	1.46997	−	2.54607i	0.0475672	−	0.0823889i
$956$		0			0
$957$	2.75457	+	4.77105i	0.0890425	+	0.154226i
$958$		0			0
$959$	−2.11640	+	2.98024i	−0.0683423	+	0.0962368i
$960$		0			0
$961$	13.7713	+	23.8527i	0.444237	+	0.769441i
$962$		0			0
$963$	−4.09306	+	7.08940i	−0.131897	+	0.228453i
$964$		0			0
$965$	−3.93471			−0.126663
$966$		0			0
$967$	38.8161			1.24824			0.624121	−	0.781328i	$-0.285457\pi$
$967$	38.8161			1.24824			0.624121	+	0.781328i	$0.285457\pi$
$968$		0			0
$969$	8.78588	−	15.2176i	0.282243	−	0.488859i
$970$		0			0
$971$	−13.9836	−	24.2203i	−0.448755	−	0.777266i	0.549550	−	0.835461i	$-0.314799\pi$
$971$	−13.9836	−	24.2203i	−0.448755	−	0.777266i	−0.998305	+	0.0581943i	$0.981466\pi$
$972$		0			0
$973$	−1.55727	−	0.146666i	−0.0499237	−	0.00470190i
$974$		0			0
$975$	12.7975	+	22.1659i	0.409847	+	0.709876i
$976$		0			0
$977$	22.1750	−	38.4082i	0.709440	−	1.22879i	−0.255625	−	0.966776i	$-0.582281\pi$
$977$	22.1750	−	38.4082i	0.709440	−	1.22879i	0.965065	−	0.262010i	$-0.0843853\pi$
$978$		0			0
$979$	10.1406			0.324095
$980$		0			0
$981$	−2.75905			−0.0880898
$982$		0			0
$983$	26.3495	−	45.6387i	0.840419	−	1.45565i	−0.0491227	−	0.998793i	$-0.515643\pi$
$983$	26.3495	−	45.6387i	0.840419	−	1.45565i	0.889541	−	0.456855i	$-0.151024\pi$
$984$		0			0
$985$	0.580193	+	1.00492i	0.0184865	+	0.0320195i
$986$		0			0
$987$	−29.8976	−	2.81581i	−0.951652	−	0.0896282i
$988$		0			0
$989$	46.9405	+	81.3034i	1.49262	+	2.58530i
$990$		0			0
$991$	−16.2740	+	28.1873i	−0.516959	+	0.895400i	0.482847	+	0.875705i	$0.339603\pi$
$991$	−16.2740	+	28.1873i	−0.516959	+	0.895400i	−0.999806	+	0.0196949i	$0.993731\pi$
$992$		0			0
$993$	−26.6993			−0.847278
$994$		0			0
$995$	−7.38680			−0.234177
$996$		0			0
$997$	−18.2128	+	31.5455i	−0.576805	+	0.999055i	0.419038	+	0.907969i	$0.362367\pi$
$997$	−18.2128	+	31.5455i	−0.576805	+	0.999055i	−0.995843	+	0.0910866i	$0.970966\pi$
$998$		0			0
$999$	−20.9127	−	36.2219i	−0.661649	−	1.14601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.j.529.3		6
4.3	odd	2		308.2.i.b.221.1	yes	6
7.2	even	3	inner	1232.2.q.j.177.3		6
7.3	odd	6		8624.2.a.cg.1.3		3
7.4	even	3		8624.2.a.cp.1.1		3
12.11	even	2		2772.2.s.e.2377.2		6
28.3	even	6		2156.2.a.k.1.1		3
28.11	odd	6		2156.2.a.g.1.3		3
28.19	even	6		2156.2.i.j.177.3		6
28.23	odd	6		308.2.i.b.177.1	✓	6
28.27	even	2		2156.2.i.j.1145.3		6
84.23	even	6		2772.2.s.e.793.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.i.b.177.1	✓	6	28.23	odd	6
308.2.i.b.221.1	yes	6	4.3	odd	2
1232.2.q.j.177.3		6	7.2	even	3	inner
1232.2.q.j.529.3		6	1.1	even	1	trivial
2156.2.a.g.1.3		3	28.11	odd	6
2156.2.a.k.1.1		3	28.3	even	6
2156.2.i.j.177.3		6	28.19	even	6
2156.2.i.j.1145.3		6	28.27	even	2
2772.2.s.e.793.2		6	84.23	even	6
2772.2.s.e.2377.2		6	12.11	even	2
8624.2.a.cg.1.3		3	7.3	odd	6
8624.2.a.cp.1.1		3	7.4	even	3

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.745432 - 1.29113i) q^{3} +(0.143231 + 0.248083i) q^{5} +(-2.63409 - 0.248083i) q^{7} +(0.388663 + 0.673184i) q^{9} +(0.500000 - 0.866025i) q^{11} -3.49086 q^{13} +0.427076 q^{15} +(-0.888663 + 1.53921i) q^{17} +(-3.31574 - 5.74303i) q^{19} +(-2.28384 + 3.21602i) q^{21} +(-4.30660 - 7.45925i) q^{23} +(2.45897 - 4.25906i) q^{25} +5.63148 q^{27} -3.69527 q^{29} +(-0.929693 + 1.61028i) q^{31} +(-0.745432 - 1.29113i) q^{33} +(-0.315739 - 0.689008i) q^{35} +(-3.71354 - 6.43204i) q^{37} +(-2.60220 + 4.50714i) q^{39} -2.63671 q^{41} -10.8997 q^{43} +(-0.111337 + 0.192842i) q^{45} +(3.80660 + 6.59323i) q^{47} +(6.87691 + 1.30695i) q^{49} +(1.32488 + 2.29475i) q^{51} +(3.74543 - 6.48728i) q^{53} +0.286462 q^{55} -9.88663 q^{57} +(-1.18164 + 2.04667i) q^{59} +(-0.777326 - 1.34637i) q^{61} +(-0.856769 - 1.86965i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(-3.06379 + 5.30664i) q^{67} -12.8411 q^{69} -12.3137 q^{71} +(4.22716 - 7.32165i) q^{73} +(-3.66599 - 6.34968i) q^{75} +(-1.53189 + 2.15715i) q^{77} +(5.19788 + 9.00300i) q^{79} +(3.03189 - 5.25139i) q^{81} +16.1861 q^{83} -0.509136 q^{85} +(-2.75457 + 4.77105i) q^{87} +(5.07031 + 8.78203i) q^{89} +(9.19527 + 0.866025i) q^{91} +(1.38605 + 2.40070i) q^{93} +(0.949833 - 1.64516i) q^{95} +3.04551 q^{97} +0.777326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 2 q^{5} - 2 q^{7} - 4 q^{9} + 3 q^{11} - 6 q^{13} - 2 q^{15} + q^{17} - 9 q^{19} - 8 q^{21} + 5 q^{25} + 12 q^{27} + 10 q^{29} - 9 q^{31} + 3 q^{33} + 9 q^{35} - 20 q^{37} - 7 q^{39} - 10 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 2 * q^5 - 2 * q^7 - 4 * q^9 + 3 * q^11 - 6 * q^13 - 2 * q^15 + q^17 - 9 * q^19 - 8 * q^21 + 5 * q^25 + 12 * q^27 + 10 * q^29 - 9 * q^31 + 3 * q^33 + 9 * q^35 - 20 * q^37 - 7 * q^39 - 10 * q^41 - 16 * q^43 - 7 * q^45 - 3 * q^47 + 12 * q^49 + 12 * q^51 + 15 * q^53 + 4 * q^55 + 4 * q^57 - 10 * q^59 + 8 * q^61 - 4 * q^63 - 3 * q^65 - 8 * q^67 - 54 * q^69 - 6 * q^71 - 12 * q^73 - 3 * q^75 - 4 * q^77 + 7 * q^79 + 13 * q^81 + 50 * q^83 - 18 * q^85 - 24 * q^87 + 27 * q^89 + 23 * q^91 - 6 * q^93 - 19 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more